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.



Physics & Space Science

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