Please consult the attached file for the answer. . If you want, I can send to you the variable separation procedure for to obtain Eq. (2) of file.

Thanks a lot Sir. You are a life saver. By the way could you help me with matlab programm on how to solve this equation?

Thanks once more for your help

Please Sir could you send me the procedure to have the final equation? I will really appreciate that. Thanks a lot

Yes of course. Give me one or two days.

Thank you Sir. I will be waiting.

The analytical solution of 1D rectangular unsteady heat conduction problem solved by variable separation and its extension to 3D problem with a demonstration of superposition principle is described in the attached file. The MatLab code for solving this problem will be send later (may be two days).

The analytical solution of 1D rectangular unsteady heat conduction problem solved by variable separation and its extension to 3D problem with a demonstration of superposition principle is described in the attached file with three equations (bold in yellow) corrected. The MatLab code for solving this problem is attached in the zip folder. In order to solve you must run first “eigen.m” which generates the eigenvalues. The example is with a limit in the argument of eigenvalues generator equation (Eq. 13) of 200, which generate 64 eigenvalues. You must save the eigenvalues in lam.dat file. Then, you can run the “hcRe1D.m” with generate a history of analytical solution for 1D rectangular heat conduction problem in dimensionless form. You can obtain only the required value by fixing the maximal Fourrier number in the desired value. If you need 2D or 3D solution you can apply Eq. (38).You can consult a much complex problem solved by Laplace transform (in this case the variable separation cannot be applied) in my paper attached.