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heat equation derivation in mathematics. The heat equation is a parabolic partial differential equation describing the distribution of heat in a given space over time. In the anisotropic case where the coefficient matrix A is not scalar andor.
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Divide both sides by kXT and get 1 kT dT dt 1 X d2X dx2. The heat equation is then beginequationfracpartial upartial t kfracpartial 2upartial x2 fracQleft xt rightcrho labeleqeq4endequation To most people this is what they mean when they talk about the heat equation and in fact it will be the equation that well be solving. C is the energy required to raise a unit mass of the substance 1 unit in temperature.
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Then we will state and explain the various relevant experimental laws of physics. The coefficient k x is the inverse of specific heat of the substance at x density of the substance at x. Then we will state and explain the various relevant experimental laws of physics. The heat equation in other words solutions of the form uxt XxTt.
