A boundary layer analysis is presented for hypersonic flow at an axisymmetric stagnation point region of a blunt body under isothermal and adiabatic boundary conditions. Consideration is given to variable properties of air. It has been shown that surface drag and heat transfer rates may be controlled by applying magnetic field and vectored surface mass transfer. The range of Mach numbers considered is 1–10. As the magnetic field strength M increases, friction factor and heat transfer rate (in the case of isothermal surface) or surface temperature (in the case of adiabatic surface) increase.Friction factor and surface temperature (in the case of adiabatic surface) can be reduced by applying vectored surface mass transfer.

A boundary layer analysis is presented for the stagnation point flow towards a nonlinearly stretching/shrinking sheet immersed in a micropolar non-Newtonian nanofluid. As the material parameter, namely, the vortex viscosity parameter K increases, the friction factor and wall couple stresses decrease whereas the heat and mass transfer rates decrease. As the thermophoresis parameter N-T increases, friction factor as well as heat and mass transfer rates increase. As the Brownian motion parameter N-B increases, friction factor and mass transfer rates increase, whereas the heat transfer rates decrease. As the parameter Nc increases, heat transfer rate increases whereas the mass transfer rates decrease. As the Scmidt number, Sc increases, the friction factor, Nusselt and Sherwood numbers increase.

A boundary layer analysis is presented for the natural convection past an isothermal vertical wavy surface in a nanofluid. The boundary layer regime when the Grashof number Gr is large is considered in detail. Using appropriate variables, the basic equations are transformed into non-similar form. These equations are mapped into the domain of a flat vertical plate, and then solved numerically employing the implicit finite difference method together with Keller’s box scheme. The effects of the surface wave amplitude on the rate of heat and mass transfer and the surface shear stress are presented graphically for parametric variations of the buoyancy ratio parameter, Brownian motion parameter, thermophoresis parameter and Lewis number. The presented analysis estimates the effect of roughness of the surface on the nanofluid boundary layer.

An analysis is presented for the MHD boundary layer flow past a wedge in a non-Newtonian nanofluid. The micropolar model is chosen for the non-Newtonian fluid since the spinning motion of the nanoparticles as they move along the streamwise direction can be best described by the micropolar fluid model. The transformed nonlinear system of equations is solved by using an implicit finite difference method known as the Keller box scheme along with Newton's linearization technique. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the magnetic parameter M, Brownian motion parameter N-B, thermophoresis parameter NT, vortex viscosity parameter K, wedge angle parameter m and Schmidt number Sc. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) on these parameters has been discussed.

A boundary layer analysis is presented for the warm, laminar nanoliquid flow to a melting vertical plate surface in a moving non-Newtonian nanoliquid. We consider the natural convection boundary layer regime. Using the appropriate variables, the basic equations are transformed to non-similar form. These equations are solved numerically, employing the implicit finite difference method together with Keller box scheme. The rates of heat and mass transfer and the surface shear stress are presented graphically for parametric variations in the melting parameter M, buoyancy ratio parameter N-r, Brownian motion parameter N-b, thermophoresis parameter N-t, Lewis number Le and the power law exponent n.

An unsteady flow, heat and mass transfer in a nanofluid over a stretching sheet is considered. The governing momentum, heat and transfer equations are reduced to a set of nonlinear ordinary differential equations using suitable similarity transformations. The reduced equations are then solved using the second order implicit finite difference technique, Keller-Box method. The influence of flow pertinent parameters like unsteady parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number and Schmidt number on velocity, temperature and concentration have been studied. Some interesting behaviors of nanofluid are given based on plotted figures and Tables.

A boundary layer analysis is presented for the mixed convection past a horizontal plate in a porous medium saturated with a nano fluid. The prescribed heat and mass flux boundary conditions are considered. The entire regime of the mixed convection is included, as the mixed convection parameter ξ varies from 0 (pure free convection) to 1 (pure forced convection). The transformed nonlinear system of equations is solved by using an implicit infinite difference method. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

The effect of partial heating/cooling of the wall on the mixed convection with thermal radiation in incompressible laminar pipe flow has been investigated. The gas is assumed to be gray, emitting and absorbing with constant thermophysical properties except the density variation in the buoyancy term. The partial heating/cooling of the wall has significant effect on the Nusselt number. The radiation parameter increases the heat transfer, but reduces the effect of buoyancy. The heat transfer also increases with the optical thickness until a certain value, beyond which it decreases.

