Abstarct: In this thesis, conductive heat transfer in a porous media is studied under local thermal non equilibrium (LTNE). When the temperature at the bounding surface changes significantly with respect to time, the local rate of temperature change for the two phases will not be equal. In the present study, the boundary temperature change produces LTNE. First three domains are defining, the first one is a one dimensional porous media and the other two ones are 2-D Porous Medias. In first domain, the temperature changes suddenly at the starting point of domain while in domains tow and three the boundary lines temperatures are changed to a fixed and positioned related value respectively. To solve the domains, LTNE energy equations are firstly non-dimensionalized and then take the new forms by the use of natural coordinates which have been calculated by an innovative method. These new equations are solved by numerical and analytical methods. The finite difference compact method and fourth order Rung Kuta method are used in numerical solution and for analytical solution, perturbation method is used. As mentioned, temperature change is one of the reasons producing LTNE. This non equilibrium is affected by diffusivity ratio and conductivity ratio of both phases. The increment of conductivity ratio causes the fluid rate of heat transfer decreases while solid rate of heat transfer increases. Consequently, when this parameter approaches to infinity, solid curve get a line form. Also conductivity ratio increment is increasing the equilibrium time.