First semester 1434/1435
King Saud University
College of Engineering
Chemical Engineering Department
ChE 317
Tutorial # 1
10/11/1434
.
Conduction
1.
The inner and outer surfaces of a 5-m x 6-m brick wall of thickness 30 cm and thermal conductivity 0.69 W/m · °C are maintained at temperatures of 20°C and
5°C, respectively. Determine the rate of heat transfer through the wall, in W.
2.
The heat generated in the circuitry on the surface of a silicon chip ( k = 130 W/m ·
°C) is conducted to the ceramic substrate to which it is attached. The chip is 6 mm x 6 mm in size and 0.5 mm thick and dissipates 3Wof power. Disregarding any heat transfer through the 0.5-mm-high side surfaces, determine the temperature difference between the front and back surfaces of the chip in steady operation.
3.
An aluminum pan whose thermal conductivity is 237 W/m · °C has a flat bottom with diameter 20 cm and thickness 0.4 cm. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of 800 W. If the inner surface of the bottom of the pan is at 105°C, determine the temperature of the outer surface of the bottom of the pan
Q (1) Q (2) Q (3)
4.
A gas at 450 K is flowing inside a 2-in. steel pipe, schedule 40. The pipe is insulted with 51 mm of lagging having a mean k = 0.0623 W/m. K. The convective heat-transfer coefficient of the gas inside the pipe is 30.7
W/m
2
. K and the convective coefficient on the outside of the lagging is
10.8. The air is at a temperature of 300 K. a.
Calculate the heat loss per unit length of 1 m of pipe using resistances. b.
Repeat using the overall U o
based on the outside area A o
.
Dr. Mohamed Gaily
Office: A B 81, Building 3

First semester 1434/1435
5.
A steel pipeline, 2-in. schedule 40 pipe, contains saturated steam at 121.1
ºC. The line is insulated with 25.4 mm of asbestos. Assuming that the inside surface temperature of the metal wall is at 121.1 ºC and the outer surface of the insulation is at 26.7 ºC, calculate the heat loss for 30.5 m of pipe. Also, calculate the kg of steam condensed per hour in the pipe due to the heat loss. The average k for steel is 45W/m.K
6.
A section of a composite wall with the dimensions shown in fig. (1) [to be distributed in the class] has uniform temperatures of 200 ºC and 50 ºC over the left and the right surfaces, respectively. If the thermal conductivities of the wall materials are: k
A
=70 W/m K, k
B
= 60W/m K, k
C
= 40W/m K, and k
D
= 20W/m K, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces.
Fig. (1)
7.
A home owner wants to replace an electric hot-water heater. There are two models in the store. The inexpensive model cost SR280 and has no insulation between the inner and the outer wall. Due to natural convection the space between the inner and the outer wall have an effective conductivity three times that of air.
The more expensive model cost SR310 and has fiberglass insulation in the gap between the walls. Both models are 3.0 m tall and have a cylindrical shape with an inner wall diameter of 0.6 m and a 5 cm gap. The surrounding air is at 25 ºC, and the convection heat transfer coefficient on the outside is 15 W/m 2 K. The hot water inside the tank results in an inside wall temperature of 60 ºC. If energy costs
6 Hallalah per kilowatt-hour, estimate how long it will take to pay back the extra investment in the more expensive hot water heater. State your assumptions.
8.
A food cold storage room is to be constructed of an inner layer of 19.1 mm of pine wood, a middle layer of cork-board, and an outer layer of 50.8 mm of concrete. The inside wall surface temperature is –17.8 ºC and the outside surface temperature is 29.4 ºC at the outer concrete surface. The mean conductivities are for pine, 0.151; cork, 0.0433; and concrete, 0.762 W/m. K. The total inside surface area of the room to use in calculation is approximately 39 m 2 . What thickness of cork board is needed to keep the heat loss to 586 W?
Dr. Mohamed Gaily
Office: A B 81, Building 3

