ASSIGNMENT 1 BMM3513_1415/2

FACULTY OF MECHANICAL ENGINEERING

BMM3513 HEAT TRANSFER

Assignment 1(CO1)

NAME MATRIC NO.

1. What are the mechanisms of heat transfer? How are they distinguished from each other?

2. Write down the expressions for the physical laws that govern each mode of heat transfer, and identify

the variables involved in each relation.

3. Consider heat transfer through a windowless wall of a house in a winter day. Discuss the parameters

that affect the rate of heat conduction through the wall.

4. What is a blackbody? How do real bodies differ from blackbodies?

5. Write down the expressions for the physical laws that govern each mode of heat transfer, and identify

the variables involved in each relation.

6. Write down the one-dimensional transient heat conduction equation for a long cylinder with constant

thermal conductivity and heat generation, and indicate what each variable represents.

7. Starting with an energy balance on a spherical shell (Fig. 1) volume element, derive the one-

dimensional transient heat conduction equation for a sphere with constant thermal conductivity and no

heat generation.

Figure 1

8. Consider a medium in which the heat conduction equation is given in its simplest form as

(a) Is heat transfer steady or transient? (b) Is heat transfer one-, two-, or three-dimensional? (c) Is there

heat generation in the medium? (d) Is the thermal conductivity of the medium constant or variable?

9. Consider the north wall of a house of thickness L (Fig. 2). The outer surface of the wall exchanges

heat by both convection and radiation. The interior of the house is maintained at 1T , while the

ambient air temperature outside remains at 2T . The sky, the ground, and the surfaces of the

surrounding structures at this location can be modeled as a surface at an effective temperature of Tsky

for radiation exchange on the outer surface. The radiation exchange between the inner surface of the

wall and the surfaces of the walls, floor, and ceiling it faces is negligible. The convection heat transfer

coefficients on the inner and outer surfaces of the wall are h1 and h2, respectively. The thermal

conductivity of the wall material is k and the emissivity of the outer surface is 2 . Assuming the heat

transfer through the wall to be steady and one-dimensional, express the mathematical formulation (the

/100 UMP

ASSIGNMENT 1 BMM3513_1415/2

differential equation and the boundary and initial conditions) of this heat conduction problem. Do not

solve.

Figure 2

10. Water flows through a pipe (Fig. 3) at an average temperature of T =50°C. The inner and outer radii

of the pipe are r1=6 cm and r2= 6.5 cm, respectively. The outer surface of the pipe is wrapped with a

thin electric heater that consumes 300 W per m length of the pipe. The exposed surface of the heater is

heavily insulated so that the entire heat generated in the heater is transferred to the pipe. Heat is

transferred from the inner surface of the pipe to the water by convection with a heat transfer

coefficient of h=55 W/m2 · °C. Assuming constant thermal conductivity and one-dimensional heat

transfer, express the mathematical formulation (the differential equation and the boundary conditions)

of the heat conduction in the pipe during steady operation. Do not solve.

Figure 3