Explain how the finite difference form of a heat conduction problem is obtained by the energy balance method.
What will be an ideal response?
The finite difference form of a heat conduction problem by the energy balance method is obtained by subdividing the medium into a sufficient number of volume elements, and then applying an energy balance on each element. This is done by first selecting the nodal points (or nodes) at which the temperatures are to be determined, and then forming elements (or control volumes) over the nodes by drawing lines through the midpoints between the nodes. The properties at the node such as the temperature and the rate of heat generation represent the average properties of the element. The temperature is assumed to vary linearly between the nodes, especially when expressing heat conduction between the elements using Fourier’s law.
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