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2D Cylindircal Heat Equation

2D Cylindircal Heat Equation

2D Cylindircal Heat Equation

(OP)
Please Review my derivation for the 2D cylindrical Heat Equation shown below. The '0' superscript refers to temperatures at time t; temperatures at time level t + ∆t are not superscripted.

The fourth picture (last picture) shows a solution from an online literature. My problem is that the online solution contains a 'ln(rs/rp)' term in the coefficients while mine does not. Is this because my solution contains an ap0 term? Or is there a mistake in my solution? Please provide any input you can.




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