Analysis Study On Some Abnormal Diffusion And Heat Transfer Problems

Abnormal diffusion and heat transfer are very important problems due to its applications in science and engineering.Many researchers have been working on this field to investigate various of new applications.In the dissertation,we perform some new study on abnormal diffusion and heat transfer including:the n-diffusion equation with reaction in which the effects of their parameters are considered,the steady boundary layer flow which with potential applications in science and engineering by means of approximate analytical method.For a class of recombination reaction with n-diffusion equation,which takes the effects of various parameters,the innovative constitutive models of Philip n-diffusion,n-diffusion Cattaneo telegraph,p-Fisher-KPP,m-Zeldovitch Lakrov and Stefan-Boltzmann’s law are developed.Adomian decomposition method(ADM),Homotopy perturbation method(HPM)and Homotopy analysis method(HAM)are used to get the approximate analytical solutions for these problems.Some interesting results are obtained and given the good agreement.Moreover,the involved parameters have strong effects on the temperature distribution which are presented graphically and discussed in detail.For the steady boundary layer flow,we analytical approximate the transformed boundary layer equations by Adomian decomposition method and Homotopy analysis method.The solutions are obtained and the effects of speed proportional parameter and Prandlt number on the velocity and temperature fields are presented,discussed and analyzed graphically in detail.Using Adomian decomposition and Homotopy analysis methods shows a good agreement between their solutions.Thorough approximately studies on these nonlinear differential equations,utilizing ADM,HPM and HAM,we provide analytical approximate solutions for abnormal diffusion and heat transfer problems,which are uniformly valid in the development of abnormal diffusion and heat conduction and further verified the accuracy and effectiveness of ADM,HPM and HAM.