assignment 2 heat transfer

ASSIGNMENT 2 BMM3513_1415/2

FACULTY OF MECHANICAL ENGINEERING

BMM3513 HEAT TRANSFER

Assignment 2(CO2)

NAME MATRIC NO.

1. Consider the base plate (Fig. 1) of a 800-W household iron with a thickness of L = 0.6 cm, base area

of A= 160 cm2, and thermal conductivity of k = 20 W/mC. The inner surface of the base plate is

subjected to uniform heat flux generated by the resistance heaters inside. When steady operating

conditions are reached, the outer surface temperature of the plate is measured to be 85C.

Disregarding any heat loss through the upper part of the iron, (a) express the differential equation and

the boundary conditions for steady one-dimensional heat conduction through the plate, (b) obtain a

relation for the variation of temperature in the base plate by solving the differential equation, and (c)

evaluate the inner surface temperature

Figure 1

2. When a long section of a compressed air line passes through the outdoors, it is observed that the

moisture in the compressed air freezes in cold weather, disrupting and even completely blocking the

air flow in the pipe. To avoid this problem, the outer surface of the pipe is wrapped with electric strip

heaters and then insulated. Consider a compressed air pipe (Fig. 2) of length L = 6 m, inner radius r1 =

3.7 cm, outer radius r2 = 4.0 cm, and thermal conductivity k = 14 W/mC equipped with a 300-Wstrip

heater. Air is flowing through the pipe at an average temperature of -10C, and the average convection

heat transfer coefficient on the inner surface is h = 30 W/m2C. Assuming 15 percent of the heat

generated in the strip heater is lost through the insulation, (a) express the differential equation and the

boundary conditions for steady one-dimensional heat conduction through the pipe, (b) obtain a relation

for the variation of temperature in the pipe material by solving the differential equation, and (c)

evaluate the inner and outer surface temperatures of the pipe.

Figure 2

/100 UMP


3. In a food processing facility, a spherical container (Fig. 3) of inner radius r1 = 40 cm, outer radius r2 =

41 cm, and thermal conductivity k = 1.5 W/mC is used to store hot water and to keep it at 100C at

all times. To accomplish this, the outer surface of the container is wrapped with a 500-W electric strip

heater and then insulated. The temperature of the inner surface of the container is observed to be

nearly 100C at all times. Assuming 10 percent of the heat generated in the heater is lost through the

insulation, (a) express the differential equation and the boundary conditions for steady one-

dimensional heat conduction through the container, (b) obtain a relation for the variation of

temperature in the container material by solving the differential equation, and (c) evaluate the outer

surface temperature of the container. Also determine how much water at 100C this tank can supply

steadily if the cold water enters at 20C.

Figure 3

4. Consider a 5-m-high, 8-m-long, and 0.22-m-thick wall (Fig. 4) whose representative cross section is

as given in the figure. The thermal conductivities of various materials used, in W/mC, are kA = kF =

2, kB=8, kC=20, kD=15, and kE = 35. The left and right surfaces of the wall are maintained at uniform

temperatures of 300C and 100C, respectively. Assuming heat transfer through the wall to be one-

dimensional, determine (a) the rate of heat transfer through the wall; (b) the temperature at the point

where the sections B, D, and E meet; and (c) the temperature drop across the section F. Disregard any

contact resistances at the interfaces.

Figure 4


5. A 50-m-long section of a steam pipe in Fig. 5 whose outer diameter is 10 cm passes through an open

space at 15C. The average temperature of the outer surface of the pipe is measured to be 150C. If the

combined heat transfer coefficient on the outer surface of the pipe is 20 W/m2C, determine (a) the

rate of heat loss from the steam pipe, (b) the annual cost of this energy lost if steam is generated in a

natural gas furnace that has an efficiency of 75 percent and the price of natural gas is $0.52/therm (1

therm 105,500 kJ), and (c) the thickness of fiberglass insulation (k = 0.035 W/m C) needed in

order to save 90 percent of the heat lost. Assume the pipe temperature to remain constant at 150C

Figure 5

6. A 5-m-internal-diameter spherical tank made of 1.5-cm-thick stainless steel (k = 15 W/mC) is used

to store iced water at 0C shown in Fig. 6. The tank is located in a room whose temperature is 30C.

The walls of the room are also at 30C. The outer surface of the tank is black (emissivity = 1), 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

80 W/m2C and 10 W/m

2C, respectively. Determine (a) the rate of heat transfer to the iced water in

the tank and (b) the amount of ice at 0C that melts during a 24-h period. The heat of fusion of water

at atmospheric pressure is hif = 333.7 kJ/kg.

Figure 6

7. A 2-mm-diameter and 10-m-long electric wire (Fig. 7) is tightly wrapped with a 1-mm-thick plastic

cover whose thermal conductivity is k = 0.15 W/mC. Electrical measurements indicate that a current

of 10 A passes through the wire and there is a voltage drop of 8 V along the wire. If the insulated wire

is exposed to a medium at T = 30C with a heat transfer coefficient of h = 24 W/m2C, determine the

temperature at the interface of the wire and the plastic cover in steady operation. Also determine if

doubling the thickness of the plastic cover will increase or decrease this interface temperature.


Figure 7

8. En. Karim recently bought an old furnace to install in his steel factory. He found that the furnace

operates at a lost due to its 2 m x 1.5 m section of wall is not insulated. He plan to insulate the furnace

wall with glass wool (k = 0.038 W/m.K) in order to keep the heat loss at 90%. The furnace is located

at area where the room temperature is 32 oC and the temperature at furnace outer surface is measured

at 110oC. The combined convection and radiation heat transfer coefficient at the furnace outer surface

is 10 W/m2.K. The furnace will operate everyday non-stop throughout the year. Once the insulation

done, the furnace has an efficiency of 75%. The installation work will cost RM200 for material and

RM50 for labor. As an engineer assigned to do the task, determine

a) the heat transfer Q without insulation,

b) the thickness of the glass wool insulation, and

c) how long does it take to get back the installation cost from the energyit saves if the price of natural

gas is RM1.10/therm ( 1 therm =105,500 kJ of energy content).

(Mid Sem Exam for Sem 1 2013/2014)

9. A wall with surface temperature of 300 oC is attached with a rectangular fin as shown in Figure 9.

The fin with thermal conductivity of 220 W/m.K is exposed to an ambient air temperature of 30 oC

and the convection heat transfer coefficient is 145 W/m2.K. It was designed with a length of 60 mm,

a width of 120 mm and 5 mm thick. Determine the efficiency, heat transfer rate, and effectiveness of

each fin using,

a) Table 3-3 in page 170

b) Figure 3-43 in page 172

(Mid Sem Exam for Sem 1 2013/2014)

Figure 9


10. A hot surface at 100C is to be cooled by attaching rectangular aluminum pin fins (k = 237 W/mC)

to it, with 3-cm-long, 0.25-cm-thickness, 0.3-cm-width and a center-to-center distance of 0.6 cm

shown in Fig. 10. The temperature of the surrounding medium is 30C, and the heat transfer

coefficient on the surfaces is 35 W/m2C. Determine the rate of heat transfer from the surface for a 1-

m X 1-m section of the plate. Also determine the overall effectiveness of the fins.

Figure 10

assignment 2 heat transfer

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