A.S. Gupta

Temperature field in flow over a stretching sheet with uniform heat flux

Abstract An analysis is made of the temperature distribution in the flow of a viscous incompressible fluid caused by the stretching of a sheet which issues from a slit into the fluid. The velocity of the sheet is proportional to the distance from the slit and the sheet is subject to uniform heat flux. It is shown that temperature at a point decreases with increase in the Prandtl number P. For a given surface heat flux, the temperature of the stretching sheet is also determined for several values of P.

Stagnation-point flow of a viscoelastic fluid towards a stretching surface

Abstract An analysis is made of the steady two-dimensional stagnation-point flow of an incompressible viscoelastic fluid over a flat deformable surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that for a viscoelastic fluid of short memory (obeying Walters’ B′ model), a boundary layer is formed when the stretching velocity of the surface is less than the inviscid free-stream velocity and velocity at a point increases with increase in the elasticity of the fluid. On the other hand, an inverted boundary layer is formed when the surface stretching velocity exceeds the velocity of the free stream and the velocity decreases with increase in the elasticity of the fluid. A novel result of the analysis is that the flow near the stretching surface is that corresponding to an inviscid stagnation-point flow when the surface stretching velocity is equal to the velocity of the free stream. Temperature distribution in the boundary layer is found when the surface is held at constant temperature and surface heat flux is determined. It is found that temperature at a point decreases with increase in the elasticity of the fluid.

Magnetohydrodynamic Viscous Flow Separation in a Channel With Constrictions

An analysis is made of the flow of an electrically conducting fluid in a channel with constrictions in the presence of a uniform transverse magnetic field. A solution technique for governing magnetohydrodynamic (MHD) equations in primitive variable formulation is developed. A coordinate stretching is used to map the long irregular geometry into a finite computational domain. The governing equations are discretized using finite difference approximations and the well-known staggered grid of Harlow and Welch is used. Pressure Poisson equation and pressure-velocity correction formulas are derived and solved numerically

Analytical solution of magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface

A new kind of analytic technique, namely the homotopy analysis method (HAM), is employed to give an explicit analytical solution of the steady two-dimensional stagnation-point flow of an electrically conducting power-law fluid over a stretching surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. A uniform transverse magnetic field is applied normal to the surface. An explicit analytical solution is given by recursive formulae for the first-order power-law (Newtonian) fluid when the ratio of free stream velocity and stretching velocity is not equal to unity. For second and real order power-law fluids, an analytical approach is proposed for magnetic field parameter in a quite large range. All of our analytical results agree well with numerical results. The results obtained by HAM suggest that the solution of the problem under consideration converges.

Momentum and Heat Transfer in MHD Stagnation-Point Flow Over a Shrinking Sheet

The steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an electrically conducting incompressible viscous fluid toward a shrinking sheet is investigated. The sheet is shrunk in its own plane with a velocity proportional to the distance from the stagnation-point and a uniform magnetic field is applied normal to the sheet. Velocity component parallel to the sheet is found to increase with an increase in the magnetic field parameter M. A region of reverse flow occurs near the surface of the shrinking sheet. It is shown that as M increases, the tendency of this flow reversal decreases. It is also observed that the nonalignment of the stagnation-point flow and the shrinking sheet considerably complicates the flow structure. The effect of the magnetic parameter M on the streamlines is shown for both aligned and nonaligned cases. The temperature distribution in the boundary layer is found when the surface is held at constant temperature. The analysis reveals that the temperature at a point increases with increasing M in a certain neighborhood of the surface but beyond this, the temperature decreases with increasing M. For fixed M, the surface heat flux decreases with increase in the shrinking rate.

RADIATION EFFECT ON HYDROMAGNETIC CONVECTION IN A VERTICAL CHANNEL

Abstract The effect of radiation on the combined free and forced convection flow of an electrically conducting fluid inside an open-ended vertical channel and permeated by a uniform transverse magnetic field is considered. Closed form solutions for the velocity, temperature and the induced magnetic field are obtained in the optically thin limit case when the wall temperatures are varying linearly with the vertical distance. It is found that radiation tends to increase the rate of heat transport to the fluid thereby reducing the effect of natural convection. Velocity and the induced magnetic field increase and the temperature difference between the wall and the fluid decreases with increase in the radiation parameter. In the unstable situation corresponding to heating of the channel from below, both radiation and magnetic field exert stabilizing influence on the flow.

Bed-to-wall heat transfer behavior in a pressurized circulating fluidized bed

An experimental investigation has been made to study the effect of pressure and other relevant operating parameters on bed hydrodynamics and bed-to-wall heat transfer in a pressurized circulating fluidized bed (PCFB) riser column of 37.5 mm internal diameter and 1940 mm height. The experiments have been conducted with and without bed material for the consideration of frictional pressure drop due to gas density at elevated pressures. The pressure drop measured without sand particles is assumed as the pressure drop due to gas density for the calculation of bed voidage and suspension density profiles. The specially designed heat transfer probe is used to measure the bed-to-wall heat transfer coefficient. The experimental results have been compared with the published literature and good agreement has been observed. The axial bed voidage is less in the bottom zone of the riser column and is increasing along the height of the bed. With the increase in system pressure, the bed voidage is found to be increasing in the bottom zone and decreasing in the top zone. The heat transfer coefficient increases with the increase in system pressure as well as with the gas superficial velocity. The heat transfer coefficient is also observed to be increasing with the increase in average suspension density.

Flow and heat transfer in the hydromagnetic ekman layer on a porous plate with hall effects

Abstract Flow in the Ekman layer of a conducting liquid past an infinite porous plate is investigated when the liquid is permeated by a transverse magnetic field and the Hall effects are taken into account. It is found that asymptotic solution exists both in the presence of suction or blowing at the plate. For fixed magnetic and suction parameters, the skin friction of the primary flow increases with increase in the Hall parameter ωτ, while that for the secondary flow first increases, reaches a maximum and then decreases with increase in ωτ. Steady distribution of temperature in the flow exists only for suction at the plate and for large Eckert numbers, heat flows from the liquid to the wall even if the wall temperature is higher than that of the ambient stream.

Taylor diffusion in a falling film of a non-Newtonian liquid

Abstract Diffusion of a solute in a laminar film of an Eyring liquid down a vertical plate is considered. The Taylor diffusion coefficient for this film increases with the model parameter.