Heat transfer

Mechanical Engineering Department

Northern Arizona University

Flagstaff, Arizona

ME 450 – Heat Transfer

Problem Set #2

Due Tuesday, September 10

Read: Ch 2.4-2.5 & Ch 3.1 in your text (Heat and Mass Transfer 7th Ed, Bergman Et al)

Homework:

1) Write the full heat diffusion equation in Cartesian coordinates and label all terms.

2) There are 4 classic boundary conditions (x=0) discussed in chapter 2.

i. What are they and what equation is used in each case to represent that

boundary condition (BC)?

ii. Give at least one real world example for each BC kind.

3) Starting at the heat diffusion equation, derive the final expression to identify the

temperature profile through a 1-D, steady state, plane wall with uniform generation

with one adiabatic surface (equation C.22).

Using Table 3.3 & C.1, C.2, and C.3 in the appendix as well as appendix A of your textbook,

answer the following questions:

4) A 1-D, steady state, plane wall of length L=0.3m with no generation has temperature

BC’s – Ts1=50°C (x=0) & Ts2=25°C (x=L). Calculate the temperature at .23m and heat flux

through the wall for the following two materials (separate calculations for each): Gold

and Plain Carbon Steel.

5) A 1-D, steady state, plane wall with uniform generation has the right surface (x=L) equal

27°C and the left surface (x=0) is adiabatic. The length of the wall is 0.2m, k equals 45

W/mK, and generation equals 3x105 W/m3. Find the temperature profile as a function

of x using MATLAB and calculate the heat flux for this problem.