Boundary-Layer Flow and Heat Transfer of Nanofluid Over a Vertical Plate With Convective Surface Boundary Condition

Abstract

The problem of boundary layer flow and heat transfer induced due to nanofluid over a vertical plate is investigated. The transport equations employed in the analysis include the effect of Brownian motion and thermophoresis. We used a convective heating boundary condition instead of a widely employed thermal conduction of constant temperature or constant heat flux. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., convective heating parameter A, Prandtl number Pr, Lewis number Le, Brownian motion Nb, buoyancy ratio parameter Nr, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order ordinary differential equations. These equations were solved numerically using Runge-Kutta fourth order method with shooting technique. The effects of the governing parameters on flow field and heat transfer characteristics were obtained and discussed. Numerical results are obtained for velocity, temperature, and concentration distribution as well as the local Nusselt number and Sherwood number. It is found that the local Nusselt number and Sherwood number increase with an increase in convective parameter A and Lewis number Le. Likewise, the local Sherwood number increases with an increase in both A and Le. A comparison with the previous study available in literature has been done and we found an excellent agreement with them.

Viscous and Joule Heating in the Stagnation Point Nanofluid Flow Through a Stretching Sheet With Homogenous–Heterogeneous Reactions and Nonlinear Convection

“…Equations (19) and (20) under this assumption reduce tô s " + / g '-* g ( l -g ) 2 = 0 (24) and are subject to the boundary conditions g' = Ksg at rj = 0, and g -> 1 as rf -► oo (25) The problem now reduces to the problem of solving Eqs. (17), (18), and (24) subject to the conditions provided in Eqs.…”

“…(17), (18), and (24) subject to the conditions provided in Eqs. (21), (22), and (25). The other physical quantities which need to be investigated are the skin friction coefficient Cf, the local Nusselt number Nux which may be obtained by using the following results:…”

“…The transport equations included the effects of Brownian motion and thermophoresis. The boundary-layer flow and heat transfer of nanofluid over a vertical plate with a convective surface boundary condition was studied by Ibrahim and Shanker [25]. The investigation of boundary-layer stagnation point flow of a nanofluid past a permeable flat surface with Newtonian heating was carried by Olanrewaju and Makinde [26] , They used the Brownian motion and thermophoresis effects to describe the nanofluid model.…”

“…(21),(22), and(25) are solved using the SLM[39][40][41]. The SLM algorithm starts with the assumption that the functions f(r\), 0(t/), and g(rf) can be expressed as fW = /( '?…”

The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

“…Still further, Wubshet and Shanker [29] have numerically examined the boundary-layer flow and heat transfer of Nanofluid over a vertical plate with convective surface boundary condition. Their study indicated that the local Nusselt number and Sherwood number increase with an increase in convective parameter and Lewis number.…”