Heat Transfer Problems

ME 341 HEAT TRANSFER FOR ENGINEERING Exam 2

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1) For the geometry given below, solve డ మ்

డ௫మ + డ

మ் డ௬మ

= 0 to get each of the unknown temperature values (T1 through T6) as indicated. At the points on the upper and right- hand side boundaries, T=100. The left-hand side boundary of the geometry is perfectly insulated. At points on the lower boundary, there is a flux with a temperature gradient of డ்

డ௬ = െ5. Lower left corner of the grid is at (x, y) = (0, 0).

The grid spacing is ݔ߂ = ݕ߂ = 1.5. Use unit thermal conductivity. a) Develop the discretization equations for all six points and program them into

Excel spreadsheet cells to obtain the temperature values. Provide a 3-D surface plot of the domain.

b) Plot the temperature T2 as a function of the thermal conductivity by halving, doubling and quadrupling the thermal conductivity. Comment on your findings.

(30 points)

Y

X

Upper

Lower

RightLeft T1 T2 T3

T4 T5 T6

'x

'y