Flow and Heat Transfer Analysis MHD Nanofluid due to Convective Stretching Sheet

Abstract

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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“…(17) Equations ( 7), (16), and ( 17) are the fundamental differential equations for the characteristic method as applied to the hyperbolic type differential equation. We shall discuss the approximate solution of these equations for flow problems later.…”

“…The characteristic equations which hold along these characteristic curves are equations ( 8), (16), and (17). For the first family of characteristics, with as parameter, we have the following three relations along the characteristic C':…”

Cauchy Characteristics and Some Fluid Flow Problems

“…(17) Equations ( 7), (16), and ( 17) are the fundamental differential equations for the characteristic method as applied to the hyperbolic type differential equation. We shall discuss the approximate solution of these equations for flow problems later.…”

“…The characteristic equations which hold along these characteristic curves are equations ( 8), (16), and (17). For the first family of characteristics, with as parameter, we have the following three relations along the characteristic C':…”