Krishnendu Bhattacharyya

Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Sheet

An analysis is made to study boundary layer flow and heat transfer over an exponentially shrinking sheet. Using similarity transformations in exponential form, the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations, which are then solved numerically using a very efficient shooting method. The analysis reveals the conditions for the existence of steady boundary layer flow due to exponential shrinking of the sheet and it is found that when the mass suction parameter exceeds a certain critical value, steady flow is possible. The dual solutions for velocity and temperature distributions are obtained. With increasing values of the mass suction parameter, the skin friction coefficient increases for the first solution and decreases for the second solution.

CHEMICALLY REACTIVE SOLUTE DISTRIBUTION IN MHD BOUNDARY LAYER FLOW OVER A PERMEABLE STRETCHING SHEET WITH SUCTION OR BLOWING

The main objective of this work is to analyze the distribution of reactant solute undergoing first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible fluid over a permeable stretching sheet subjected to suction or blowing. The flow is permeated by an externally applied magnetic field normal to the plane of flow. The governing partial differential equations along with appropriate boundary conditions for flow field and reactive solute are transformed into a set of nonlinear ordinary differential equations using similarity variables. The self-similar equations thus obtained are solved numerically by the finite difference method using quasi-linearization technique. The velocity and concentration profiles are drawn for various values of the parameters, and the characteristic features are analyzed. The analysis reveals that the rate of solute transfer is enhanced with increasing values of suction as well as magnetic parameter and its rate is diminished with the increase of blowing parameter. Also, the rate of solute transfer decreases significantly due to increase of initial solute distribution over the sheet.

Dual Solutions in Unsteady Stagnation-Point Flow over a Shrinking Sheet

An analysis is made to study the dual nature of solution of unsteady stagnation-point flow due to a shrinking sheet. Using similarity transformations, the governing boundary layer equations are transformed into the self-similar nonlinear ordinary differential equations. The transformed equations are solved numerically using a very efficient shooting method. The study reveals the conditions of existence, uniqueness and non-existence of unsteady similarity solution. The dual solutions for velocity distribution exist for certain values of velocity ratio parameter (c/a), and the increment in the unsteadiness parameter A increases the range of c/a where solution exists. Also, with increasing A, the skin friction coefficient increases for the first solution and decreases for the second.

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

In this analysis, the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied. Using similarity transformations, the governing equations are converted to an ordinary differential equation and then solved analytically. The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case. The similarity solution is always unique in the stretching case, and in the shrinking case the solution shows dual nature for certain values of the parameters. For stronger magnetic field, the similarity solution for the shrinking sheet case becomes unique.

MHD Stagnation-Point Flow of Casson Fluid and Heat Transfer over a Stretching Sheet with Thermal Radiation

The two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of electrically conducting non-Newtonian Casson fluid and heat transfer towards a stretching sheet have been considered. The effect of thermal radiation is also investigated. Implementing similarity transformations, the governing momentum, and energy equations are transformed to self-similar nonlinear ODEs and numerical computations are performed to solve those. The investigation reveals many important aspects of flow and heat transfer. If velocity ratio parameter (B) and magnetic parameter (M) increase, then the velocity boundary layer thickness becomes thinner. On the other hand, for Casson fluid it is found that the velocity boundary layer thickness is larger compared to that of Newtonian fluid. The magnitude of wall skin-friction coefficient reduces with Casson parameter (β). The velocity ratio parameter, Casson parameter, and magnetic parameter also have major effects on temperature distribution. The heat transfer rate is enhanced with increasing values of velocity ratio parameter. The rate of heat transfer is enhanced with increasing magnetic parameter M for B > 1 and it decreases with M for B < 1. Moreover, the presence of thermal radiation reduces temperature and thermal boundary layer thickness.

MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate

An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate.

Slip Effects on an Unsteady Boundary Layer Stagnation-Point Flow and Heat Transfer towards a Stretching Sheet

An analysis is presented for an unsteady boundary layer stagnation-point flow of a Newtonian fluid and the heat transfer towards a stretching sheet taking non-conventional partial slip conditions at the sheet. The self-similar equations are obtained using similarity transformations and solved numerically by the shooting method. Effects of the parameters involved in the equations, especially velocity slip and thermal slip parameters on the velocity and temperature profiles, are analyzed extensively. It is revealed that due to the velocity and thermal slip parameters, the rate of heat transfer from the sheet and the wall skin friction change significantly.

Magnetohydrodynamic Boundary Layer Flow of Nanofluid over an Exponentially Stretching Permeable Sheet

A mathematical model of the steady boundary layer flow of nanofluid due to an exponentially permeable stretching sheet with external magnetic field is presented. In the model, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, the wall mass transfer parameter, the Prandtl number, the Lewis number, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction. The magnetic field makes enhancement in temperature and nanoparticle volume fraction, whereas the wall mass transfer through the porous sheet causes reduction of both. For the Brownian motion, the temperature increases and the nanoparticle volume fraction decreases. Heat transfer rate becomes low with increase of Lewis number. For thermophoresis effect, the thermal boundary layer thickness becomes larger.

SLIP EFFECT ON DIFFUSION OF CHEMICALLY REACTIVE SPECIES IN BOUNDARY LAYER FLOW OVER A VERTICAL STRETCHING SHEET WITH SUCTION OR BLOWING

In the present investigation, we study the effects of slip boundary condition on the diffusion of chemically reactive species in steady boundary layer flow of viscous incompressible fluid over a vertical stretching sheet with suction or blowing. The first-order chemical reaction is considered and wall concentration varies linearly along the sheet. The self-similar equations are obtained using similarity transformations and are solved numerically using shooting method. Our study reveals that due to the increase of diffusion parameter and blowing, the velocity increases, and it decreases with suction, Schmidt number, and reaction rate parameter. Importantly, for increase of slip parameter, the boundary layer thickness increases. In contrast, the concentration at a point increases only for increasing slip and blowing, while it decreases for increase of all other parameters.

UNSTEADY MHD BOUNDARY LAYER FLOW WITH DIFFUSION AND FIRST-ORDER CHEMICAL REACTION OVER A PERMEABLE STRETCHING SHEET WITH SUCTION OR BLOWING

In this study, unsteady MHD boundary layer flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet with suction or blowing and also with power-law variation in wall concentration is investigated. Using similarity transformation, the governing partial differential equations are converted into nonlinear self-similar ordinary differential equations. The transformed equations are then solved by the finite difference method using the quasi-linearization technique. Due to the increase in the unsteadiness parameter, the velocity initially decreases, but after a certain point it increases. A similar effect is also observed in case of concentration distribution. The increase in magnetic parameter causes a decrease in velocity and an increase in concentration. For increasing strength of applied suction both momentum and concentration boundary layer thicknesses decrease. On the other hand, applied blowing has reverse effects. Moreover, the mass transfer from the sheet is enhanced with increasing values of Schmidt number, reaction rate parameter, and also power-law exponent (related to wall concentration distribution). For high negative values of the power-law exponent, mass absorption at the sheet occurs. Moreover, due to increase of unsteadiness, this mass absorption is prevented.