Determine the temperature at the four nodes shown in the sketch. Assume steady conditions and two-dimensional heat conduction. The four faces of the square shape are each at different temperatures as shown.
GIVEN
Square shape with four different face temperatures
FIND
Temperature at four interior nodes
SKETCH
If the shape is divided into square control volumes then according to, the temperature at
each node is the average of its four neighbors. The equation for each node is therefore
The equations can be solved by the iterative method. A table showing the calculation for the first 10
iterations is given below. The zero iteration is the initial guess of the temperature at the four nodes.
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