• Home
  • Textbooks
  • Chemical Engineering. Solutions to the Problems in Chemical Engineering
  • Heat Transfer

Chemical Engineering. Solutions to the Problems in Chemical Engineering

Richardson J.F., Backhurst J.R., Harker J.H.

Chapter 9

Heat Transfer - all with Video Answers

Educators

Chapter Questions

03:23

Problem 1

Calculate the time taken for the distant face of a brick wall, of thermal diffusivity, $D_H=$ $0.0042 \mathrm{~cm}^2 / \mathrm{s}$ and thickness $l=0.45 \mathrm{~m}$, initially at 290 K , to rise to 470 K if the near face is suddenly raised to a temperature of $\theta^{\prime}=870 \mathrm{~K}$ and maintained at that temperature. Assume that all the heat flow is perpendicular to the faces of the wall and that the distant face is perfectly insulated.

Anand Jangid
Anand Jangid
Numerade Educator

Problem 2

Calculate the time for the distant face to reach 470 K under the same conditions as Problem 9.1, except that the distant face is not perfectly lagged but a very large thickness of material of the same thermal properties as the brickwork is stacked against it.

Check back soon!

Problem 3

Benzene vapour, at atmospheric pressure, condenses on a plane surface 2 m long and 1 m wide maintained at 300 K and inclined at an angle of $45^{\circ}$ to the horizontal. Plot the thickness of the condensate film and the point heat transfer coefficient against distance from the top of the surface.

Check back soon!

Problem 4

It is desired to warm $0.9 \mathrm{~kg} / \mathrm{s}$ of air from 283 to 366 K by passing it through the pipes of a bank consisting of 20 rows with 20 pipes in each row. The arrangement is in-line with centre to centre spacing, in both directions, equal to twice the pipe diameter. Flue gas, entering at 700 K and leaving at 366 K , with a free flow mass velocity of $10 \mathrm{~kg} / \mathrm{m}^2 \mathrm{~s}$, is passed across the outside of the pipes. Neglecting gas radiation, how long should the pipes be?

For simplicity, outer and inner pipe diameters may be taken as 12 mm . Values of $k$ and $\mu$, which may be used for both air and flue gases, are given below. The specific heat capacity of air and flue gases is $1.0 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$.
$$
\begin{array}{ccc}
\hline \begin{array}{c}
\text { Temperature } \\
(\mathrm{K})
\end{array} & \begin{array}{c}
\text { Thermal conductivity } \\
k(\mathrm{~W} / \mathrm{m} \mathrm{~K})
\end{array} & \begin{array}{c}
\text { Viscosity } \\
\mu\left(\mathrm{mN} \mathrm{~s} / \mathrm{m}^2\right)
\end{array} \\
\hline 250 & 0.022 & 0.0165 \\
500 & 0.044 & 0.0276 \\
800 & 0.055 & 0.0367
\end{array}
$$

Check back soon!
01:40

Problem 5

A cooling coil, consisting of a single length of tubing through which water is circulated, is provided in a reaction vessel, the contents of which are kept uniformly at 360 K by means of a stirrer. The inlet and outlet temperatures of the cooling water are 280 K and 320 K respectively. What would be the outlet water temperature if the length of the cooling coil were increased by 5 times? Assume the overall heat transfer coefficient to be constant over the length of the tube and independent of the water temperature.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
04:03

Problem 6

In an oil cooler, $216 \mathrm{~kg} / \mathrm{h}$ of hot oil enters a thin metal pipe of diameter 25 mm . An equal mass of cooling water flows through the annular space between the pipe and a larger concentric pipe; the oil and water moving in opposite directions. The oil enters at 420 K and is to be cooled to 320 K . If the water enters at 290 K , what length of pipe will be required? Take coefficients of $1.6 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$ on the oil side and $3.6 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$ on the water side and $2.0 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ for the specific heat of the oil.

Penny Riley
Penny Riley
Numerade Educator
02:23

Problem 7

The walls of a furnace are built of a 150 mm thickness of a refractory of thermal conductivity $1.5 \mathrm{~W} / \mathrm{m} \mathrm{K}$. The surface temperatures of the inner and outer faces of the refractory are 1400 K and 540 K respectively. If a layer of insulating material 25 mm thick of thermal conductivity $0.3 \mathrm{~W} / \mathrm{m} \mathrm{K}$ is added, what temperatures will its surfaces attain assuming the inner surface of the furnace to remain at 1400 K ? The coefficient of heat transfer from the outer surface of the insulation to the surroundings, which are at 290 K , may be taken as $4.2,5.0,6.1$, and $7.1 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$ for surface temperatures of $370,420,470$, and 520 K respectively. What will be the reduction in heat loss?

Narayan Hari
Narayan Hari
Numerade Educator

Problem 8

A pipe of outer diameter 50 mm , maintained at 1100 K , is covered with 50 mm of insulation of thermal conductivity $0.17 \mathrm{~W} / \mathrm{m} \mathrm{K}$. Would it be feasible to use a magnesia insulation, which will not stand temperatures above 615 K and has a thermal conductivity of $0.09 \mathrm{~W} / \mathrm{m} \mathrm{K}$, for an additional layer thick enough to reduce the outer surface temperature to 370 K in surroundings at 280 K ? Take the surface coefficient of heat transfer by radiation and convection as $10 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.

Check back soon!

Problem 9

In order to heat $0.5 \mathrm{~kg} / \mathrm{s}$ of a heavy oil from 311 K to 327 K , it is passed through tubes of inside diameter 19 mm and length 1.5 m forming a bank, on the outside of which steam is condensing at 373 K . How many tubes will be needed?
In calculating $N u, P r$, and $R e$, the thermal conductivity of the oil may be taken as $0.14 \mathrm{~W} / \mathrm{m} \mathrm{K}$ and the specific heat as $2.1 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$, irrespective of temperature. The viscosity is to be taken at the mean oil temperature. Viscosity of the oil at 319 and 373 K is 154 and $19.2 \mathrm{mN} \mathrm{s} / \mathrm{m}^2$ respectively.

Check back soon!

Problem 10

A metal pipe of 12 mm outer diameter is maintained at 420 K . Calculate the rate of heat loss per metre run in surroundings uniformly at 290 K , (a) when the pipe is covered with 12 mm thickness of a material of thermal conductivity $0.35 \mathrm{~W} / \mathrm{mK}$ and surface emissivity 0.95 , and (b) when the thickness of the covering material is reduced to 6 mm , but the outer surface is treated so as to reduce its emissivity to 0.10 . The coefficients of radiation from a perfectly black surface in surroundings at 290 K are $6.25,8.18$, and $10.68 \mathrm{~W} / \mathrm{m}^2$ K at $310 \mathrm{~K}, 370 \mathrm{~K}$, and 420 K respectively. The coefficients of convection may be taken as $1.22(\theta / d)^{0.25} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, where $\theta(\mathrm{K})$ is the temperature difference between the surface and the surrounding air and $d(\mathrm{~m})$ is the outer diameter.

