1. In class, we examined solutions to the heat equation where there the boundary conditions were...

 

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1. In class, we examined solutions to the heat equation where there the boundary conditions were either fixed temperatures or zero temperature gradients. In many cases of practical interests, such as a cooling fin dissipating heat from a CPU, the boundary condition is fixed heat flux, qin. For example for a boundary at x = 0: gin -k 0 Using a one-sided approximation for the first derivative, T T-Tio Ax show that the appropriate value for the temperature at the boundary node, To, is. Ax To Ti+qin k 1. In class, we examined solutions to the heat equation where there the boundary conditions were either fixed temperatures or zero temperature gradients. In many cases of practical interests, such as a cooling fin dissipating heat from a CPU, the boundary condition is fixed heat flux, qin. For example for a boundary at x = 0: gin -k 0 Using a one-sided approximation for the first derivative, T T-Tio Ax show that the appropriate value for the temperature at the boundary node, To, is. Ax To Ti+qin k