If you are on an infinite domain, use a Fourier Transform.
I am trying to solve this equation, but I have problem with the second boundary condition. I am trying to use combination of variables but it wont work. Could you please give me some hints about how to tackle this problem, using any solving method.
(∂^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)]