Analytical approach to micro scale bio-film heat transport using homotopy perturbation method

In this article, we use Homotopy Perturbation Method (HPM) to find the approximate analytical solution of initial valued three dimensional microscale heat transport equation. This transport equation is at first converted into the equation of two functions. First one have both the first order time derivative and second order space derivatives, while second one has only second order space derivative. Then HPM is applied to obtain the solution. By providing suitable examples, it is proved that the obtained solution is very close to the analytical solution. It is observed that for small duration of time the source term does not affect the fundamental structure of the solution though it affects the solution for large duration of time which are depicted through graphs.