AME 331, Spring 2008

Problem set #2

Assigned: February 8, 2008

Due: February 15, 2008, 4:30 pm in OHE 430

Analytical problem: Holman 3-2 (Answer: 0.92;
8% error)

Shape factor
problem: 3-10

Shape
factor problem: 3-20 (Answer: 640 W/m)

Numerical
problems:

- Calculating nodal equations: 3-35 (Answer: assuming Dx = Dy, T
_{m,n-1}+ T_{m+1,n}-2T_{m,n}= - qdot Dx^{2}/2k) - Numerical problem with insulated boundary:
3-52 (Partial answer: T
_{3}= 30ūC) - Plain vanilla numerical problem: 3-53 (Partial answer: T
_{1}= 27.6ūC) - With heat source: 3-58 (note that the heat source strength is 90 MW/m
^{3}as stated below the figure, not 90 MW/m^{2}as given in the problem statement; 90 MW/m^{2 }fails the smoke test – shame on Holman!) (Partial answer: T_{3}= 1120ūC) - With radiative boundary (not in text): repeat problem 3-58 if, in
addition to the convection boundary, the top surface (nodes 1, 2, 3) have
an emissivity of 0.5 and "see" cold surroundings whose temperature
is -20ūC.

For the numerical
problems check the accuracy of your results by increasing the resolution in the
x and y directions by a factor of 2 (that is, decrease both Dx and Dy by a factor of 2).

You can download and use the blank Excel
spreadsheet from the website at Steady2DConduction.xls

Two example worked
spreadsheets are also available on the website:

Comparison of analytical and numerical results for
the problem in section 3-2

Numerical solution for Holman example 3-10