Recent content by deepakphysics

I think I did little mistake in the first post. There should have been a minus sign in the left hand side of both equations representing spatial boundary conditions. Also I did mistake in my previous reply. I think I have corrected those mistake this time. Please find the outcome in the...

Thank you for the correction. Please find the updated results in the attachments.

Thank you. I have tried to answer your question. I have attached a screen shot in the previous reply (forgot to mention about the attached screen shot).

This is what I got. One more thing, T_infty is not the temperature corresponding to steady state solution. It is a ambient temperature. For some reason it should be taken as a variable. The results need to be expressed in terms of T_infty and T_max and other material parameters (h, l, k ).

Hi I have following analytical solution (Please find it in the attachment). T1 and T2 are temperature at the surface of inner and outer wall.

Thank you for the solution. It is possible to find C1 and C2. I got as follows (picture attached) a = alpha Tm = T_max, Ti = T_inf. I am stuck again..how can we find inverse laplace ?

Yes doing that we will arrive at solution T(x,t) = (A*cos(w*x)+Bsin(w*x))*T_inf*e^(-alpha*w^2*t). I have problem now finding values of A, B and W with given boundary conditions.

T_max is a constant value. T_infinity is also a constant value.

Differential equation \begin{align} \frac{{\partial}^2 T (x,t)}{\partial x^2} = \frac{1}{\alpha}\frac{\partial T(x,t)}{\partial t}, \end{align} boundary conditions \begin{equation} \begin{aligned} T(x, 0) = T_\infty \\ -k\frac{\partial T(0,t)}{\partial x}= h(T_{max} - T(0,t)) \\...