Check back soon!
02:25

Problem 11

A condenser consists of 30 rows of parallel pipes of outer diameter 230 mm and thickness 1.3 mm with 40 pipes, each 2 m long in each row. Water, at an inlet temperature of 283 K , flows through the pipes at $1 \mathrm{~m} / \mathrm{s}$ and steam at 372 K condenses on the outside of the pipes. There is a layer of scale 0.25 mm thick of thermal conductivity $2.1 \mathrm{~W} / \mathrm{m} \mathrm{K}$ on the inside of the pipes. Taking the coefficients of heat transfer on the water side as 4.0 and on the steam side as $8.5 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$, calculate the water outlet temperature and the total mass flow of steam condensed. The latent heat of steam at 372 K is $2250 \mathrm{~kJ} / \mathrm{kg}$. The density of water is $1000 \mathrm{~kg} / \mathrm{m}^3$.

Anand Jangid
Anand Jangid
Numerade Educator
04:03

Problem 12

In an oil cooler, water flows at the rate of $360 \mathrm{~kg} / \mathrm{h}$ per tube through metal tubes of outer diameter 19 mm and thickness 1.3 mm , along the outside of which oil flows in the opposite direction at the rate of $6.675 \mathrm{~kg} / \mathrm{s}$ per tube. If the tubes are 2 m long and the inlettemperatures of the oil and water are 370 K and 280 K respectively, what will be the outlet oil temperature? The coefficient of heat transfer on the oil side is $1.7 \mathrm{kw} / \mathrm{m}^2 \mathrm{~K}$ and on the water side $2.5 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$ and the specific heat of the oil is $1.9 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$.

Penny Riley
Penny Riley
Numerade Educator

Problem 13

Waste gases flowing across the outside of a bank of pipes are being used to warm air which flows through the pipes. The bank consists of 12 rows of pipes with 20 pipes, each 0.7 m long, per row. They are arranged in-line, with centre-to-centre spacing equal, in both directions, to one-and-a-half times the pipe diameter. Both inner and outer diameter may be taken as 12 mm . Air with a mass velocity of $8 \mathrm{~kg} / \mathrm{m}^2 \mathrm{~s}$ enters the pipes at 290 K . The initial gas temperature is 480 K and the total mass flow of the gases crossing the pipes is the same as the total mass flow of the air through them.

Neglecting gas radiation, estimate the outlet temperature of the air. The physical constants for the waste gases, assumed the same as for air, are:
$$
\begin{array}{ccc}
\hline \begin{array}{c}
\text { Temperature } \\
(\mathrm{K})
\end{array} & \begin{array}{c}
\text { Thermal conductivity } \\
(\mathrm{W} / \mathrm{m} \mathrm{~K})
\end{array} & \begin{array}{c}
\text { Viscosity } \\
\left(\mathrm{mN} \mathrm{~s} / \mathrm{m}^2\right)
\end{array} \\
\hline 250 & 0.022 & 0.0165 \\
310 & 0.027 & 0.0189 \\
370 & 0.030 & 0.0214 \\
420 & 0.033 & 0.0239 \\
480 & 0.037 & 0.0260 \\
\hline
\end{array}
$$
Specific heat $=1.00 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$.

Check back soon!

Problem 14

Oil is to be heated from 300 K to 344 K by passing it at $1 \mathrm{~m} / \mathrm{s}$ through the pipes of a shell-and-tube heat exchanger. Steam at 377 K condenses on the outside of the pipes, which have outer and inner diameters of 48 and 41 mm respectively, though due to fouling, the inside diameter has been reduced to 38 mm , and the resistance to heat transfer of the pipe wall and dirt together, based on this diameter, is $0.0009 \mathrm{~m}^2 \mathrm{~K} / \mathrm{W}$.

It is known from previous measurements under similar conditions that the oil side coefficients of heat transfer for a velocity of $1 \mathrm{~m} / \mathrm{s}$, based on a diameter of 38 mm , vary with the temperature of the oil as follows:

$$
\begin{array}{lrrrrr}
\text { Oil temperature }(\mathrm{K}) & 300 & 311 & 322 & 333 & 344 \\
\text { Oil side coefficient of heat transfer }\left(\mathrm{W} / \mathrm{m}^2 \mathrm{~K}\right) & 74 & 80 & 97 & 136 & 244
\end{array}
$$

The specific heat and density of the oil may be assumed constant at $1.9 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ and $900 \mathrm{~kg} / \mathrm{m}^3$ respectively and any resistance to heat transfer on the steam side may be neglected.

Find the length of tube bundle required?

Check back soon!

Problem 15

It is proposed to construct a heat exchanger to condense $7.5 \mathrm{~kg} / \mathrm{s}$ of $n$-hexane at a pressure of $150 \mathrm{kN} / \mathrm{m}^2$, involving a heat load of 4.5 MW . The hexane is to reach the condenser from the top of a fractionating column at its condensing temperature of 356 K . From experience it is anticipated that the overall heat transfer coefficient will be $450 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. Cooling water is available at 289 K . Outline the proposals that you would make for the type and size of the exchanger, and explain the details of the mechanical construction that you consider require special attention.

Check back soon!

Problem 16

A heat exchanger is to be mounted at the top of a fractionating column about 15 m high to condense $4 \mathrm{~kg} / \mathrm{s}$ of $n$-pentane at $205 \mathrm{kN} / \mathrm{m}^2$, corresponding to a condensing temperature of 333 K . Give an outline of the calculations you would make to obtain an approximate idea of the size and construction of the exchanger required.

For purposes of standardisation, 19 mm outside diameter tubes of 1.65 mm wall thickness will be used and these may be $2.5,3.6$, or 5 m in length. The film coefficient for condensing pentane on the outside of a horizontal tube bundle may be taken as $1.1 \mathrm{~kW} / \mathrm{m}^2$ K . The condensation is effected by pumping water through the tubes, the initial water temperature being 288 K . The latent heat of condensation of pentane is $335 \mathrm{~kJ} / \mathrm{kg}$.

For these 19 mm tubes, a water velocity of $1 \mathrm{~m} / \mathrm{s}$ corresponds to a flowrate of $0.2 \mathrm{~kg} / \mathrm{s}$ of water.

Check back soon!

Problem 17

An organic liquid is boiling at 340 K on the inside of a metal surface of thermal conductivity $42 \mathrm{~W} / \mathrm{m} \mathrm{K}$ and thickness 3 mm . The outside of the surface is heated by condensing steam. Assuming that the heat transfer coefficient from steam to the outer metal surface is constant at $11 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$, irrespective of the steam temperature, find the value of the steam temperature would give a maximum rate of evaporation.

