This application solves the Heat Equation in one dimension with a discretized lumped parameter network for a bar heated at one end. The bar has a length of 1, and each segment has a length of 1/nLayers, where nLayers is the number of segments. Each segment contains a thermal conductor (of thermal conductance K=α•nLayers where α is the thermal diffusivity in the Heat Equation) and a lumped mass (of heat capacity C = 1/nLayers). The temperature can be probed at various points along the bar. Heat sources can be placed at various points along the bar if desired. The principles in this model can be extended to more spatial dimensions.

Attachments:
1) Attached to this model is a Maple worksheet that solves the problem mathematically.
The results agree with those given by MapleSim.
2) The second worksheet simulates the temperature variation along the bar, and represents the temperature gradient.