Convective Surface Boundary Condition Research Articles

MHD Heat and Mass Transfer of Chemical Reaction Fluid Flow over a Moving Vertical Plate in Presence of Heat Source with Convective Surface Boundary Condition

This paper aims to investigate the influence of chemical reaction and the combined effects of internal heat generation and a convective boundary condition on the laminar boundary layer MHD heat and mass transfer flow over a moving vertical flat plate. The lower surface of the plate is in contact with a hot fluid while the stream of cold fluid flows over the upper surface with heat source and chemical reaction. The basic equations governing the flow, heat transfer, and concentration are reduced to a set of ordinary differential equations by using appropriate transformation for variables and solved numerically by Runge-Kutta fourth-order integration scheme in association with shooting method. The effects of physical parameters on the velocity, temperature, and concentration profiles are illustrated graphically. A table recording the values of skin friction, heat transfer, and mass transfer at the plate is also presented. The discussion focuses on the physical interpretation of the results as well as their comparison with previous studies which shows good agreement as a special case of the problem.

Entropy Generation Analysis in a Variable Viscosity MHD Channel Flow with Permeable Walls and Convective Heating

This paper examines the effects of the thermodynamic second law on steady flow of an incompressible variable viscosity electrically conducting fluid in a channel with permeable walls and convective surface boundary conditions. The nonlinear model governing equations are solved numerically using shooting quadrature. Numerical results of the velocity and temperature profiles are utilised to compute the entropy generation number and the Bejan number. The results revealed that entropy generation minimization can be achieved by appropriate combination of the regulated values of thermophysical parameters controlling the flow systems.

MHD Forced Convection Laminar Boundary Layer Flow of Alumina-Water Nanofluid over a Moving Permeable Flat Plate with Convective Surface Boundary Condition

This paper analyses a two-dimensional steady forced convection boundary layer viscous incompressible flow of alumina-water nanofluid over a moving permeable vertical flat plate under the effect of a magnetic field normal to the plate. Thermal convective surface boundary condition is applied. The nanofluid formulated in the present study is water dispersed with various volumetric fractions of the alumina (Al2O3) nanoparticles. The plate velocity and the free stream velocities are considered to be proportional to , while the magnetic field and suction velocities are taken to be proportional to . The similarity solution of the governing problem is obtained. Numerical studies are presented to show the effect of the nanoparticle volume fraction the convective heat transfer parameter , the power law exponent , the wall velocity parameter , and the suction parameter fw on the velocity, temperature, skin-friction coefficient, and Nusselt number.

Soret and Dufour Effects on Hydro Magnetic Heat and Mass Transfer over a Vertical Plate with a Convective Surface Boundary Condition and Chemical Reaction

This paper examined the hydro magnetic boundary layer flow with heat and mass transfer over a vertical plate in the presence of magnetic field with Soret and Dufour effects, chemical reaction and a convective heat exchange at the surface with the surrounding has been studied. The similarity solution is used to transform the system of partial differential equations and an efficient numerical technique is implemented to solve the reduced system by using the Runge-Kutta fourth order method with shooting technique. A comparison study with the previous results shows a very good agreement. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters.

Scaling group transformation for MHD boundary layer free convective heat and mass transfer flow past a convectively heated nonlinear radiating stretching sheet

Free convective heat and mass transfer flow over a moving permeable flat vertical stretching sheet in the presence of non-uniform magnetic field is numerically investigated. Effects of thermal radiation and convective surface boundary condition on steady boundary layer flow of a viscous incompressible electrically conducting fluid are considered. A scaling group of transformation is applied to the governing equations and the boundary conditions. After finding three absolute invariants a third order ordinary differential equation corresponding to the momentum equation and two second order ordinary differential equations corresponding to energy and diffusion equations are derived. Furthermore the similarity equations with the corresponding boundary conditions are solved numerically by using Runge–Kutta–Felberg fourth–fifth order numerical method. Numerical results for velocity, temperature, and concentration distributions as well as skin friction coefficient, local Nusselt, and Sherwood numbers are discussed for various values of physical parameters.

Internal Heat Generation Effect on Thermal Boundary Layer with a Convective Surface Boundary Condition

In this study, we examine the combined effects of internal heat generation and a convective boundary condition on the laminar boundary layer flow over a flat plate. It is assumed that lower surface of the plate is in contact with a hot fluid while a stream of cold fluid flows steadily over the upper surface with a heat source that decays exponentially. Using a similarity variable, the governing non-linear partial differential equations have been transformed into a set of coupled non-linear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth order Runge-Kutta integration scheme. The effects of Prandtl number, local Biot number, and the internal heat generation parameter on the velocity and temperature profiles are illustrated and interpreted in physical terms. A comparison with previously published results on special case of the problem shows excellent agreement

Boundary-Layer Flow and Heat Transfer of Nanofluid Over a Vertical Plate With Convective Surface Boundary Condition

