Heat Transfer Assignment 1
Content
ASSIGNMENT 1
BMM3513_1415/2
UMP
FACULTY OF MECHANICAL ENGINEERING BMM3513 HEAT TRANSFER Assignment 1(CO1) NAME
/100
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 onedimensional 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 T1 , while the ambient air temperature outside remains at T 2 . 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
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
BMM3513_1415/2
UMP
FACULTY OF MECHANICAL ENGINEERING BMM3513 HEAT TRANSFER Assignment 1(CO1) NAME
/100
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 onedimensional 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 T1 , while the ambient air temperature outside remains at T 2 . 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
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
