ECH 2032-43 Heat and Mass Transfer
Assignment #1
School of Chemical Engineering, Sungkyunkwan University, Suwon, Republic of Korea
2023 Fall semester (Prof. Wooseok Yang, wooseok.yang@skku.edu)
Due by 22nd September (Fri) 18:00 to 25535A
1. Derive the general three-dimensional heat-conduction equation in cylindrical coordinates
where the temperature may be changing with time and heat sources may be present within the
body.
2. Derive a relation for the critical radius of insulation for a sphere.
3. Derive an expression for the temperature distribution in a sphere of radius r with uniform
heat generation ˙q and constant surface temperature Tw. Assume steady state and 1-dimension
heat transfer.
4. Find the heat transfer per unit area through the composite wall in the figure below. Assume
one-dimensional heat flow.
5. An insulating glass window is constructed of two 5-mm glass plates separated by an air layer
having a thickness of 4 mm. The air layer may be considered stagnant so that pure conduction
is involved. The convection coefficients for the inner and outer surfaces are 12 and 50 W/m2 ·
◦
C, respectively. Calculate the overall heat-transfer coefficient for this arrangement, and the R
value. Repeat the calculation for a single glass plate 5 mm thick. (kair = 0.026 W/m·K, kglass =
0.78 W/m·K)
6. A 1.5-mm-diameter stainless-steel rod [k =19 W/m·oC] protrudes from a wall maintained at
45oC. The rod is 12 mm long, and the convection coefficient is 500W/m2·oC. The environment
temperature is 20oC. Calculate the heat lost by the rod. Repeat the calculation for h=200 and
1500 W/m2·oC.
7. A circumferential fin of rectangular profile having a thickness of 1.0 mm and a length of 2.0
cm is placed on a 2.0-cm-diameter tube. The tube temperature is 150 oC, the environment
temperature is 20 oC, and h=150 W/m2·oC. The fin is aluminum (k = 204 W/m·K). Calculate
the heat lost by the fin.