PERTURBATION ANALYSIS OF HEAT TRANSFER AND A NOVEL METHOD FOR CHANGING THE THIRD KIND BOUNDARY CONDITION INTO THE FIRST KIND

Heat transfer phenomena play a vital role in many problems, such as transport of flow through a porous medium. In this article, a singular perturbation method and Laplace transform are used to solve the one-dimensional heat transfer problem in semi-infinite porous media divided into inner and outer solutions. To prevent the mistakes of other researchers' analyses, a new approach for outer and inner matching boundary conditions is suggested. In addition, the boundary condition of the third kind (Robin boundary condition) at y = 0 is changed into first kind by means of a novel structure. This approach shows a good accuracy with direct use of the first kind of boundary condition. However, when the slop value at y = 0 requires high accuracy of measurement, applying such an approach is not recommended. On the other hand, by applying the new matching idea, results of an asymptotic solution show good agreement with a numerical solution.