The coefficients of heat transfer from the inner metal surface to the boiling liquid which depend upon the temperature difference are:
$$
\begin{array}{cc}
\hline \begin{array}{c}
\text { Temperature difference between metal } \\
\text { surface and boiling liquid }(\text { deg } \mathrm{K})
\end{array} & \begin{array}{c}
\text { Heat transfer coefficient metal surface } \\
\text { to boiling liquid }\left(\mathrm{kW} / \mathrm{m}^2 \mathrm{~K}\right)
\end{array} \\
\hline 22.2 & 4.43 \\
27.8 & 5.91 \\
33.3 & 7.38 \\
36.1 & 7.30 \\
38.9 & 6.81 \\
41.7 & 6.36 \\
44.4 & 5.73 \\
50.0 & 4.54 \\
\hline
\end{array}
$$

Check back soon!

Problem 18

It is desired to warm an oil of specific heat $2.0 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ from 300 to 325 K by passing it through a tubular heat exchanger containing metal tubes of inner diameter 10 mm . Along the outside of the tubes flows water, inlet temperature 372 K , and outlet temperature 361 K .

The overall heat transfer coefficient from water to oil, based on the inside area of the tubes, may be assumed constant at $230 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, and $0.075 \mathrm{~kg} / \mathrm{s}$ of oil is to be passed through each tube.

The oil is to make two passes through the heater and the water makes one pass along the outside of the tubes. Calculate the length of the tubes required.

Check back soon!

Problem 19

A condenser consists of a number of metal pipes of outer diameter 25 mm and thickness 2.5 mm . Water, flowing at $0.6 \mathrm{~m} / \mathrm{s}$, enters the pipes at 290 K , and it should be discharged at a temperature not exceeding 310 K .

If $1.25 \mathrm{~kg} / \mathrm{s}$ of a hydrocarbon vapour is to be condensed at 345 K on the outside of the pipes, how long should each pipe be and how many pipes would be needed?

Take the coefficient of heat transfer on the water side as 2.5 , and on the vapour side as $0.8 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$ and assume that the overall coefficient of heat transfer from vapour to water, based upon these figures, is reduced $20 \%$ by the effects of the pipe walls, dirt and scale.

The latent heat of the hydrocarbon vapour at 345 K is $315 \mathrm{~kJ} / \mathrm{kg}$.

Check back soon!

Problem 20

An organic vapour is being condensed at 350 K on the outside of a bundle of pipes through which water flows at $0.6 \mathrm{~m} / \mathrm{s}$; its inlet temperature being 290 K . The outer and inner diameters of the pipes are 19 mm and 15 mm respectively, although a layer of scale, 0.25 mm thick and of thermal conductivity $2.0 \mathrm{~W} / \mathrm{m} \mathrm{K}$, has formed on the inside of the pipes.

If the coefficients of heat transfer on the vapour and water sides are 1.7 and $3.2 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$ respectively and it is required to condense $0.025 \mathrm{~kg} / \mathrm{s}$ of vapour on each of the pipes, how long should these be, and what will be the outlet temperature of water?
The latent heat of condensation is $330 \mathrm{~kJ} / \mathrm{kg}$.
Neglect any resistance to heat transfer in the pipe walls.

Check back soon!

Problem 21

A heat exchanger is required to cool continuously $20 \mathrm{~kg} / \mathrm{s}$ of water from 360 K to 335 K by means of $25 \mathrm{~kg} / \mathrm{s}$ of cold water, inlet temperature 300 K . Assuming that the water velocities are such as to give an overall coefficient of heat transfer of $2 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$, assumed constant, calculate the total area of surface required (a) in a counterflow heat exchanger, i.e. one in which the hot and cold fluids flow in opposite directions, and (b) in a multipass heat exchanger, with the cold water making two passes through the tubes, and the hot water making one pass along the outside of the tubes. In case (b) assume that the hot-water flows in the same direction as the inlet cold water, and that its temperature over any cross-section is uniform.

Check back soon!
02:23

Problem 22

Find the heat loss per unit area of surface through a brick wall 0.5 m thick when the inner surface is at 400 K and the outside at 310 K . The thermal conductivity of the brick may be taken as $0.7 \mathrm{~W} / \mathrm{m} \mathrm{K}$.

Narayan Hari
Narayan Hari
Numerade Educator
02:23

Problem 23

A furnace is constructed with 225 mm of firebrick, 120 mm of insulating brick, and 225 mm of building brick. The inside temperature is 1200 K and the outside temperature 330 K . If the thermal conductivities are $1.4,0.2$, and $0.7 \mathrm{~W} / \mathrm{m} \mathrm{K}$, find the heat loss per unit area and the temperature at the junction of the firebrick and insulating brick.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 24

Calculate the total heat loss by radiation and convection from an unlagged horizontal steam pipe of 50 mm outside diameter at 415 K to air at 290 K .

Check back soon!

Problem 25

Toluene is continuously nitrated to mononitrotoluene in a cast-iron vessel 1 m in diameter fitted with a propeller agitator of 0.3 m diameter driven at 2 Hz . The temperature is maintained at 310 K by circulating cooling water at $0.5 \mathrm{~kg} / \mathrm{s}$ through a stainless steel coil of 25 mm outside diameter and 22 mm inside diameter wound in the form of a helix of 0.81 m diameter. The conditions are such that the reacting material may be considered to have the same physical properties as $75 \%$ sulphuric acid. If the mean water temperature is 290 K , what is the overall heat transfer coefficient?

Check back soon!

Problem 26

$7.5 \mathrm{~kg} / \mathrm{s}$ of pure iso-butane is to be condensed at a temperature of 331.7 K in a horizontal tubular exchanger using a water inlet temperature of 301 K . It is proposed to use 19 mm outside diameter tubes of 1.6 mm wall arranged on a 25 mm triangular pitch. Under these conditions the resistance of the scale may be taken as $0.0005 \mathrm{~m}^2 \mathrm{~K} / \mathrm{W}$. Determine the number and arrangement of the tubes in the shell.

Check back soon!

Problem 27

$37.5 \mathrm{~kg} / \mathrm{s}$ of crude oil is to be heated from 295 to 330 K by heat transferred from the bottom product from a distillation column. The bottom product, flowing at $29.6 \mathrm{~kg} / \mathrm{s}$ is to be cooled from 420 to 380 K . There is available a tubular exchanger with an inside shell diameter of 0.60 m , having one pass on the shell side and two passes on the tube side. It has 324 tubes, 19 mm outside diameter with 2.1 mm wall and 3.65 m long, arranged on a 25 mm square pitch and supported by baffles with a $25 \%$ cut, spaced at 230 mm intervals. Would this exchanger be suitable?

Check back soon!
02:24

Problem 28

A 150 mm internal diameter steam pipe, carrying steam at 444 K , is lagged with 50 mm of $85 \%$ magnesia. What will be the heat loss to the air at 294 K ?

Anand Jangid
Anand Jangid
Numerade Educator

Problem 29

A refractory material with an emissivity of 0.40 at 1500 K and 0.43 at 1420 K is at a temperature of 1420 K and is exposed to black furnace walls at a temperature of 1500 K . What is the rate of gain of heat by radiation per unit area?

