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Fundamentals of Food Process Engineering

Romeo T. Toledo

Chapter 12

Dehydration - all with Video Answers

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Chapter Questions

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Problem 1

Pork has $\mathrm{a}_{\mathrm{w}}$ of 1.00 at a moisture content of $50 \%$ (wet basis) and higher. If pork is infused with sucrose and $\mathrm{NaCl}$ and dehydrated such that at the end of the dehydration process the moisture content is $60 \%$ (wet basis) and the concentration of sugar and $\mathrm{NaCl}$ are $10 \%$ and $3 \%$, respectively, calculate the $\mathrm{a}_w$ of the cured product.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
00:55

Problem 2

What concentration of $\mathrm{NaCl}$ in water would give the same water activity as a $20 \%$ solution of sucrose?

Nishant Kumar
Nishant Kumar
Numerade Educator
03:03

Problem 3

The following data were obtained on the dehydration of a food product: initial moisture content $=89.7 \%$ (wet basis).
$$
\begin{array}{cc}
\hline \text { Drying time }(\mathrm{min}) & \text { Net weight }(\mathrm{kg}) \\
\hline 0 & 24.0 \\
10 & 17.4 \\
20 & 12.9 \\
30 & 9.7 \\
40 & 7.8 \\
50 & 6.2 \\
60 & 5.2 \\
70 & 4.5 \\
80 & 3.9 \\
90 & 3.5 \\
\hline
\end{array}
$$
Draw the drying curve for this material and construct a curve for the drying rate as a function of the moisture content.
(a) What is the critical moisture content for each of the falling rate zones?
(b) What is the constant drying rate?
(c) Determine the residual moisture content for each of the falling rate stages.
(d) The dehydration was conducted at an air flow rate of $50 \mathrm{~m} / \mathrm{s}$ at a dry bulb temperature of $82^{\circ} \mathrm{C}$ and a wet bulb temperature of $43^{\circ} \mathrm{C}$. The wet material has a density of $947 \mathrm{~kg} / \mathrm{m}^3$ and were dried in a layer $2.5 \mathrm{~cm}$ thick. If the same conditions were used but the initial moisture content was $91 \%$ (wet basis) and a thicker layer of material $(3.5 \mathrm{~cm})$ were used on the drying trays, how long will it take to dry this material to a final moisture content of $12 \%(\mathrm{wb})$ ?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
20:31

Problem 4

A continuous countercurrent drier is to be designed to dry $500 \mathrm{~kg} / \mathrm{h}$ of food product from $60 \%$ (wet basis) moisture to $10 \%$ (wet basis) moisture. The equilibrium moisture content for the material is $5 \%$ (wet basis) and the critical moisture content is $30 \%$ (wet basis). The drying curve of the material in preliminary drying studies showed only one falling rate zone. Air at $66^{\circ} \mathrm{C}$ dry bulb and $30^{\circ} \mathrm{C}$ wet bulb will be used for drying. The exit air relative humidity is $40 \%$. Assume adiabatic humidification of the air. The drying air is drawn from room temperature at $18^{\circ} \mathrm{C}$ and $50 \% \mathrm{RH}$. The wet material has a density of $920 \mathrm{~kg} / \mathrm{m}^3$. The drying tunnel should use trucks that hold a stack of 14 trays, each $122 \mathrm{~cm}$ wide, $76 \mathrm{~cm}$ deep along the length of the tunnel, and $5 \mathrm{~cm}$ thick. The distance between trays on the stack is $10 \mathrm{~cm}$. The drying tunnel has a cross-sectional area of $2.93 \mathrm{~m}^2$. The material in the trays will be loaded at a depth $12.7 \mathrm{~mm}$. Calculate:
(a) The number of trays of product through the tunnel/h.
(b) The rate of travel by the trucks through the tunnel. Assume distance between trucks is 30 $\mathrm{cm}$.
(c) The constant drying rate and the total time for drying.
(d) The length of the tunnel.
(e) If air recycling is used, the fraction of the inlet air to the drier that must come from recycled air.
(f) The capacity of the heater required for the operation with recycling.