The problem of boundary layer flow and heat transfer induced due to nanofluid over a vertical plate is investigated. The transport equations employed in the analysis include the effect of Brownian motion and thermophoresis. We used a convective heating boundary condition instead of a widely employed thermal conduction of constant temperature or constant heat flux. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., convective heating parameter A, Prandtl number Pr, Lewis number Le, Brownian motion Nb, buoyancy ratio parameter Nr, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order ordinary differential equations. These equations were solved numerically using Runge-Kutta fourth order method with shooting technique. The effects of the governing parameters on flow field and heat transfer characteristics were obtained and discussed. Numerical results are obtained for velocity, temperature, and concentration distribution as well as the local Nusselt number and Sherwood number. It is found that the local Nusselt number and Sherwood number increase with an increase in convective parameter A and Lewis number Le. Likewise, the local Sherwood number increases with an increase in both A and Le. A comparison with the previous study available in literature has been done and we found an excellent agreement with them.

Effect of variable viscosity on thermal boundary layer over a permeable flat plate with radiation and a convective surface boundary condition

In this paper, the combined effects of radiation, temperature dependent viscosity, suction and injection on thermal boundary layer over a permeable flat plate with a convective heat exchange at the surface are investigated. By taking suitable similarity variables, the governing boundary layer equations are transformed into a boundary value problem of coupled nonlinear ordinary differential equations and solved numerically using the shooting technique with sixth-order Runge-Kutta integration scheme. The solutions for the velocity and temperature distributions together with the skin friction coefficient and Nusselt number depend on six parameters; Prandtl number Pr, Brinkmann number Br, the radiation parameter Ra, the viscosity variation parameter a, suction/injection parameter fw and convection Biot number Bi. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on thermal boundary layer. The thermal boundary layer thickens with a rise in the local temperature as the viscous dissipation, wall injection, and convective heating each intensifies, but decreases with increasing suction and thermal radiation. For fixed Pr, Ra, Br and Bi, both the skin friction coefficient and the Nusselt number increase with a decrease in fluid viscosity and an increase in suction. A comparison with previously published results on special case of the problem shows excellent agreement.

Three-dimensional flow of Jeffery fluid with convective surface boundary conditions

Three-dimensional flow of Jeffery fluid over a stretched surface with convective boundary condition is examined in this article. The equations governing this flow are modeled. The series solutions of nonlinear equations are constructed. Results for velocity and temperature are analyzed. Further, numerical values of Nusselt number are computed and discussed. The present analysis in a limiting sense is compared with the previous results. An excellent agreement is noted.

Numerical Study of Chemically-Reacting Hydromagnetic Boundary Layer Flow with Soret/Dufour Effects and a Convective Surface Boundary Condition

Numerical Study of Chemically-Reacting Hydromagnetic Boundary Layer Flow with Soret/Dufour Effects and a Convective Surface Boundary Condition

Entropy analysis for MHD boundary layer flow and heat transfer over a flat plate with a convective surface boundary condition

This paper presents the application of the second law of thermodynamics analysis to magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with a convective surface boundary condition. Using a similarity solution technique and shooting quadrature, the velocity and temperature profiles are obtained numerically and utilised to compute the entropy generation number. The effects of magnetic parameter, Brinkmann number, the Prandtl number and local Biot number on the fluid velocity, temperature profile, local skin friction, Nusselt number and entropy generation rate in the flow regime are depicted graphically and discussed quantitatively.

Mixed Convection Boundary Layer Flow towards a Vertical Plate with a Convective Surface Boundary Condition

The steady mixed convection flow towards an impermeable vertical plate with a convective surface boundary condition is investigated. The governing partial differential equations are first reduced to ordinary differential equations using a similarity transformation, before being solved numerically. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that dual solutions exist for the opposing flow, whereas for the assisting flow, the solution is unique. Moreover, increasing the convective parameter is to increase the skin friction coefficient and the heat transfer rate at the surface.

Radiation effects on heat and mass transfer in MHD stagnation-point flow over a permeable flat plate with thermal convective surface boundary condition, temperature dependent viscosity and thermal conductivity

Abstract We study a steady laminar 2-D MHD viscous incompressible flow over a permeable flat plate with thermal convective boundary condition and radiation effects. The viscosity and thermal conductivity of fluid are assumed to vary linearly with temperature. Similarity representation of the governing partial differential equations is obtained via group method. Similarity equations are then solved numerically by implicit finite difference technique. Effects of convective heat transfer parameter ( b ), radiation parameter ( R ,) magnetic field parameter ( M ), the thermal conductivity parameter ( S ), suction parameter ( fw ), Prandtl number (Pr) and Schmidt number (Sc) on the dimensionless axial velocity, temperature, concentration, wall temperature, the rate of heat transfer and the rate of mass transfer are investigated. Good agreement is found between the numerical results of the present paper with published result for special case.

