Volume 7, Issue 4

In this paper, the influence of mixed convection in a porous square enclosure under the effect of radiation is numerically examined. The top and bottom walls are maintained at uniform temperature θ c while some portion of the vertical walls is partially heated with temperature θ h and rest of the vertical walls are thermally insulated, with θ h > θ c . The non-dimensional governing equations are solved by MAC (Marker and Cell) method. The effect of various parameters (thermal Grashof number, Darcy number, Prandtl number, Reynolds number) on flow patterns and heat transfer has been presented.

In this paper, first order linear homogeneous difference equation is evaluated in fuzzy environment. Difference equations become more notable when it is studied in conjunction with fuzzy theory. Hence, here amelioration of these equations is demonstrated by three different tactics of incorporating fuzzy numbers.Subsequently, the existence and stability analysis of the attained solutions of fuzzy difference equations (FDEs) are then discussed under different cases of impreciseness. In addition, considering triangular and generalized triangular fuzzy numbers, numerical experiments are illustrated and efficient solutions are depicted, graphically and in tabular form.

In this paper, we propose an efficient method to solve linear and nonlinear singular initial value problems of Lane-Emden type equations by combining Laplace transformation and homotopy perturbation methods. The method is based upon Laplace transform, polynomial series and perturbation technique. Several examples, including some well-known Lane-Emden problems, are presented to show the ability and accuracy of the modify method.

In this paper, the fractional derivatives in the sense of modified Riemann–Liouville and the Riccati-Bernoulli Sub-ODE method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Zoomeron equation and the (3 + 1) dimensional space-time fractional mKDV-ZK equation. These nonlinear fractional equations can be turned into another nonlinear ordinary differential equation by complex transform method. This method is efficient and powerful in solving wide classes of nonlinear fractional order equations. The Riccati-Bernoulli Sub-ODE method appears to be easier and more convenient by means of a symbolic computation system.

In the present work, the problem of Hiemenz flow through a porous medium of a incompressible non-Newtonian Rivlin-Ericksen fluid with heat transfer is presented and newly developed analytic method, namely the homotopy analysis method (HAM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. This flow impinges normal to a plane wall with heat transfer. It has been attempted to show capabilities and wide-range applications of the homotopy analysis method in comparison with the numerical method in solving this problem. Also the convergence of the obtained HAM solution is discussed explicitly. Our reports consist of the effect of the porosity of the medium and the characteristics of the Non-Newtonian fluid on both the flow and heat.

A hybrid method of Sumudu transforms and homotopy perturbation method (HPM) is used to solve nonlinear partial differential equation. Here the nonlinear terms are handled with He’s polynomial to obtain the series solution. But, for the authenticity of the obtained solution, the condition of convergence and uniqueness of the solution is derived. The facts are obtained in reference to convergence and error analysis of this solution. Finally, the established fact is supported by finding solution of two well known equations Newell-Whitehead Segel and Fisher’s equation

An analysis of this paper is examined, two-dimensional, laminar with heat transfer on natural convective flow in an electro-conductive polymer on the external surface of a vertical plate under radial magnetic field and slip effects is considered. The coupled governing partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller Box Method (KBM). The computed results for the velocity and temperature profiles as well as heat transfer and skin-friction coefficient have been depicted and discussed in detail through graphs for various parametric conditions. Increasing thermal slip strongly decreases skin friction and Nusselt number. Skin friction is also depressed with increasing magnetic body force parameter. Increasing momentum slip is observed to decrease skin friction. The model is relevant to the simulation of magnetic polymer materials processing.

In this work, we aim to apply a reliable analytic algorithm based on homotopy perturbation Sumudu transform method (HPSTM) to examine the nonlinear time-fractional coupled Burger’s equations. The approximate analytical solution and some numerical examples show the accuracy and efficiency of the proposed method, which is simple and accurate in comparison to the Adomain decomposition method (ADM), homotopy perturbation method (HPM) and generalized differential transform method (GDTM).