Niamat Khuda
Niamat Khuda
Numerade Educator
05:39

Problem 5

A laboratory drier is operated with a wet bulb temperature of $115^{\circ} \mathrm{F}$ and a dry bulb temperature of $160^{\circ} \mathrm{F}$. The air leaving the drier is at $145^{\circ} \mathrm{F}$ dry bulb. Assume adiabatic operation. Part of the discharge air is recycled. Ambient air at $70^{\circ} \mathrm{F}$ and $60 \% \mathrm{RH}$ is heated and mixed with the recycled hot air. Calculate the proportion of fresh air and recycled hot air that must be mixed to achieve the desired inlet dry and wet bulb temperatures.

M Hassan Anwar
M Hassan Anwar
Numerade Educator
04:49

Problem 6

If it takes 8 hours to dry a material in a freeze drier from $80 \% \mathrm{H}_2 \mathrm{O}$ to $10 \% \mathrm{H}_2 \mathrm{O}$ (wet basis) at an absolute pressure of $100 \Phi \mathrm{m}$ and a temperature of $110^{\circ} \mathrm{F}\left(43.3^{\circ} \mathrm{C}\right)$, how long will it take to dry this material from $80 \%$ to $40 \%$ water if the dehydration is carried out at $500 \Phi \mathrm{m}$ and $80^{\circ} \mathrm{F}$ $\left(26.7^{\circ} \mathrm{C}\right)$. The material is $25 \mathrm{~mm}$ thick, has a density of $950 \mathrm{~kg} / \mathrm{m}^3$, and the thermal conductivity of the dried material is $0.35 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$. Thermal conductivity and heat transfer coefficients are independent of plate temperature and vacuum.

Zachary Warner
Zachary Warner
Numerade Educator

Problem 7

Calculate the constant rate of drying in a countercurrent continuous belt dehydrator that processes $200 \mathrm{lb} / \mathrm{h}(90.8 \mathrm{~kg} / \mathrm{h})$ of wet material containing $80 \%$ water to $30 \%$ water. Air at $80^{\circ} \mathrm{EF}$ $\left(26.7^{\circ} \mathrm{C}\right)$ and $80 \% \mathrm{RH}$ is heated to $180^{\circ} \mathrm{F}\left(82.2^{\circ} \mathrm{C}\right)$ in an electric heater, enters the drier and leaves at $10 \% \mathrm{RH}$. The critical moisture content of the material is $28 \%$. The drier is $4 \mathrm{ft}(1.21$ $\mathrm{m}$ ) wide, the belt loaded to a depth of $2 \mathrm{in} .(5.08 \mathrm{~cm})$ of material, and the clearance from the top of the drier to the top of the material on the belt is $10 \mathrm{in} .(25.4 \mathrm{~cm})$. The density of the dry solids in the material is $12 \mathrm{lb} / \mathrm{ft}^3\left(193 \mathrm{~kg} / \mathrm{m}^3\right)$.

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Problem 8

In a spray drying experiment, a sample containing $2.15 \%$ solids and $97.8 \%$ water was fed at the rate of $6.9 \mathrm{lb}$ per hour $(3.126 \mathrm{~kg} / \mathrm{h})$ and this sample was dried at $392^{\circ} \mathrm{F}\left(200^{\circ} \mathrm{C}\right)$ inlet air temperature. The exit air temperature was $200^{\circ} \mathrm{F}\left(93.3^{\circ} \mathrm{C}\right)$. The dried product was $94.5 \%$ solids and the outside air was at $79^{\circ} \mathrm{F}\left(26.1^{\circ} \mathrm{C}\right)$ and $20 \% \mathrm{RH}$. Calculate:
(a) The weight water evaporated per hour.
(b) The \% RH of the exit air.
(c) The mass flow rate of air through the drier in weight dry air/h.
(d) In this same drier, if the inlet air temperature is changed to $440^{\circ} \mathrm{F}\left(226.7^{\circ} \mathrm{C}\right)$ and the $\%$ $\mathrm{RH}$ of the exit air were kept the same as in (b), weight of a sample containing $5 \%$ solids and $98 \%$ water can be dried to $2 \%$ water in 1 hour? (Air flow rate is the same as before.) What would be the exit temperature of the air from the dried under the conditions? Assume adiabatic drying.

