This paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.,The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.,Results found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.,The problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

Mixed convective three-dimensional flow of Williamson nanofluid subject to chemical reaction

This work aims at evaluating the effect of Magnetohydrodynamic (MHD) on the steady two-dimensional (2-D) mixed convection flow induced by nonlinear surface in carbon nanotubes. Water and kerosene are used as a base fluid with single and multi-wall carbon nanotubes (CNTs). Using a similarity transformation, the governing equations are converted to an ordinary differential equation which are then solved analytically. The novelty of this research is the exact analytical solution obtained for nonlinear flow in carbon nanotubes. The influence of governing parameters, i.e., magnetic, suction and nanoparticle volume fraction parameter on temperature and velocity profiles are discussed and analyzed in the graphical forms. The solution shows a unique solution for stretching case. However, the solution shows a dual nature for some values of parameters for shrinking case. Therefore, the stability analysis is executed using the bvp4c package in Matlab software to determine which solution is linearly stable and valid physically. It is also found that an addition of 0.05 vol fraction of carbon nanotube in water base fluid causes an increment for about 26% in skin friction and heat transfer rate.

Analytical and stability analysis of MHD flow past a nonlinearly deforming vertical surface in Carbon Nanotubes

Aiding (opponent) flow of hybrid copper–aluminum oxide nanofluid towards an exponentially extending (lessening) sheet with thermal radiation and heat source (sink) impact

Salient aspects of thermo-diffusion and diffusion thermo on unsteady dissipative flow with entropy generation

In this article, an analytical solution of the boundary layer fluid flow and heat transfer of a quiescent viscous fluid over a non-linearly stretching surface is presented. The thermal radiation effects are included in the energy governing equation. Surface velocity and temperature conditions are assumed to be of the power-law form with an exponent of 1/3 for velocity and arbitrary exponent m for surface temperature or heat flux conditions. The system of nonlinear differential equations is solved by Homotopy Analysis Method (HAM) for two cases of Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF). The results of this method appear in the form of series expansions, the convergence of which is analyzed carefully. Graphical results are finally presented in order to investigate the influence of Prandtl number (Pr) and thermal radiation on heat transfer phenomena.

S.M. Musavi

Papers

Analytical solution of convective heat transfer of a quiescent fluid over a nonlinearly stretching surface using Homotopy Analysis Method