Problem 1 (43 pts): Oil is cooled in a concentric tube heat exchanger by a counterflow of cold water (Figure 3). The specific temperatures and heat capacity rates, along with average water and oil properties, as well as a fouling factor for the water side of the heat exchanger (there is no fouling on the oil side), are included in the table below. The wall thickness between the hot oil and cold water has negligible thickness relative to $D_1$ and $D_2$.
Parameter
Variable
Value
Temperature of cold water entering the heat exchanger
$T_{C,IN}$
30°C
Temperature of cold water leaving the heat exchanger
$T_{C,OUT}$
40°C
Temperature of hot oil entering the heat exchanger
$T_{H,IN}$
100°C
Temperature of hot oil leaving the heat exchanger
$T_{H,OUT}$
60°C
Mass flow rate of hot oil into the heat exchanger
$\dot{m}_H$
0.1 kg/sec
Inner diameter of annular tube
$2r_1=D_1$
0.035m
Outer diameter of annulus
$2r_2=D_2$
0.045m
Fouling factor for the cold-water surface
$R''_{f,cold}$
0.0004 $m^2*K/W$
Water density
$\rho_c$
994.1 kg/$m^3$
Water Prandtl number
$Pr_c$
4.85
Water specific heat
$cp_c$
4179 J/kgK
Water thermal conductivity
$k_c$
0.621 W/mK
Water kinematic viscosity
$\nu_c$
7.26e-7 $m^2$/sec
Oil density
$\rho_h$
854.0kg/$m^3$
Oil Prandtl number
$Pr_h$
546.0
Oil specific heat
$cp_h$
2118 J/kgK
Oil thermal conductivity
$k_h$
0.138 W/mK
Oil kinematic viscosity
$\nu_h$
41.7e-6 $m^2$/sec
WATER
OIL
Figure 3. Cross-sectional view of the concentric heat exchanger, showing fouling (in green, exaggerated) on the cold-water side.
Problem 1. part a
Determine the effectiveness of this heat exchanger.
Problem 1, part b. Determine the convective heat transfer coefficient for the oil. If necessary to assume constant surface tempera
Problem 1, part c
Determine the convective heat transfer coefficient for the water, if laminar, use $Nu_{D_h}$ = 5.2.
Problem 1, part d. How long does this heat exchanger need to be to accomplish the heat transfer from the oil (in meters)?
Problem 1, part e
Do you think that doubling the oil flow rate or doubling the water flow rate would have a larger effect on the overall rate of heat transfer? Why? Answer in 1-3 sentences.
"I'm looking for your thought process more so than correct answers"
Please justify your answer in your pdf
Oil
Water