Check back soon!
02:09

Problem 30

The total emissivity of clean chromium as a function of surface temperature, $T \mathrm{~K}$, is given approximately by: $\mathbf{e}=0.38(1-263 / T)$.

Obtain an expression for the absorptivity of solar radiation as a function of surface temperature, and calculate the values of the absorptivity and emissivity at 300,400 and 1000 K .

Assume that the sun behaves as a black body at 5500 K .

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator

Problem 31

Repeat Problem 9.30 for the case of aluminium, assuming the emissivity to be 1.25 times that for chromium.

Check back soon!

Problem 32

Calculate the heat transferred by solar radiation on the flat concrete roof of a building, 8 m by 9 m , if the surface temperature of the roof is 330 K . What would be the effect of covering the roof with a highly reflecting surface, such as polished aluminium, separated from the concrete by an efficient layer of insulation? The emissivity of concrete at 330 K is 0.89 , whilst the total absorptivity of solar radiation (sun temperature $=5500 \mathrm{~K}$ ) at this temperature is 0.60 .

Use the data for aluminium from Problem 9.31 which should be solved first.

Check back soon!

Problem 33

A rectangular iron ingot $15 \mathrm{~cm} \times 15 \mathrm{~cm} \times 30 \mathrm{~cm}$ is supported at the centre of a reheating furnace. The furnace has walls of silica-brick at 1400 K , and the initial temperature of the ingot is 290 K . How long will it take to heat the ingot to 600 K ?

It may be assumed that the furnace is large compared with the ingot, and that the ingot is always at uniform temperature throughout its volume. Convection effects are negligible.

The total emissivity of the oxidised iron surface is 0.78 and both emissivity and absorptivity may be assumed independent of the surface temperature. (Density of iron $=$ $7.2 \mathrm{Mg} / \mathrm{m}^3$. Specific heat capacity of iron $=0.50 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$.)

Check back soon!
01:12

Problem 34

A wall is made of brick, of thermal conductivity $1.0 \mathrm{~W} / \mathrm{m} \mathrm{K}, 230 \mathrm{~mm}$ thick, lined on the inner face with plaster of thermal conductivity $0.4 \mathrm{~W} / \mathrm{m} \mathrm{K}$ and of thickness 10 mm . If a temperature difference of 30 K is maintained between the two outer faces, what is the heat flow per unit area of wall?

Mayukh Banik
Mayukh Banik
Numerade Educator

Problem 35

A 50 mm diameter pipe of circular cross-section and with walls 3 mm thick is covered with two concentric layers of lagging, the inner layer having a thickness of 25 mm and a thermal conductivity of $0.08 \mathrm{~W} / \mathrm{m} \mathrm{K}$, and the outer layer a thickness of 40 mm and a thermal conductivity of $0.04 \mathrm{~W} / \mathrm{m} \mathrm{K}$. What is the rate of heat loss per metre length of pipe if the temperature inside the pipe is 550 K and the outside surface temperature is 330 K ?

Check back soon!
01:40

Problem 36

The temperature of oil leaving a co-current flow cooler is to be reduced from 370 to 350 K by lengthening the cooler. The oil and water flowrates, the inlet temperatures and the other dimensions of the cooler will remain constant. The water enters at 285 K and oil at 420 K . The water leaves the original cooler at 310 K . If the original length is 1 m , what must be the new length?

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator

Problem 37

In a countercurrent-flow heat exchanger, $1.25 \mathrm{~kg} / \mathrm{s}$ of benzene (specific heat $1.9 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ and density $880 \mathrm{~kg} / \mathrm{m}^3$ ) is to be cooled from 350 K to 300 K with water which is available at 290 K . In the heat exchanger, tubes of 25 mm external and 22 mm internal diameter are employed and the water passes through the tubes. If the film coefficients for the water and benzene are 0.85 and $1.70 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$ respectively and the scale resistance can be neglected, what total length of tube will be required if the minimum quantity of water is to be used and its temperature is not to be allowed to rise above 320 K ?

Check back soon!

Problem 38

Calculate the rate of loss of heat from a 6 m long horizontal steam pipe of 50 mm internal diameter and 60 mm external diameter when carrying steam at $800 \mathrm{kN} / \mathrm{m}^2$. The temperature of the surroundings is 290 K .

What would be the cost of steam saved by coating the pipe with a 50 mm thickness of $85 \%$ magnesia lagging of thermal conductivity $0.07 \mathrm{~W} / \mathrm{m} \mathrm{K}$, if steam costs $£ 0.5 / 100 \mathrm{~kg}$ ? The emissivity of both the surface of the bare pipe and the lagging may be taken as 0.85 , and the coefficient $h$ for the heat loss by natural convection is given by:

$$
h=1.65(\Delta T)^{0.25} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}
$$

where $\Delta T$ is the temperature difference in deg K . The Stefan-Boltzmann constant is $5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}^4$.

Check back soon!

Problem 39

A stirred reactor contains a batch of 700 kg reactants of specific heat $3.8 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ initially at 290 K , which is heated by dry saturated steam at $170 \mathrm{kN} / \mathrm{m}^2$ fed to a helical coil. During the heating period the steam supply rate is constant at $0.1 \mathrm{~kg} / \mathrm{s}$ and condensate leaves at the temperature of the steam. If heat losses are neglected, calculate the true temperature of the reactants when a thermometer immersed in the material reads 360 K . The bulb of the thermometer is approximately cylindrical and is 100 mm long by 10 mm in diameter with a water equivalent of 15 g , and the overall heat transfer coefficient to the thermometer is $300 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. What temperature would a thermometer with a similar bulb of half the length and half the heat capacity indicate under these conditions?

Check back soon!

Problem 40

How long will it take to heat $0.18 \mathrm{~m}^3$ of liquid of density $900 \mathrm{~kg} / \mathrm{m}^3$ and specifi $2.1 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ from 293 to 377 K in a tank fitted with a coil of area $1 \mathrm{~m}^2$ ? The coil with steam at 383 K and the overall heat transfer coefficient can be taken as cons $0.5 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$. The vessel has an external surface of $2.5 \mathrm{~m}^2$, and the coefficient fc transfer to the surroundings at 293 K is $5 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.

The batch system of heating is to be replaced by a continuous countercurrer exchanger in which the heating medium is a liquid entering at 388 K and leaving at If the heat transfer coefficient is $250 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, what heat exchange area is required losses may be neglected.

Check back soon!
01:25

Problem 41

The radiation received by the earth's surface on a clear day with the sun overhead is $1 \mathrm{~kW} / \mathrm{m}^2$ and an additional $0.3 \mathrm{~kW} / \mathrm{m}^2$ is absorbed by the earth's atmosphere. Calculate approximately the temperature of the sun, assuming its radius to be $700,000 \mathrm{~km}$ and the distance between the sun and the earth to be $150,000,000 \mathrm{~km}$. The sun may be assumed to behave as a black body.

