Abstract
Three dimensional problems reflect more imperative understanding to real world issues in comparison to two dimensional problems. Keeping this fact in mind, a mathematical model is designed to deliberate the 3D magnetohydrodynamic couple stress nanofluid flow with joule heating and viscous dissipation effects past an exponential stretched surface. The analysis is performed keeping in mind the physical effects of Brownian motion and thermophoresis combined with convective heat condition. This paper also distinctly introduces a more realistic boundary constraint for nanoliquid flow model. For instance, zero mass flux condition has been instituted for the first time for 3D couple stress nanofluid model as far as the exponential stretched surface is concerned. Self-similar transformations are engaged to obtain a system of ordinary differential equations possessing high nonlinearity from the system of boundary layer partial differential equations. Analytic solution is constructed in the form of series using Homotopy Analysis Method (HAM). Numerically calculated values of Skin friction and local Nusselt number are also given with suitable analysis. Moreover, the influences of sundry parameters on velocity distribution, and heat and mass transfer rates are deliberated and depicted through relevant graphs. The results obtained clearly show that the Biot number and Hartmann number possess increasing effect on temperature distribution. To authenticate our obtained results, a comparison in limiting case is also given.
Highlights
The term “nanofluid” refers to the nanoparticles suspended into the base fluid
Choi and Eastman[1] were the pioneer to introduce the term nanofluid and the fact that several heat transfer physiognomies of the base fluids, such as thermal conductivity is enhanced by insertion of nanoparticles into it
Wang and Arun[2] deliberated that convective characteristics of base fluid are enhanced by addition of metallic and non-metallic particles into it. This was followed by an experimental study by Eastman[3] who claimed that thermal conductivity of the ethylene glycol is improved by 40% once copper nanoparticles are inserted in it
Summary
Consider a 3D incompressible couple stress nanofluid flow past an exponential stretched surface with convective x+y x+y heat and zero mass flux conditions. The second term in equation 2 represents the couple stress fluid component along x− direction and third term relates the component of magnetic field along x− direction. The second and third terms in equation 3 point out the couple stress fluid component and magnetic field component along y− direction. K, M, α, Pr, Sc, Ec, Nb, γ and Nt represent dimensionless couple stress parameter, Hartmann number, ratio of rates parameter, Prandtl number, Schmidt number, Eckert number, Brownian motion parameter, Biot number and thermophoresis parameter respectively. Values of these parameters are given as under: K v′a v2.
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