A boundary layer analysis has been presented for the natural convection flow of a non-Newtonian nanofluid past a sphere. Solutions of the set of nonsimilarity equations are obtained by employing the implicit finite difference method together with Keller box elimination method. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the material parameters, buoyancy ratio parameter [Formula: see text], Brownian motion parameter N B , thermophoresis parameter N T and Schmidt number Sc. The dependency of the surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed. It was found that the heat transfer rate decreases and mass transfer rates increase as Schmidt number increases. The friction factor and heat transfer rates decrease as the cross viscosity parameter [Formula: see text] increases. The heat transfer rates increase and mass transfer rates decrease as the buoyancy ratio parameter N increases. As the thermophoresis parameter N T increases, the heat and mass transfer rates increase. As the Brownian parameter N B increases, the heat and mass transfer rates decrease. Brownian motion decelerates the flow in the nanofluid boundary layer. Brownian diffusion promotes heat conduction. The Brownian motion and thermophoresis of nanoparticles increase the effective thermal conductivity of the nanofluid. Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are similar to the familiar Soret and Dufour cross diffusion terms that arise with a binary fluid.

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.

The transient natural convection flow with thermal stratification in a rectangular cavity filled with fluid saturated porous medium obeying Darcy's law has been studied. Prior to the time t* = 0, the flow in the cavity is assumed to be motionless and all four walls of the cavity are at the same constant temperature. At time t* = 0, the temperatures of the vertical walls are suddenly increased which vary linearly with the distance y and at the same time on the bottom wall an isothermal heat source is placed centrally. This sudden change in the wall temperatures gives rise to unsteadiness in the problem. The horizontal temperature difference induces and sustains a buoyancy driven flow in the cavity which is then controlled by the vertical temperature difference. The partial differential equations governing the transient natural convection flow have been solved numerically. The local and average Nusselt numbers decrease rapidly in a small time interval after the start of the impulsive change in the wall temperatures and the steady state is reached quickly. The time required to reach the steady state depends on the Rayleigh number and the thermal stratification parameter.

A boundary layer analysis has been presented for the mixed convection flow of a non-Newtonian nanofluid past a vertical cylinder. Solutions of the set of non-similarity equations are obtained by employing the implicit finite difference method together with Keller box elimination method. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the material parameters, buoyancy ratio parameter lambda(T), Brownian motion parameter N-B, thermophoresis parameter N-T and Schmidt number Sc. The dependency of the surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed. It was found that the heat transfer rate decreases and mass transfer rates increase as Schmidt number increases. The friction factor and heat transfer decreases as the cross viscosity parameter Delta increases. The heat transfer rates increase and mass transfer rates decrease as the buoyancy ratio parameter lambda(T) increases. As the thermophoresis parameter N-T increases, the heat and mass transfer rates decrease. As the Brownian parameter N-B increases, the heat transfer rate decreases. Brownian motion decelerates the flow in the nanofluid boundary layer. Brownian diffusion promotes heat conduction. The Brownian motion and thermophoresis of nanoparticles increases the effective thermal conductivity of the nanofluid. Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are similar to the familiar Soret and Dufour cross diffusion terms that arise with a binary fluid.

A boundary layer analysis is presented for the mixed convection flow of a non-Newtonian nanofluid on a nonlinearly stretching sheet. The micropolar model is chosen for the non-Newtonian fluid since the spinning motion of the nanoparticles as they move along the streamwise direction can be best described by the micropolar fluid model. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the micropolar material parameters, Brownian motion parameter N-B, thermophoresis parameter N-T and Schmidt number Sc. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

The unsteady rotating flow of an incompressible laminar viscous electrically conducting fluid over an impulsively rotated infinite disk in the presence of magnetic field and suction is investigated. We have considered the situation where there is a steady state initially (i.e., at t = 0, the fluid is rotating with constant angular velocity over a stationary disk). Then at t > 0, the disk is suddenly rotated with a constant angular velocity either in the same direction or in opposite direction to that of the fluid rotation which causes unsteadiness in the flow field. The effect of the impulsive motion is found to be more pronounced on the tangential shear stress than on the radial shear stress. When the disk and the fluid rotate in the same direction, the tangential shear stress at the surface changes sign in a small time interval immediately after the start of the impulsive motion.

