Objectives:The study of flow and heat transfer on a permeable stretching sheet of Magnetohydrodynamic nanofluid under the influence of convective boundary condition is presented in this article. Mathematical modeling for the law of conservation of mass, momentum, heat and concentration of nanoparticles is executed. Methods: Governing nonlinear partial differential equations are reduced into nonlinear ordinary differential equations and then shooting method with fourth order Adams-Moulton Method is employed for its solution. Findings: The effects of magnetic parameter (0 ≤ M ≤ 2), Thermophoresis parameter (0.1 ≤ Nt ≤ 0.7) Lewis number (1 ≤ Le ≤ 4), Suction parameter (0 ≤ f w ≤ 3), Biot number(0.1 ≤ Bi ≤ 0.7) and Viscous dissipation(0 ≤ Ec ≤ 4) on axial velocity, temperature and concentration profiles are shown graphically. Numerical results were compared with another numerical approach and an excellent agreement was observed. The solutions under the impacts of different physical governing parameters are illustrated by means of graphs and tables. Effects of viscous dissipation is also discussed. Novelty: Despite the enormous importance and repeated application of nanofluids in industry and science, no attempt has been made to investigate the viscous dissipation effect on heat transfer with a permeable linear stretch sheet.

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As part of our research, we investigate the analysis influence of radiation on heat and mass transfer free convection of micropolar MHD fluids over a stretched porosity sheet involving suction and injection. The governing energy, rotational momentum, and concentration and momentum partial differential equations are transformed into ordinary differential equation ones via a similarity transformation. This system of equations is then solved by using MATLAB's built‐in solver. The Sherwood numbers, Nusselt, friction factor, wall couple shear stress, and dimensionless profiles are all influenced by the various physical parameters of the flow. When the material parameter is increased, velocity rises but decreases when the magnetic parameter and surface condition factor are increased.

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Prediction of performance losses by particle impingements on component surface for physico-chemical aspects under two phase flows are very expensive and complicated. Though mathematical models via software engineering provides general design data, still a major break through is yet to be made. When solid particles are suspended in flowing gasses equilibrium conditions of fluid will get disturbed. This paper makes an attempt to study the phenomena for fine particles under laminar flows for thermal boundary layer analysis aspects through computer software. Solution techniques are adopted for FDM to obtain convergent solutions.