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02:53

Problem 9

A dehydrator when operated in the winter where the outside air was $10^{\circ} \mathrm{F}\left(-12.2^{\circ} \mathrm{C}\right)$ and $100 \%$ $\mathrm{RH}(\mathrm{H}=0.001)$ can dry $100 \mathrm{lb}(45.5 \mathrm{~kg})$ of fruit per hour from $90 \%$ water to $10 \%$ water. The inlet temperature of the air to the drier is $150^{\circ} \mathrm{F}\left(65.6^{\circ} \mathrm{C}\right)$ and leaves at $100^{\circ} \mathrm{F}\left(37.8^{\circ} \mathrm{C}\right)$. In the summer when the outside air is at $90^{\circ} \mathrm{F}\left(32.2^{\circ} \mathrm{C}\right)$ and $80 \% \mathrm{RH}$, determine the moisture content of the product leaving the drier if the operator maintains the same rate of $100 \mathrm{lb}$ $(45.4 \mathrm{~kg})$ of wet fruit/hr and the exit air from the drier has the same \% RH as it was in the winter.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 10

The desorption isotherm of water in carrots at $70^{\circ} \mathrm{EC}$ is reported to fit Iglesias and Chirife's equation (Eq. 12.36) with the constants $B_1=3.2841$ and $B_2=1.3923$.
(a) Determine the moisture contents where a shift in drying rate may be expected in the dehydration of carrots.
(b) The following data represents the equilibrium water activity $\left(\mathrm{a}_{\mathrm{w}}\right)$ for carrots at various moisture contents in $\mathrm{kg}$ water $/ \mathrm{kg}$ dry matter $(\mathrm{X}):\left(\mathrm{a}_{\mathrm{w}}, \mathrm{X}\right)$; $(0.02,0.0045),(0.04,0.009)$, $(0.06,0.0125),(0.08,0.016),(0.10,0.019),(0.12,0.0225),(0.14,0.025),(0.016,0.028)$, $(0.18,0.031),(0.20,0.034)$. Fit this data to the BET isotherm and determine the moisture content for a unimolecular layer, $\mathrm{X}_{\mathrm{m}}$
(c) Fit the data to the GAB equation and determine the constants.

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05:24

Problem 11

The diffusivity of water in scalded potatoes at $69^{\circ} \mathrm{EC}$ and $80 \%$ moisture (wet basis) has been determined to be $0.22 \times 10^{-5} \mathrm{~m}^2 / \mathrm{h}$. If $1 \mathrm{~cm}$ potato cubes are dried using air at $1.5 \mathrm{~m} / \mathrm{s}$ velocity and $1 \%$ relative humidity, calculate the dry bulb temperature of the air that can be used such that the diffusion rate from the interior to the surface will be equal to the surface dehydration rate. Assume the air flows parallel to the cubes and that dehydration proceeds from all faces of each cube. The density of the potato cube is $1002 \mathrm{~kg} / \mathrm{m}^3$ at $80 \%$ moisture.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:31

Problem 12

Puffing can be induced during dehydration of diced carrots if the dehydration rate at the constant rate period is of the order $1 \mathrm{~kg}$ water/(min $\mathrm{kg} \mathrm{DM})$. In a fluidized bed drier where the air contacts individual particles at a velocity of $12 \mathrm{~m} / \mathrm{s}$, calculate the minimum dry bulb temperature of the drying air that would induce this rate of drying at the constant rate period. Assume drying air has a humidity of $0.001 \mathrm{~kg}$ water $/ \mathrm{kg}$ dry air and surface temperature under these conditions is $5^{\circ} \mathrm{EC}$ higher than the wet bulb temperature.
Calculate the mass transfer rate under these conditions. Is dehydration rate heat or mass transfer controlled?

Manik Pulyani
Manik Pulyani
Numerade Educator