In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter NR, and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles.

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The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are presented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ, the order of the chemical reaction parameter m, the Soret number Sr, the buoyancy ratio N , the Lewis number Le, and the dimensionless rheological parameter Ω.

The present contribution provides a numerical treatment for the flow of unsteady natural convection of non-Newtonian Casson fluid model loaded with dusty particles over a vertical wavy plate. It is assumed that the fluid is incompressible and the dusty particles are considered to be spheres with the same size. Via the help of primitive variable formulation, the dimensionless boundary layer governing equations are reduced into a convenient coordinate system. The transformed resulting system of governing equations is tackled numerically employing the fully implicit finite difference method. The impact of various controlling physical parameters such as the amplitude of the wavy plate, the dimensionless time and fluid-particle interaction parameters on the velocity and temperature of both fluid and particle phase is analyzed. It is found that the magnitude of the velocity of both fluid and particle phase diminishes with increasing amplitude of the wavy plate parameter, while an opposite behavior is observed on temperature distributions as the amplitude of the wavy plate parameter rises. A significant impact is noticed for the heat transfer rate with enhancement values of fluid-particle interaction parameter. The numerical solutions are compared with the available data in the literature. Quantitative comparison illustrates good compatibility between the current and previous results. Keywords Dusty fluid • Wavy plate • Non-Newtonian Casson fluid • Natural convection • Finite difference List of symbolŝ a Amplitude of the wavy surface a Dimensionless amplitude of the wavy surface C Concentration of fluid C fx Local skin-friction coefficient c p Specific heat at constant pressure c s Specific heat of particle phase D Mass diffusivity of fluid D Mass concentration of the dust particle Ec Eckert number

The free convective heat transfer to the power-law non-Newtonian flow from a vertical plate in a porous medium saturated with nanofluid under laminar conditions is investigated. It is considered that the non-Newtonian nanofluid obeys the mathematical model of power-law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The partial differential system governing the problem is transformed into an ordinary system via a usual similarity transformation. The numerical solutions of the resulting ordinary system are obtained. These solutions depend on the power-law index n, Lewis number Le, buoyancy-ratio number Nr, Brownian motion number N b , and thermophoresis number Nt. For various values of n and Le, the effects of the influence parameters on the fluid behavior as well as the reduced Nusselt number are presented and discussed.