ME 345 Heat Transfer Fall 2014

READING AND HOMEWORK ASSIGNMMENTS

Assignments for

Friday 10/3/14

Reading Assignment

Read Sections 4.4 4.6* in the course textbook,

Bergman, T.L., Lavine, A.S., Incropera, F.P., and Dewitt, D.P., Fundamentals of

Heat and Mass Transfer, 7th edition, John Wiley & Sons, New York, 2011.

REMINDER: EXAM #1 will be held on Wednesday, October 3, 2014 during class.

Homework Assignment 13

Using an 11 x 11 uniform grid, find the temperature distribution inside the plane shown below.

The plane is 1m x 1m and its thermal conductivity is k = 400 W/m.K. The temperature at the left

surface is Tleft =100 oC. The temperature at the top and bottom surfaces change linearly as a

function of x as shown below. The right side has convective heat transfer with h = 250 W/m2.K

and T = 10 oC.

a) Report your results in a table, with each table element representing the calculated temperature of each node, including all 4 sides of the plane.

Your table should be 11 rows x 11 columns. Also, report the code you generated to solve

the problem. Use either EES or Matlab.

b) Plot the temperature distribution contours.

= 0,

= 1500

2.

() = (100 + 10)

= 100

() = (100 + 10)

x

y

ME 345 Heat Transfer Fall 2014

READING AND HOMEWORK ASSIGNMMENTS

Some EES tips

This problem is very EESy if you incorporate a 2-D array (i.e., a matrix) into your EES code.

For example, the temperature at each node can be specified by T[m,n] where m and n are the

node location in matrix (row, column). If you use this approach, define your m x n grid to include the outside surface temperatures. If you lay out the grid correctly, you should have an 11

x 11 matrix with 121 nodes. The temperature of the left, top and bottom surface nodes are all known. You can fill the elements of the matrix corresponding to theses surface with a couple of

DUPLICATE loops. The advantage to setting up the matrix this way is that you can use one

equation representing the internal nodes inside a set of nested DUPLICATE loops. You also

need to use a DUPLICATE loop for the convective nodes (right surface). Use the EES Help

Menu to read about DUPLCIATE loops. They are extremely helpful in this problem!

If you have installed the EES 3-D plot capability, you can produce some pretty neat contour plots

that show the temperature profile inside the bar! To make the plot, after you calculation is done,

select

plots >> new plot window >> X-Y-Z plot

In the X-Y-Z Plot Setup window, select 2-D table data type (the default is 3-column data).

X-Axis should be columns 1 to 11, and Y-Axis should be Rows 1 to 11. The minimum and

maximum of X and Y axes can be selected to be from 0 to 1 (length of each side of the square

plane)

Under Z-Axis, select Color Bands to generate colorful contours. Press OK and enjoy your artistic plot!

You can select Gradient Plot instead of Color Bands to see the temperature gradient vectors as well. This way you can see the heat flux vectors!