Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional deri...

in this paper, we apply the laplace decomposition method to obtain a series solutions of the burgers-huxley and burgers-fisher equations. the technique is based on the application of laplace transform to nonlinear partial differential equations. the method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

In the present study, analytical solutions are obtained for two-dimensional advection dispersion equation for conservative solute transport in a semi-infinite heterogeneous porous medium with pulse type input point source of uniform nature. The change in dispersion parameter due to heterogeneity is considered as linear multiple of spatially dependent function and seepage velocity whereas seepag...

In this work, we consider the problem of a semiconductor half-space formed varying thermal conductivity materials with and without Kirchhoff’s transforms. Specifically, deal one relaxation time within context generalized photothermoelastic theory. It is expected that material will vary temperature. The finite element method used to numerically solve problem. Laplace transform eigenvalues are de...

In the present study, analytical solutions are obtained for two-dimensional advection dispersion equation for conservative solute transport in a semi-infinite heterogeneous porous medium with pulse type input point source of uniform nature. The change in dispersion parameter due to heterogeneity is considered as linear multiple of spatially dependent function and seepage velocity whereas seepag...

In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations PDEs in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied semiinvariants for systems of two linear hyperbolic PDEs in two independent variables. Separately, by splitting ...

Mathematical models for transport in layered media are important for investigating how restricting layers affect rates of solute migration in soil profiles; they may also improve the analysis of solute displacement experiments. This study reports an (approximate) analytical solution for solute transport during steady-state flow in a two-layer medium requiring continuity of solute fluxes and res...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

This paper is a continuation of our preceding work on hyperbolic relaxation systems with characteristic boundaries type I. Here we focus the II, where boundary for equilibrium system and non-characteristic system. For this kind initial-boundary-value problems (IBVPs), introduce three-scale asymptotic expansion to analyze boundary-layer behaviors general multi-dimensional linear systems. Moreove...