Penny Riley
Penny Riley
Numerade Educator

Problem 42

A thermometer is immersed in a liquid which is heated at the rate of $0.05 \mathrm{~K} / \mathrm{s}$. If the thermometer and the liquid are both initially at 290 K , what rate of passage of liquid over the bulb of the thermometer is required if the error in the thermometer reading after 600 s is to be no more than 1 deg K ? Take the water equivalent of the thermometer as 30 g , the heat transfer coefficient to the bulb to be given by $U=735 u^{0.8} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. The area of the bulb is $0.01 \mathrm{~m}^2$ where $u$ is the velocity in $\mathrm{m} / \mathrm{s}$.

Check back soon!

Problem 43

In a shell-and-tube type of heat exchanger with horizontal tubes 25 mm external diameter and 22 mm internal diameter, benzene is condensed on the outside of the tubes by means of water flowing through the tubes at the rate of $0.03 \mathrm{~m}^3 / \mathrm{s}$. If the water enters at 290 K and leaves at 300 K and the heat transfer coefficient on the water side is $850 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, what total length of tubing will be required?

Check back soon!

Problem 44

In a contact sulphuric acid plant, the gases leaving the first convertor are to be cooled from 845 to 675 K by means of the air required for the combustion of the sulphur. The air enters the heat exchanger at 495 K . If the flow of each of the streams is $2 \mathrm{~m}^3 / \mathrm{s}$ at NTP, suggest a suitable design for a shell-and-tube type of heat exchanger employing tubes of 25 mm internal diameter.
(a) Assume parallel co-current flow of the gas streams.
(b) Assume parallel countercurrent flow.
(c) Assume that the heat exchanger is fitted with baffles giving cross-flow outside the tubes.

Check back soon!
02:17

Problem 45

A large block of material of thermal diffusivity $D_H=0.0042 \mathrm{~cm}^2 / \mathrm{s}$ is initially at a uniform temperature of 290 K and one face is raised suddenly to 875 K and maintained at that temperature. Calculate the time taken for the material at a depth of 0.45 m to reach a temperature of 475 K on the assumption of unidirectional heat transfer and that the material can be considered to be infinite in extent in the direction of transfer.

Nicholas Mogoi
Nicholas Mogoi
Numerade Educator

Problem 46

A $50 \%$ glycerol-water mixture is flowing at a Reynolds number of 1500 through a 25 mm diameter pipe. Plot the mean value of the heat transfer coefficient as a function of pipe length, assuming that: $N u=1.62(\operatorname{Re} \operatorname{Pr} d / l)^{0.33}$.

Indicate the conditions under which this is consistent with the predicted value $N u=4.1$ for fully developed flow.

Check back soon!

Problem 47

A liquid is boiled at a temperature of 360 K using steam fed at 380 K to a coil heater. Initially the heat transfer surfaces are clean and an evaporation rate of $0.08 \mathrm{~kg} / \mathrm{s}$ is obtained from each square metre of heating surface. After a period, a layer of scale of resistance $0.0003 \mathrm{~m}^2 \mathrm{~K} / \mathrm{W}$, is deposited by the boiling liquid on the heat transfer surface. On the assumption that the coefficient on the steam side remains unaltered and that the coefficient for the boiling liquid is proportional to its temperature difference raised to the power of 2.5 , calculate the new rate of boiling.

Check back soon!

Problem 48

A batch of reactants of specific heat $3.8 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ and of mass 1000 kg is heated by means of a submerged steam coil of area $1 \mathrm{~m}^2$ fed with steam at 390 K . If the overall heat transfer coefficient is $600 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, calculate the time taken to heat the material from 290 to 360 K if heat losses to the surroundings are neglected.

If the external area of the vessel is $10 \mathrm{~m}^2$ and the heat transfer coefficient to the surroundings at 290 K is $8.5 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, what will be the time taken to heat the reactants over the same temperature range and what is the maximum temperature to which the reactants can be raised?

What methods would you suggest for improving the rate of heat transfer?

Check back soon!
01:42

Problem 50

A longitudinal fin on the outside of a circular pipe is 75 mm deep and 3 mm thick. If the pipe surface is at 400 K , calculate the heat dissipated per metre length from the fin to the atmosphere at 290 K if the coefficient of heat transfer from its surface may be assumed constant at $5 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. The thermal conductivity of the material of the fin is $50 \mathrm{~W} / \mathrm{m} \mathrm{K}$ and the heat loss from the extreme edge of the fin may be neglected. It should be assumed that the temperature is uniformly 400 K at the base of the fin.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
04:27

Problem 51

Liquid oxygen is distributed by road in large spherical insulated vessels, 2 m internal diameter, well lagged on the outside. What thickness of magnesia lagging, of thermal conductivity $0.07 \mathrm{~W} / \mathrm{m} \mathrm{K}$, must be used so that not more than $1 \%$ of the liquid oxygen evaporates during a journey of $10 \mathrm{ks}(2.78 \mathrm{~h})$ if the vessel is initially $80 \%$ full? Latent heat of vaporisation of oxygen $=215 \mathrm{~kJ} / \mathrm{kg}$. Boiling point of oxygen $=90 \mathrm{~K}$. Density of liquid oxygen $=1140 \mathrm{~kg} / \mathrm{m}^3$. Atmospheric temperature $=288 \mathrm{~K}$. Heat transfer coefficient from the outside surface of the lagging surface to atmosphere $=4.5 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 52

Benzene is to be condensed at the rate of $1.25 \mathrm{~kg} / \mathrm{s}$ in a vertical shell and tube type of heat exchanger fitted with tubes of 25 mm outside diameter and 2.5 m long. The vapour condenses on the outside of the tubes and the cooling water enters at 295 K and passes through the tubes at $1.05 \mathrm{~m} / \mathrm{s}$. Calculate the number of tubes required if the heat exchanger is arranged for a single pass of the cooling water. The tube wall thickness is 1.6 mm .

Check back soon!
01:43

Problem 53

One end of a metal bar 25 mm in diameter and 0.3 m long is maintained at 375 K and heat is dissipated from the whole length of the bar to surroundings at 295 K . If the coefficient of heat transfer from the surface is $10 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, what is the rate of loss of heat? Take the thermal conductivity of the metal as $85 \mathrm{~W} / \mathrm{m} \mathrm{K}$.

