##### Impacts of Thermal Conductivity and Variable Viscosity on the Dissipative Heat and Species Transport of MHD Flow in Porous Media

M. A. Mohammed, J. F. Baiyeri, T. O. Ogunbayo, O. A. Esan

Asian Research Journal of Mathematics, Page 1-10
DOI: 10.9734/arjom/2021/v17i930326

The investigation of dissipative heat and species diffusion of a conducting liquid under the combined influence of buoyancy forces in a moving plate is examined in the existence of magnetic field. The flowing liquid heat conductivity and viscosity are taken to be linearly varied as a temperature function. The governing derivative equations of the problem are changed to anon-linear coupled ordinary derivative equations by applying similarity quantities. The dimensionless model is solved using shooting technique along with the Runge-Kutta method. The outcomes for the flow wall friction, heat gradient and species wall gradient are offered in table and qualitatively explained. The study revealed that the Newtonian fluid viscosity can be enhanced by increasing the fluid flow medium porosity and the magnetic field strength. Hence, the study will improve the industrial usage of Newtonian working fluid.

##### Solutions of Klein-Gordon Equation by the Laplace Decomposition Method and Modified Laplace Decomposition Method

R. M. Wayal

Asian Research Journal of Mathematics, Page 11-19
DOI: 10.9734/arjom/2021/v17i930327

In this article, the Laplace decomposition method and Modified Laplace decomposition method have been employed to obtain the exact and approximate solutions of the Klein-Gordon equation with the initial profile. An approximate solution obtained by these methods is in good agreement with the exact solution and shows that these approaches can solve linear and nonlinear problems very effectively and are capable to reduce the size of computational work.

##### Analysis of Effect of Inclined Magnetic Field on MHD Boundary Layer Flow over a Porous Exponentially Stretching Sheet Subject to Thermal Radiation

R. A. Mutegi, J. A. Okello, M. Kimathi

Asian Research Journal of Mathematics, Page 20-33
DOI: 10.9734/arjom/2021/v17i930328

MHD flow has a wide range of industrial applications such as MHD propulsion for space exploration, cooling of nuclear reactors, electronic packages, microelectronic devices, and many more. Due to this, a study on the MHD boundary layer flow of a viscous incompressible fluid over an exponentially stretching sheet with an inclined magnetic field in presence of thermal radiation is analyzed. The continuity, momentum, and energy equations governing the fluid motion are obtained. They are then transformed into a system of nonlinear ordinary differential equations using suitable similarity transformation variables. The resulting nonlinear ordinary differential equations are then transformed to a system of first-order ordinary differential equations and the numerical solution is executed using the collocation method.  The effects of the magnetic field, angle of inclination, radiation, Prandtl number, and the exponential stretching of the sheet on the velocity and temperature of the fluid are discussed. It is observed that velocity increases as the sheet is stretched and decreases as the magnetic field and angle of inclination of the magnetic field increases. Temperature increases as magnetic field, angle of inclination, and radiation increase and lowers as the stretching and stratification parameter of the sheet and Prandtl number increases. The findings of this study are in agreement with other previously related work done.

##### The Simulation of One-Step Algorithms for Treating Higher Order Initial Value Problems

J. Sabo, A. M. Ayinde, A. A. Ishaq, G. Ajileye

Asian Research Journal of Mathematics, Page 34-47
DOI: 10.9734/arjom/2021/v17i930329

The simulation of one-step methods using interpolation and collocation for the treatment of higher order initial value problems is proposed in this paper. The new approach is derived using interpolation and collocation as a basic function through power series polynomial, where the basic properties are also analyzed. The derived method is used to treat some highly stiff linear problems. The new approach compute clearly showed that the method is reliable, efficient and gives faster convergence when compared with those in literature.