The present paper deals with the unsteady magnetohydrodynamics (MHD) flow and heat transfer of some nanofluids past an accelerating infinite vertical plate in a porous medium. Water as conventional base fluid containing three different types of nanoparticles such as copper (Cu), aluminum oxide (Al2O3) and titanium oxide (TiO2) are considered. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy are converted into linear ordinary differential equations. Exact solutions of these equations are obtained with the Laplace Transform method. The influence of pertinent parameters on the fluid motion is graphically underlined. It is found that the temperature of Cu-water is higher than those of Al2O3-water and TiO2-water nanofluids.

Thermal radiation effects on MHD stagnation point flow of Williamson fluid over a stretching surface are studied. With the help of similarity transformation, the governing equations are converted to nonlinear ordinary differential equations and then solved numerically by Runge-Kutta-Fehlberg (RKF) technique. Numerical results for the reduced Nusselt number and reduced skin friction coefficient as well as the temperature and velocity profiles are elucidated through tables and graphs. The influence of Prandtl number, stretching parameter, Williamson fluid parameter, thermal radiation parameter and magnetic parameter are analyzed and discussed. It is found that, as Prandtl number and magnetic parameter increase, the temperature profiles decrease. Meanwhile, as Williamson fluid parameter and thermal radiation parameter decrease, the temperature profile increase.

Abstract. In this study, the numerical solution of the thermal radiation effects on a stagnation point flow past a stretching/shrinking sheet in a Maxwell fluid with slip condition is considered. The transformed boundary layer equations are solved numerically using the Runge-Kutta-Fehlberg (RKF) method. Numerical solutions are obtained for the skin friction coefficient and the wall temperature as well as the temperature and the velocity profiles. The features of the flow and the heat transfer characteristics for various values of Prandtl number, stretching/shrinking parameter, thermal radiation parameter, Maxwell parameter, dimensionless velocity slip parameter and thermal slip parameter are analyzed and discussed. IntroductionUnderstanding the behaviour of convective boundary layer flow on a stretching sheet is important in industrial manufacturing processes. This includes both metal and polymer sheets such as the cooling of metallic plate, blowing glass and spinning fibre for paper production. Previous study by Crane [1], proposed a mathematical solution for two-dimensional flow of stretching surface in a inert fluid. Other researchers deliberated several aspects in this problem and attained similar results. Another research paper published by Gupta and Gupta [2] had investigated the mass transfer and the heat for thin layer of viscous fluid over stretching sheet with a moving stream of suction or a blowing. Further improvement was made by analysed the performance of laminar boundary layer flow over a continuous and linearly stretching sheet and its effect on the heat transfer [3].The stagnation point of boundary layer flow over shrinking surface was introduced by Wang [4] and Salleh et al. [5]. The stagnation point is a region where maximum pressure, highest rates of heat transfer and mass loss were encountered [4]. Problem associated with boundary layer flows on stagnation point and stretching surface has fascinated many researchers. This type of problem was extended to other type of industrial fluid like a viscoelastic fluid, micropolar fluid, nanofluid and Maxwell fluid [6]- [10].

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In this paper, the effect of Magnetohydrodynamic (MHD) towards the flow and heat transfer for the upper-convected Maxwell (UCM) fluid over a stretching/shrinking sheet with prescribed heat flux (PHF) is considered. The governing equations are transformed into a set of ordinary differential equations (ODEs) by using the similarity transformation. Shooting technique is applied to solve the transform ODEs. Numerical solutions of the local temperature, reduced skin friction coefficient, velocity and temperature profiles are obtained. The features of the flow and heat transfer characteristics for various values of the Prandtl number Pr, the magnetic parameter M, the suction parameter S, the stretching/shrinking parameter and the Maxwell parameter are analyzed and discussed.