Penny Riley
Penny Riley
Numerade Educator

Problem 54

A shell-and-tube heat exchanger consists of 120 tubes of internal diameter 22 mm and length 2.5 m . It is operated as a single-pass condenser with benzene condensing at a temperature of 350 K on the outside of the tubes and water of inlet temperature 290 K passing through the tubes. Initially there is no scale on the walls, and a rate of condensation of $4 \mathrm{~kg} / \mathrm{s}$ is obtained with a water velocity of $0.7 \mathrm{~m} / \mathrm{s}$ through the tubes. After prolonged operation, a scale of resistance $0.0002 \mathrm{~m}^2 \mathrm{~K} / \mathrm{W}$ is formed on the inner surface of the tubes. To what value must the water velocity be increased in order to maintain the same rate of condensation on the assumption that the transfer coefficient on the water side is proportional to the velocity raised to the 0.8 power, and that the coefficient for the condensing vapour is $2.25 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$, based on the inside area? The latent heat of vaporisation of benzene is $400 \mathrm{~kJ} / \mathrm{kg}$.

Check back soon!

Problem 55

Derive an expression for the radiant heat transfer rate per unit area between two large parallel planes of emissivities $\mathbf{e}_1$ and $\mathbf{e}_2$ and at absolute temperatures $T_1$ and $T_2$ respectively.

Two such planes are situated 2.5 mm apart in air. One has an emissivity of 0.1 and is at a temperature of 350 K , and the other has an emissivity of 0.05 and is at a temperature of 300 K . Calculate the percentage change in the total heat transfer rate by coating the first surface so as to reduce its emissivity to 0.025 . Stefan-Boltzmann constant $=5.67 \times$ $10^{-8} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}^4$. Thermal conductivity of air $=0.026 \mathrm{~W} / \mathrm{m} \mathrm{K}$.

Check back soon!

Problem 56

Water flows at $2 \mathrm{~m} / \mathrm{s}$ through a 2.5 m length of a 25 mm diameter tube. If the tube is at 320 K and the water enters and leaves at 293 and 295 K respectively, what is the value of the heat transfer coefficient? How would the outlet temperature change if the velocity was increased by $50 \%$ ?

Check back soon!

Problem 57

A liquid hydrocarbon is fed at 295 K to a heat exchanger consisting of a 25 mm diameter tube heated on the outside by condensing steam at atmospheric pressure. The flowrate of hydrocarbon is measured by means of a 19 mm orifice fitted to the 25 mm feed pipe. The reading on a differential manometer containing hydrocarbon-over-water is 450 mm and the coefficient of discharge of the meter is 0.6 .

Calculate the initial rate of rise of temperature (deg K/s) of the hydrocarbon as it enters the heat exchanger.

The outside film coefficient $=6.0 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.
The inside film coefficient $h$ is given by:

$$
h d / k=0.023(u d \rho / \mu)^{0.8}\left(C_p \mu / k\right)^{0.4}
$$

where: $u=$ linear velocity of hydrocarbon $(\mathrm{m} / \mathrm{s}) . d=$ tube diameter $(\mathrm{m}), \rho=$ liquid density $\left(800 \mathrm{~kg} / \mathrm{m}^3\right), \mu=$ liquid viscosity $\left(9 \times 10^{-4} \mathrm{~N} \mathrm{~s} / \mathrm{m}^2\right), C_p=$ specific heat of liquid $(1.7 \times$ $\left.10^3 \mathrm{~J} / \mathrm{kgK}\right)$, and $k=$ thermal conductivity of liquid $(0.17 \mathrm{~W} / \mathrm{mK})$.

Check back soon!
01:40

Problem 58

Water passes at a velocity of $1.2 \mathrm{~m} / \mathrm{s}$ through a series of 25 mm diameter tubes 5 m long maintained at 320 K . If the inlet temperature is 290 K , at what temperature would it leave?

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
03:00

Problem 59

Heat is transferred from one fluid stream to a second fluid across a heat transfer surface. If the film coefficients for the two fluids are, respectively, 1.0 and $1.5 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$, the metal is 6 mm thick (thermal conductivity $20 \mathrm{~W} / \mathrm{m} \mathrm{K}$ ) and the scale coefficient is equivalent to $850 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, what is the overall heat transfer coefficient?

Anand Jangid
Anand Jangid
Numerade Educator

Problem 60

A pipe of outer diameter 50 mm carries hot fluid at 1100 K . It is covered with a 50 mm layer of insulation of thermal conductivity $0.17 \mathrm{~W} / \mathrm{m} \mathrm{K}$. Would it be feasible to use magnesia insulation, which will not stand temperatures above 615 K and has a thermal conductivity of $0.09 \mathrm{~W} / \mathrm{m} \mathrm{K}$ for an additional layer thick enough to reduce the outer surface temperature to 370 K in surroundings at 280 K ? Take the surface coefficient of transfer by radiation and convection as $10 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.

Check back soon!

Problem 61

A jacketed reaction vessel containing $0.25 \mathrm{~m}^3$ of liquid of density $900 \mathrm{~kg} / \mathrm{m}^3$ and specific heat $3.3 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ is heated by means of steam fed to a jacket on the walls. The contents of the tank are agitated by a stirrer rotating at 3 Hz . The heat transfer area is $2.5 \mathrm{~m}^2$ and the steam temperature is 380 K . The outside film heat transfer coefficient is $1.7 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$ and the 10 mm thick wall of the tank has a thermal conductivity of $6.0 \mathrm{~W} / \mathrm{m} \mathrm{K}$. The inside film coefficient was $1.1 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$ for a stirrer speed of 1.5 Hz and proportional to the two-thirds power of the speed of rotation. Neglecting heat losses and the heat capacity of the tank, how long will it take to raise the temperature of the liquid from 295 to 375 K ?

Check back soon!

Problem 62

By dimensional analysis, derive a relationship for the heat transfer coefficient $h$ for natural convection between a surface and a fluid on the assumption that the coefficient is a function of the following variables:
$k=$ thermal conductivity of the fluid, $C_p=$ specific heat of the fluid, $\rho=$ density of the fluid, $\mu=$ viscosity of the fluid, $\beta g=$ the product of the coefficient of cubical expansion of the fluid and the acceleration due to gravity, $l=$ a characteristic dimension of the surface, and $\Delta T=$ the temperature difference between the fluid and the surface.

Indicate why each of these quantities would be expected to influence the heat transfer coefficient and explain how the orientation of the surface affects the process.

Under what conditions is heat transfer by natural convection important in Chemical Engineering?

Check back soon!

Problem 63

A shell-and-tube heat exchanger is used for preheating the feed to an evaporator. The liquid of specific heat $4.0 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ and density $1100 \mathrm{~kg} / \mathrm{m}^3$ passes through the inside of tubes and is heated by steam condensing at 395 K on the outside. The exchanger heats liquid at 295 K to an outlet temperature of 375 K when the flowrate is $1.75 \times 10^{-4} \mathrm{~m}^3 / \mathrm{s}$ and to 370 K when the flowrate is $3.25 \times 10^{-4} \mathrm{~m}^3 / \mathrm{s}$. What is the heat transfer area and the value of the overall heat transfer coefficient when the flow rate is $1.75 \times 10^{-4} \mathrm{~m}^3 / \mathrm{s}$ ?
Assume that the film heat transfer coefficient for the liquid in the tubes is proportional to the 0.8 power of the velocity, that the transfer coefficient for the condensing steam remains constant at $3.4 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$ and that the resistance of the tube wall and scale can be neglected.

