Abstract

In this study, the boundary layer flow of an incompressible viscous fluid over an unsteady curved stretching surface is investigated in the presence of a variable applied magnetic field. Since the geometry is curved, the basic flow equations of the present problem are modeled using curvilinear coordinates. The obtained system is then reduced into nonlinear ordinary differential equations in two dependent quantities namely the fluid pressure and velocity by introducing suitable transformations. A numerical solution for fluid pressure and velocity is obtained by using a shooting method using Runge–Kutta integration scheme. The effects of various physical parameters on the fluid velocity and pressure distribution are shown through graphs and are discussed in detail. The comparison between the present and the existing results in the literature in special case for flat unsteady stretching, i.e. (K→∞K→∞ ), is found in good agreement.

Abstract

Existing solutions of the problem of axisymmetric stagnation-point flow and heat transfer on either a cylinder or a flat plate are for incompressible fluid. Here, fluid with viscosity proportional to a linear function of temperature is considered in the problem of an unaxisymmetric stagnation-point flow and heat transfer of an infinite stationary cylinder with non-uniform normal transpiration U0(φ ) and constant heat flux. The impinging free-stream is steady and with a constant strain rate k¯. A reduction of Navier–Stokes and energy equations is obtained by use of appropriate similarity transformations. The semi-similar solution of the Navier–Stokes equations and energy equation has been obtained numerically using an implicit finite-difference scheme. All the solutions aforesaid are presented for Reynolds numbers, Re=k¯a2/2υ∞, ranging from 0.01 to 100 for different values of Prandtl number and viscosity-variation parameter and for selected values of transpiration rate function, S(φ)=U0(φ)/k¯a, where a is cylinder radius and υ∞ is the reference kinematic viscosity of the fluid. Dimensionless shear-stresses corresponding to all the cases increase with the increase in Reynolds number and transpiration rate function while dimensionless shear stresses decrease with the increase in viscosity-variation parameter. The local coefficient of heat transfer (Nusselt number) increases with increasing the transpiration rate function and Prandtl number.

Abstract

Analysis has been carried out to study the stagnation point flow of Maxwell fluid towards a permeable stretching sheet in the presence of nanoparticles. Using suitable transformations, the governing partial differential equations are first converted to ordinary one and then solved numerically by fourth–fifth order Runge–Kutta–Fehlberg method with MAPLE. The flow and heat transfer characteristics are analyzed and discussed for different values of the parameters. Present work reveals that the velocity increases whereas the temperature and concentration decrease with the increase of Maxwell parameter. The thermal and concentration boundary layer thickness decreases with velocity ratio, Lewis number, Prandtl number suction, Brownian motion and thermophoresis parameters. Comparison with known results for Newtonian fluid flow is found an excellent agreement.