(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am trying to solve this PDE with variable boundary condition, and I want to use combination method. But I have problem with the second boundary condition, which is not transformed to the new variable. Can you please give me some advise?

2. Relevant equations

(∂^2 T)/(∂x^2 )=1/∝ ∂T/∂t

IC: T(x,0) = Ti

BC1: T(x→∞, t) = Ti

BC2: -k ∂T/∂x|x=0 = h[T∞ - T(0,t)]

3. The attempt at a solution

The combination variable I chose is η= x/((4∝t)^(1⁄2))

My work is attached in a PDF file, please take a look at it. The highlighted boundary condition is the problem.

Thank you

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# Homework Help: PDE with variable boundary condition

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