Solving the Nonlinear Boundary Layer Flow Equations with Pressure Gradient and Radiation

Abstract

The physical problem under consideration is the boundary layer problem of an incompressible, laminar flow, taking place over a flat plate in the presence of a pressure gradient and radiation. For the mathematical formulation of the problem, the partial differential equations of continuity, energy, and momentum are taken into consideration with the boundary layer simplifications. Using the dimensionless Falkner–Skan transformation, a nonlinear, nonhomogeneous, coupled system of partial differential equations (PDEs) is obtained, which is solved via the homotopy analysis method. The obtained analytical solution describes radiation and pressure gradient effects on the boundary layer flow. These analytical results reveal that the adverse or favorable pressure gradient influences the dimensionless velocity and the dimensionless temperature of the boundary layer. An adverse pressure gradient causes significant changes on the dimensionless wall shear parameter and the dimensionless wall heat-transfer parameter. Thermal radiation influences the thermal boundary layer. The analytical results are in very good agreement with the corresponding numerical ones obtained using a modification of the Keller’s-box method.

Impact of Inclined Lorentz Force and Schmidt Number on Chemically Reactive Newtonian Fluid Flow on a Stretchable Surface When Stefan Blowing and Thermal Radiation are Significant

“…Spalding [31] investigated the mass or species transfer in viscous flow over a flat plate, vertical plate and sphere using the Karman-Pohlhausen-Kroujiline method. Recently, Mahabaleshwar et al [32][33][34][35][36][37][38][39] and Khan et al [40][41][42][43] have investigated analytical examination to impact of different fluids with numerous parameters MHD/porous media flow.…”

An MHD Fluid Flow over a Porous Stretching/Shrinking Sheet with Slips and Mass Transpiration

“…Subjected to appropriate boundary conditions are: The heat flux q r can be defined on the basis of Rosseland's approximation as follows (see refs. [35][36][37][38][39]):…”

Darcy Brinkman Equations for Hybrid Dusty Nanofluid Flow with Heat Transfer and Mass Transpiration

“…The difference of temperature expressed as linearity function in the fourth power of temperature is an assumption. The Taylor's series expansion of the term T ∞ with the value T 4 is presented as below; see Mahabaleshwar et al [36,37]…”

“…The thermal conductivity and dynamic viscosity using hybrid nanofluid were calculated experimentally by Esfe et al [12]. Mahabaleshwar et al [13][14][15][16] extended his work with heat transfer within the sight of radiation and heat source/sink effects subsequently over the stretching sheet. Nanofluids across a stretching sheet with cross-diffusion impacts of hydromagnetics were investigated by Reddy and Chamkha [17].…”