Tangent hyperbolic nanofluid with mixed convection flow: An application of improved Fourier and Fick's diffusion model

Abstract

This article presents a tangent hyperbolic fluid with the effect of the combination of forced and natural convection flow of nanoparticle past a bidirectional extending surface. Modified Fick's and Fourier's diffusion theories are incorporated into concentration and energy equations, respectively. Convective boundary conditions and second-order slip flow are taken in the boundary condition. Nonlinear partial differential equations result after boundary layer approximations of the mathematical formulation of the flow problem. Nonlinear high order ordinary differential equations (ODEs) are formed by applying similarity transformation on the nonlinear partial differential equations. The transformed equations are solved with the bvp4c algorithm from Matlab. The numerical solution of ODEs was obtained and the effect of interesting parameters, dimensionless velocity com-ponent along x-and y-axis, temperature, and concentration particle, Re x , Re y , Nu x , and Sh x , were presented through tables and graphs and discussed thoroughly. The results indicated that a decrease in velocity along with the y-axis results from the increasing behavior of S, M, and n. Decrease in both temperature and concentration results in an increase of α but their elongation is a result of increase in Bi. An increase in concentration results in decrease of N and S but a decrease in concentration results in the widening of Sc, Nb, and λ. Furthermore, enlargement of f − ″(0) and g − ″(0) results in increase of α and modules γ and elongation of both f − ″(0) and g − ″(0) results in increase of δ e and (Sc and Nb), respectively. A comparison with previously published literature was performed and a good agreement was found. K E Y W O R D S Cattaneo-Christov heat flux model, mixed convection, nanofluid, second-order slip, tangent hyperbolic fluid, three-dimension flow

Thin Film Flow of Tangent Hyperbolic Fluid with Nonlinear Mixed Convection Flow and Entropy Generation

“…Constitutive equation of non-Newtonian fluid which is assumed in this article is presented by [66] as follows:…”

“…Furthermore, behavior of incompressible magnetohydrodynamic flow tangent hyperbolic fluid with the effect of melting heat transfer in the stagnation point has been reported by Hayat et al [63], and the analysis of tangent hyperbolic material in the presence of both nanoparticles past an exponential surface with the heat, mass, and motile microorganisms transfer rate in the magnetohydrodynamic convective flow has been performed by Shafiq et al [64]. Moreover, Alaidrous et al [65] and Ibrahim and Gizewu [66,67] have studied tangent hyperbolic nanofluid past bidirectional extending surface under the application of some physical conditions such as thermal radiation, Joule heating, activation energy, and chemical reaction of high order by employing Cattaneo-Christov heat flux model. To our knowledge, no one has attempted to investigate the effect of three-dimensional thin film flow of tangent hyperbolic fluid with nonlinear mixed convection flow and entropy generation past stretching surface.…”

Nonlinear mixed convection flow of a tangent hyperbolic fluid with activation energy

“…All the equations of conservations formed according to Ibrahim and Gizewu 46 were used, which is given as the following:…”

“…Hayat et al, 35 Khader and Megahed, 36 and Elbashbeshy et al 37 43 Saidulu et al, 44 and Shahzad et al 45 have studied MHD flow of a hyperbolic tangent fluid with the influence of heat source/sink, thermal radiation, nanoparticle, and chemical reaction past a stretching surface. And very recently, Ibrahim and Gizewu 46 have studied a tangent hyperbolic fluid with nanoparticles under the effect of mixed convection with Fick's and Fourier's theory.…”

Significance of Hall effect and Ion slip in a three-dimensional bioconvective Tangent hyperbolic nanofluid flow subject to Arrhenius activation energy

“…From this study, it is comprehended that velocity is a decreased for growing estimations of the Weissenberg number and magnetic parameter. Ibrahim and Gizewu 3 , addressed the Tangent hyperbolic nanofluid flow with double diffusion effects and a second-order slip condition at the boundary. Ramzan et al 4 discussed the second-order slip in the attendance of Cattaneo–Christov (C–C) heat flux and homogeneous–heterogeneous reactions with Tangent hyperbolic liquid flow.…”