Numerical Methods for Unsteady Heat Transfer

Unsteady heat transfer equation, no generation, constant k, two-dimensional in Cartesian coordinate:

We have learned how to discretize the Laplacian operator into system of finite difference equations using nodal network. For the unsteady problem, the temperature variation with time needs to be discretized too. To be consistent with the notation from the book, we choose to analyze the time variation in small time increment Dt, such that the real time t=pDt. The time differentiation can be approximated as:

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