Effects of internal heat generation, thermal radiation and buoyancy force on a boundary layer over a vertical plate with a convective surface boundary condition

In this paper we analyse the effects of internal heat generation, thermal radiation and buoyancy force on the laminar boundary layer about a vertical plate in a uniform stream of fluid under a convective surface boundary condition. In the analysis, we assumed that the left surface of the plate is in contact with a hot fluid whilst a stream of cold fluid flows steadily over the right surface; the heat source decays exponentially outwards from the surface of the plate. The similarity variable method was applied to the steady state governing non-linear partial differential equations, which were transformed into a set of coupled non-linear ordinary differential equations and were solved numerically by applying a shooting iteration technique together with a sixth-order Runge–Kutta integration scheme for better accuracy. The effects of the Prandtl number, the local Biot number, the internal heat generation parameter, thermal radiation and the local Grashof number on the velocity and temperature profiles are illustrated and interpreted in physical terms. A comparison with previously published results on similar special cases showed excellent agreement.

Magnetohydrodynamic Stagnation Point Flow with a Convective Surface Boundary Condition

Abstract This study analyzes the steady laminar two-dimensional stagnation point flow and heat transfer of an incompressible viscous fluid impinging normal to a horizontal plate, with the bottom surface of the plate heated by convection from a hot fluid. A uniform magnetic field is applied in a direction normal to the flat plate, with a free stream velocity varying linearly with the distance from the stagnation point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The analysis includes the effects of the magnetic parameter, the Prandtl number, and the convective parameter on the heat transfer rate at the surface. Results showed that the heat transfer rate at the surface increases with increasing values of these quantities.

Combined effects of internal heat generation and buoyancy force on boundary layer flow over a vertical plate with a convective surface boundary condition

AbstractThis paper considers the effect of buoyancy force and internal heat generation on laminar thermal boundary layer over a vertical plate with a convective surface boundary condition. We assumed that left surface of the plate is in contact with a hot fluid while a stream of cold fluid flows steadily over the right surface with a heat source that decays exponentially. Using a similarity variable, the steady state governing non‐linear partial differential equations have been transformed into a set of coupled non‐linear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth order Runge–Kutta integration scheme. The effects of Prandtl number, local Biot number, the internal heat generation parameter and the local Grashof number on the velocity and temperature profiles are illustrated and interpreted in physical terms. A comparison with previously published results on special case of the problem shows excellent agreement. From our results, an overshoot of fluid velocity within the boundary layer is observed due to combined effect of buoyancy force and internal heat generation, in addition, internal heat generation causes thickening of thermal boundary layer. © 2011 Canadian Society for Chemical Engineering

Double-diffusive convection from a permeable vertical surface under convective boundary condition

The objective of the present study is to investigate the simultaneous effects of thermal and concentration diffusions on a mixed convection boundary layer flow over a permeable surface under convective surface boundary condition. Using the local similarity method, it has been shown that a set of suitable similarity transformations reduce the non-linear coupled partial differential equations governing the flow, thermal and concentration fields into a set of non-linear coupled ordinary differential equations. Next, two point boundary value problem for non-linear coupled ordinary differential equations have been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. It is interesting to note that dual solutions exist for buoyancy assisting flow, besides that usually reported in literature for buoyancy opposing flow. Further, the buoyancy assisting force causes considerable overshoot in the velocity profile. Prandtl and Schmidt numbers strongly affect the thermal and concentration boundary layer thicknesses, respectively.

Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid

The problem of a steady boundary layer shear flow over a stretching/shrinking sheet in a nanofluid is studied numerically. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique. Two types of nanofluids, namely, Cu-water and Ag-water are used. The effects of nanoparticle volume fraction, the type of nanoparticles, the convective parameter, and the thermal conductivity on the heat transfer characteristics are discussed. It is found that the heat transfer rate at the surface increases with increasing nanoparticle volume fraction while it decreases with the convective parameter. Moreover, the heat transfer rate at the surface of Cu-water nanofluid is higher than that at the surface of Ag-water nanofluid even though the thermal conductivity of Ag is higher than that of Cu.

Stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition

AbstractThe problem of a steady laminar two‐dimensional stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition is studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically using the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter and the convective parameter on the fluid flow and heat transfer characteristics are disscussed. It is found that the skin friction coefficient and the heat transfer rate at the surface decrease with increasing values of the material parameter. Moreover, dual solutions are found to exist for the shrinking case, while for the stretching case, the solution is unique. © 2011 Canadian Society for Chemical Engineering

The forced convection flow of a uniform stream over a flat surface with a convective surface boundary condition

The forced convection heat transfer resulting from the flow of a uniform stream over a flat surface on which there is a convective boundary condition is considered. In previous papers [5–8] it was assumed that the convective heat transfer parameter h f associated with the hot surface depended on x, where x measures distance along the surface, so that problem could be reduced to similarity form. Here it is assumed that this heat transfer parameter h f is a constant, with the result that the temperature profiles and overall heat transfer characteristics evolve as the solution develops from the leading edge. The heat transfer near the leading edge (small x), which we find to be dominated by the surface heat flux, the solution at large distances along the surface (large x), which dominated by the surface temperature, are discussed. A numerical solution to the full problem is then obtained for a range of values of the Prandtl number to join these two solution regimes.