Steady state two-dimensional mixed convection flow in a square cavity filled with a non-Darcy fluid-saturated porous medium with internal heat generation is investigated numerically. The two vertical surfaces of the square enclosure are adiabatic and the horizontal surfaces are kept at constant temperature where the top surface is moving with constant velocity. The Navier-Stokes equations and the energy equation governing the mixed convection flow are nondimensionalized and then solved by using the penalty finite element method with bi-quadratic square elements. The flow and heat transfer are strongly influenced by the Richardson number. The porous medium within the cavity is not a real force but expressed via friction which induces a force opposite to the flow direction that resists the motion. This results in a reduction in the thermal currents of the flows.

A boundary layer analysis is presented for the mixed convection past a vertical wedge in a porous medium saturated with a nanofluid. The entire regime of the mixed convection is included since the mixed convection parameter of ξ varies from zero (pure free convection) to one (pure forced convection). The transformed non-linear system of equations is solved by using an implicit infinite difference method. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) on these parameters has been discussed. The results indicate that as Nr and Nt increase, the heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) decrease. As Nb increases, the surface mass transfer rates increase whereas the surface heat transfer rate decreases. As Le increases, the heat transfer rate decreases whereas the mass transfer rate increases. As the wedge angle increases, the heat and mass transfer rates increase.

The transient boundary layer flow and heat transfer of a viscous incompressible electrically conducting non-Newtonian power-law fluid in a stagnation region of a two-dimensional body in the presence of an applied magnetic field have been studied when the motion is induced impulsively from rest. The nonlinear partial differential equations governing the flow and heat transfer have been solved by the homotopy analysis method and by an implicit finite-difference scheme. For some cases, analytical or approximate solutions have also been obtained. The special interest are the effects of the power-law index, magnetic parameter and the generalized Prandtl number on the surface shear stress and heat transfer rate. In all cases, there is a smooth transition from the transient state to steady state. The shear stress and heat transfer rate at the surface are found to be significantly influenced by the power-law index N except for large time and they show opposite behaviour for steady and unsteady flows. The magnetic field strongly affects the surface shear stress, but its effect on the surface heat transfer rate is comparatively weak except for large time. On the other hand, the generalized Prandtl number exerts strong influence on the surface heat transfer. The skin friction coefficient and the Nusselt number decrease rapidly in a small interval 0 < t* < 1 and reach the steady-state values for t* >= 4. (C) 2010 Published by Elsevier Ltd.

Transient natural convection flow on a heated cylinder buried in a semi-infinite liquid-saturated porous medium has been studied. The unsteadiness in the problem arises due to the cylinder which is heated (cooled) suddenly and then maintained at that temperature. The coupled partial differential equations governing the flow and heat transfer are cast into stream function-temperature formulation, and the solutions are obtained from the initial time to the time when steady state is reached. The heat transfer is found to change significantly with increasing time in a small time interval immediately after the start of the impulsive change, and steady state is reached after some time. The average Nusselt number is found to increase with Rayleigh number When the surface of the cylinder is suddenly cooled, there is a change in the direction of the heat transfer in a small time interval immediately after the start of the impulsive change in the surface temperature;however when the surface temperature is suddenly increased, no such phenomenon is observed.

An analysis has been carried out to study the non-Darcy natural convention flow of Newtonian fluids on a vertical cone embedded in a saturated porous medium with power-law variation of the wall temperature/concentration or heat/mass flux and suction/injection with the streamwise distance x. Both non-similar and self-similar solutions have been obtained. The effects of non-Darcy parameter, ratio of the buoyancy forces due to mass and heat diffusion, variation of wall temperature/concentration or heat/mass flux and suction/injection on the Nusselt and Sherwood numbers have been studied.