Check back soon!

Problem 64

$0.1 \mathrm{~m}^3$ of liquid of specific heat capacity $3 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ and density $950 \mathrm{~kg} / \mathrm{m}^3$ is heated in an agitated tank fitted with a coil, of heat transfer area $1 \mathrm{~m}^2$, supplied with steam at 383 K . How long will it take to heat the liquid from 293 to 368 K , if the tank, of external area $20 \mathrm{~m}^2$ is losing heat to the surroundings at 293 K ? To what temperature will the system fall in 1800 s if the steam is turned off? Overall heat transfer coefficient in coil $=2000 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. Heat transfer coefficient to surroundings $=10 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.

Check back soon!

Problem 65

The contents of a reaction vessel are heated by means of steam at 393 K supplied to a heating coil which is totally immersed in the liquid. When the vessel has a layer of lagging 50 mm thick on its outer surfaces, it takes one hour to heat the liquid from 293 to 373 K . How long will it take if the thickness of lagging is doubled? Outside temperature $=293 \mathrm{~K}$. Thermal conductivity of lagging $=0.05 \mathrm{~W} / \mathrm{mK}$. Coefficient for heat loss by radiation and convection from outside surface of vessel $=10 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. Outside area of vessel $=8 \mathrm{~m}^2$. Coil area $=0.2 \mathrm{~m}^2$. Overall heat transfer coefficient for steam coil $=300 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.

Check back soon!
View

Problem 66

A smooth tube in a condenser which is 25 mm internal diameter and 10 m long is carrying cooling water and the pressure drop over the length of the tube is $2 \times 10^4 \mathrm{~N} / \mathrm{m}^2$. If vapour at a temperature of 353 K is condensing on the outside of the tube and the temperature of the cooling water rises from 293 K at inlet to 333 K at outlet, what is the value of the overall heat transfer coefficient based on the inside area of the tube? If the coefficient for the condensing vapour is $15,000 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, what is the film coefficient for the water? If the latent heat of vaporisation is $800 \mathrm{~kJ} / \mathrm{kg}$, what is the rate of condensation of vapour?

Susan Hallstrom
Susan Hallstrom
Numerade Educator

Problem 67

A chemical reactor, 1 m in diameter and 5 m long, operates at a temperature of 1073 K . It is covered with a 500 mm thickness of lagging of thermal conductivity $0.1 \mathrm{~W} / \mathrm{m} \mathrm{K}$. The heat loss from the cylindrical surface to the surroundings is 3.5 kW . What is the heat transfer coefficient from the surface of the lagging to the surroundings at a temperature of 293 K ? How would the heat loss be altered if the coefficient were halved?

Check back soon!

Problem 68

An open cylindrical tank 500 mm diameter and 1 m deep is three-quarters filled with a liquid of density $980 \mathrm{~kg} / \mathrm{m}^3$ and of specific heat capacity $3 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$. If the heat transfer coefficient from the cylindrical walls and the base of the tank is $10 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$ and from the surface is $20 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, what area of heating coil, fed with steam at 383 K , is required to heat the contents from 288 K to 368 K in a half hour? The overall heat transfer coefficient for the coil may be taken as $100 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. The surroundings are at 288 K . The heat capacity of the tank itself may be neglected.

Check back soon!
04:27

Problem 69

Liquid oxygen is distributed by road in large spherical vessels, 1.82 m in internal diameter. If the vessels were unlagged and the coefficient for heat transfer from the outside of the vessel to the atmosphere were $5 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, what proportion of the contents would evaporate during a journey lasting an hour? Initially the vessels are $80 \%$ full.

What thickness of lagging would be required to reduce the losses to one tenth? Atmospheric temperature $=288 \mathrm{~K}$. Boiling point of oxygen $=90 \mathrm{~K}$. Density of oxygen $=$ $1140 \mathrm{~kg} / \mathrm{m}^3$. Latent heat of vaporisation of oxygen $=214 \mathrm{~kJ} / \mathrm{kg}$. Thermal conductivity of lagging $=0.07 \mathrm{~W} / \mathrm{m} \mathrm{K}$.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 70

Water at 293 K is heated by passing it through a 6.1 m coil of 25 mm internal diameter pipe. The thermal conductivity of the pipe wall is $20 \mathrm{~W} / \mathrm{m} \mathrm{K}$ and the wall thickness is 3.2 mm . The coil is heated by condensing steam at 373 K for which the film coefficient is $8 \mathrm{~kW} / \mathrm{m}^2 \mathrm{~K}$. When the water velocity in the pipe is $1 \mathrm{~m} / \mathrm{s}$, its outlet temperature is 309 K . What will the outlet temperature be if the velocity is increased to $1.3 \mathrm{~m} / \mathrm{s}$, if the coefficient of heat transfer to the water in the tube is proportional to the velocity raised to the 0.8 power?

Check back soon!

Problem 71

Liquid is heated in a vessel by means of steam which is supplied to an internal coil in the vessel. When the vessel contains 1000 kg of liquid it takes half an hour to heat the contents from 293 to 368 K if the coil is supplied with steam at 373 K . The process is modified so that liquid at 293 K is continuously fed to the vessel at the rate of $0.28 \mathrm{~kg} / \mathrm{s}$. The total contents of the vessel are always being maintained at 1000 kg . What is the equilibrium temperature which the contents of the vessel will reach, if heat losses to the surroundings are neglected and the overall heat transfer coefficient remains constant?

Check back soon!
02:23

Problem 72

The heat loss through a firebrick furnace wall 0.2 m thick is to be reduced by addition of a layer of insulating brick to the outside. What is the thickness of insulating brick necessary to reduce the heat loss to $400 \mathrm{~W} / \mathrm{m}^2$ ? The inside furnace wall temperature is 1573 K , the ambient air adjacent to the furnace exterior is at 293 K and the natural convection heat transfer coefficient at the exterior surface is given by $h_o=3.0 \Delta T^{0.25} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, where $\Delta T$ is the temperature difference between the surface and the ambient air. Thermal conductivity of firebrick $=1.5 \mathrm{~W} / \mathrm{m} \mathrm{K}$. Thermal conductivity of insulating brick $=0.4 \mathrm{~W} / \mathrm{m} \mathrm{K}$.

Narayan Hari
Narayan Hari
Numerade Educator
04:03

Problem 73

$2.8 \mathrm{~kg} / \mathrm{s}$ of organic liquid of specific heat capacity $2.5 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ is cooled in a heat exchanger from 363 to 313 K using water whose temperature rises from 293 to 318 K flowing countercurrently. After maintenance, the pipework is wrongly connected so that the two streams, flowing at the same rates as previously, are now in co-current flow. On the assumption that overall heat transfer coefficient is unaffected, show that the new outlet temperatures of the organic liquid and the water will be 320.6 K and 314.5 K , respectively.