First semester 1434/1435
9.
Water at an average of 70 ºF is flowing in a 2-in. steel pipe, schedule 40. Steam at
220 ºF is condensing on the outside of the pipe. The convective coefficient for the water inside the pipe is h w
= 500 Btu/h. ft ºF and the convective steam coefficient on the outside is h s
= 1500 Btu/h. ft ºF. a.
Draw the thermal resistance diagram. b.
calculate the heat loss per unit length of 1 ft of the pipe using resistances. c.
Repeat using the overall U i
based on the inside area A i
.
d.
Repeat using U o
.
10.
A hot gas pipe, 0.3 m outside diameter, is covered with a layer of insulation (A),
0.025 m thick, and a layer of insulation (B), 0.04 m thick. The surface temperature of the pipe it self was found to be 400 ºC when the outer surface of layer (B) was 40 ºC. After an additional layer of insulation of thickness of 0.02 m and thermal conductivity 0.2 W/m K, was added to the outer surface of layer (B) the pipe temperature was found to be 500 ºC, the outer surface of layer (B) 180
ºC, and the outer surface of the new insulation 30 ºC. What is the rate of heat loss per meter length of pipe before and after the addition of the new insulation?
Dr. Mohamed Gaily
Office: A B 81, Building 3

First semester 1434/1435
The Cost of Heat Loss through a Roof
The roof of an electrically heated home is 6 m long, 8 m wide, and 0.25 m thick, and is made of a flat layer of concrete whose thermal conductivity is k = 0.8 W/m · °C. The temperatures of the inner and the outer surfaces of the roof one night are measured to be
15°C and 4°C, respectively, for a period of 10 hours. Determine:
( a ) The rate of heat loss through the roof that night.
( b ) The cost of that heat loss to the home owner if the cost of electricity is $0.08/kWh.
SOLUTION The inner and outer surfaces of the flat concrete roof of an electrically heated home are maintained at specified temperatures during a night. The heat loss through the roof and its cost that night are to be determined.
Assumptions
1 Steady operating conditions exist during the entire night since the surface temperatures of the roof remain constant at the specified values.
2 Constant properties can be used for the roof.
Properties The thermal conductivity of the roof is given to be k = 0.8 W/m · °C.
Analysis
(a) Noting that heat transfer through the roof is by conduction and the area of the roof is
A = 6 m x 8 m = 48 m
2
,
The steady rate of heat transfer through the roof is determined to be
Q = kA (
T
1
- T
2
)
L
=
(0.8 W/m · °C) (48 m 2
) (15 - 4) °C = 1690 W = 1.69 kW
0.25 m
( b ) The amount of heat lost through the roof during a 10-hour period and its cost are determined from q = Q.
Δ t= (1.69 kW) (10 h) = 16.9 kWh
Cost = (Amount of energy) (Unit cost of energy)
= (16.9 kWh) ($0.08/kWh) = $1.35
Discussion The cost to the home owner of the heat loss through the roof that night was
$1.35. The total heating bill of the house will be much larger since the heat losses through the walls are not considered in these calculations.
Dr. Mohamed Gaily
Office: A B 81, Building 3

Dr. Mohamed Gaily
Office: A B 81, Building 3
First semester 1434/1435
A 3-m internal diameter spherical tank made of 2-cm-thick stainless steel ( k = 15
W/m · °C) is used to store iced water at
T
1
= 0°C. The tank is located in a room whose temperature is T
2
= 22°C. The walls of the room are also at 22°C. The outer surface of the tank is black and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are h
1
= 80 W/m 2 · °C and h
2
= 10 W/m
2
· °C, respectively. Determine a.
The rate of heat transfer to the iced water in the tank b.
The amount of ice at 0°C that melts during a 24-h period.

First semester 1434/1435
Dr. Mohamed Gaily
Office: A B 81, Building 3

First semester 1434/1435
Dr. Mohamed Gaily
Office: A B 81, Building 3

First semester 1434/1435
Dr. Mohamed Gaily
Office: A B 81, Building 3