Study of local thermal nonequilibrium in porous media due to temperature sudden change and heat generation

In this paper we examine the effects of temperature sudden change in boundary x = 0 and great heat generating on the creation of local thermal nonequilibrium (LTNE) in the semiinfinite stagnant porous media. Two energy equations in the transient state and in the presence of heat generating are used as the governing equations in each phase. These partial governing equations solve numerically. For partial derivatives, we use from Compact finite difference method that is the continuous method for calculation of derivatives and for progress in time, we use from RK4. So we test values of heat transfer rate for early and late times using perturbation and shooting methods. Rate of heat transfer between phases depict in the figures. Results show that effects of heat generating and LTNE are restrained at very late times and graphs slope decrease to zero. In this time, the temperature gradient moves towards the infinite with a constant value. Also, effect of different nondimension parameters on behavior of temperature gradients is verified. When diffusivity ratio α increases, time to counteract heat generation effect increases. Fluid and solid graphs are stabilized in the negative value of temperature gradient with the constant slop zero and different diffusivity ratios α don't affect on this value. So for α > 1, the difference between solid and fluid phases will increase and vice versa, for α < 1 it will decrease. Heat generation effect is counteracted in earlier times when conductivity ratio γ increases. So The graphs state that when y increases, the value of the difference decreases and temperature gradient of the phases are more coinciding and Contact point of the phases tend to earlier time. Other characterizations are explained in detailed.