Penny Riley
Penny Riley
Numerade Educator
04:03

Problem 74

An organic liquid is cooled from 353 to 328 K in a single-pass heat exchanger. When the cooling water of initial temperature 288 K flows countercurrently its outlet temperature is 333 K . With the water flowing co-currently, its feed rate has to be increased in order to give the same outlet temperature for the organic liquid, the new outlet temperature of the water is 313 K . When the cooling water is flowing countercurrently, the film heat transfer coefficient for the water is $600 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.
What is the coefficient for the water when the exchanger is operating with cocurrent flow if its value is proportional to the 0.8 power of the water velocity?

Calculate the film coefficient from the organic liquid, on the assumptions that it remains unchanged, and that heat transfer resistances other than those attributable to the two liquids may be neglected.

Penny Riley
Penny Riley
Numerade Educator

Problem 75

A reaction vessel is heated by steam at 393 K supplied to a coil immersed in the liquid in the tank. It takes 1800 s to heat the contents from 293 K to 373 K when the outside temperature is 293 K . When the outside and initial temperatures are only 278 K , it takes 2700 s to heat the contents to 373 K . The area of the steam coil is $2.5 \mathrm{~m}^2$ and of the external surface is $40 \mathrm{~m}^2$. If the overall heat transfer coefficient from the coil to the liquid in the vessel is $400 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, show that the overall coefficient for transfer from the vessel to the surroundings is about $5 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.

Check back soon!

Problem 76

Steam at 403 K is supplied through a pipe of 25 mm outside diameter. Calculate the heat loss per metre to surroundings at 293 K , on the assumption that there is a negligible drop in temperature through the wall of the pipe. The heat transfer coefficient $h$ from the outside of the pipe of the surroundings is given by:

$$
h=1.22(\Delta T / d)^{0.25} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}
$$

where $d$ is the outside diameter of the pipe (m) and $\Delta T$ is the temperature difference (deg K) between the surface and surroundings.
The pipe is then lagged with a 50 mm thickness of lagging of thermal conductivity $0.1 \mathrm{~W} / \mathrm{m} \mathrm{K}$. If the outside heat transfer coefficient is given by the same equation as for the bare pipe, by what factor is the heat loss reduced?

Check back soon!

Problem 77

A vessel contains 1 tonne of liquid of specific heat capacity $4.0 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$. It is heated by steam at 393 K which is fed to a coil immersed in the liquid and heat is lost to the surroundings at 293 K from the outside of the vessel. How long does it take to heat the liquid from 293 to 353 K and what is the maximum temperature to which the liquid can be heated? When the liquid temperature has reached 353 K , the steam supply is turned off for two hours and the vessel cools. How long will it take to reheat the material to 353 K ? Coil: Area $0.5 \mathrm{~m}^2$. Overall heat transfer coefficient to liquid, $600 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. Outside of vessel: Area $6 \mathrm{~m}^2$. Heat transfer coefficient to surroundings, $10 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$.

Check back soon!
03:32

Problem 78

A bare thermocouple is used to measure the temperature of a gas flowing through a hot pipe. The heat transfer coefficient between the gas and the thermocouple is proportional to the 0.8 power of the gas velocity and the heat transfer by radiation from the walls to the thermocouple is proportional to the temperature difference.

When the gas is flowing at $5 \mathrm{~m} / \mathrm{s}$ the thermocouple reads 323 K . When it is flowing at $10 \mathrm{~m} / \mathrm{s}$ it reads 313 K , and when it is flowing at $15.0 \mathrm{~m} / \mathrm{s}$ it reads 309 K . Show that the gas temperature is about 298 K and calculate the approximate wall temperature. What temperature will the thermocouple indicate when the gas velocity is $20 \mathrm{~m} / \mathrm{s}$ ?

Gaurav Gupta
Gaurav Gupta
Numerade Educator
04:03

Problem 79

A hydrocarbon oil of density $950 \mathrm{~kg} / \mathrm{m}^3$ and specific heat capacity $2.5 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$ is cooled in a heat exchanger from 363 to 313 K by water flowing countercurrently. The temperature of the water rises from 293 to 323 K . If the flowrate of the hydrocarbon is $0.56 \mathrm{~kg} / \mathrm{s}$, what is the required flowrate of water?

After plant modifications, the heat exchanger is incorrectly connected so that the two streams are in co-current flow. What are the new outlet temperatures of hydrocarbon and water, if the overall heat transfer coefficient is unchanged?

Penny Riley
Penny Riley
Numerade Educator

Problem 80

A reaction mixture is heated in a vessel fitted with an agitator and a steam coil of area $10 \mathrm{~m}^2$ fed with steam at 393 K . The heat capacity of the system is equal to that of 500 kg of water. The overall coefficient of heat transfer from the vessel of area $5 \mathrm{~m}^2$ is $10 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. It takes 1800 s to heat the contents from ambient temperature of 293 to 333 K . How long will it take to heat the system to 363 K and what is the maximum temperature which can be reached? Specific heat capacity of water $=4200 \mathrm{~J} / \mathrm{kgK}$.

Check back soon!

Problem 81

A pipe, 50 mm outside diameter, is carrying steam at 413 K and the coefficient of heat transfer from its outer surface to the surroundings at 288 K is $10 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. What is the heat loss per unit length?

It is desired to add lagging of thermal conductivity $0.03 \mathrm{~W} / \mathrm{m} \mathrm{K}$ as a thick layer to the outside of the pipe in order to cut heat losses by $90 \%$. If the heat transfer from the outside surface of the lagging is $5 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$, what thickness of lagging is required?

Check back soon!

Problem 82

It takes $1800 \mathrm{~s}(0.5 \mathrm{~h})$ to heat a tank of liquid from 293 to 323 K using steam supplied to an immersed coil when the steam temperature is 383 K . How long will it take when the steam temperature is raised to 393 K ? The overall heat transfer coefficient from the steam coil to the tank is 10 times the coefficient from the tank to surroundings at a temperature of 293 K , and the area of the steam coil is equal to the outside area of the tank.

Check back soon!
01:01

Problem 83

A thermometer is situated in a duct in an air stream which is at a constant temperature. The reading varies with the gas flowrate as follows:
$$
\begin{array}{cc}
\hline \text { air velocity }(\mathrm{m} / \mathrm{s}) & \text { thermometer reading }(\mathrm{K}) \\
\hline 6.1 & 553 \\
7.6 & 543 \\
12.2 & 533 \\
\hline
\end{array}
$$
The wall of the duct and the gas stream are at somewhat different temperatures. If the heat transfer coefficient for radiant heat transfer from the wall to the thermometer remains constant, and the heat transfer coefficient between the gas stream and thermometer is proportional to the 0.8 power of the velocity, what is the true temperature of the air stream? Neglect any other forms of heat transfer.

Narayan Hari
Narayan Hari
Numerade Educator