Hydromagnetic mixed convection stagnation point flow with radiative heat and mass transfer past a vertical plate embedded in a porous medium

A study has been carried out to obtain the solutions for hydromagnetic mixed convection stagnation point flow with radiative heat and mass transfer past a vertical plate embedded in a porous medium. The governing two dimensional equations are transformed using a similarity transformation and then solved numerically by shooting method coupled with Runge-Kutta iteration technique. Comparison with previously published work is performed and full agreement is obtained. A parametric study illustrating the influence of the magnetic field parameter, thermal radiation parameter, thermal Grashof number, Grashof numbers, Prandtl number, Schmidt number, on the velocity, temperature, and concentration field as well as the local friction coefficient, the local Nusselt number and the Sherwood number is carried out. The results are illustrated graphically and in tabular form to depict special features of the solutions

Effect of Variable Viscosity, Dissipation and Hall Currents on Convective Heat and Mass Transfer Flow Past a Stretching Sheet

We consider the influence dissipation, variable viscosity, Hall current of a magneto-hydrodynamic free-convective flow and heat and mass transfer flow past a stretching sheet in the presence of heat generation/absorption. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The boundary-layer equations governing the fluid flow, heat and mass transfer under consideration have been reduced to a system of non-linear ordinary differential equations by employing a similarity transformation. Using the finite difference scheme, numerical solutions to the transform ordinary differential equations have been obtained and the results are presented graphically. The rare of heat anf mass transfer sre discussed numerically for different variations. Keywords: Radiation absorption, Variable viscosity, Soret effect, MHD, Hall current, Heat and mass transfer

Mathematical models for heat and mass transfer in nanofluid flows.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The behaviour and evolution of most physical phenomena is often best described using mathematical models in the form of systems of ordinary and partial differential equations. A typical example of such phenomena is the flow of a viscous impressible fluid which is described by the Navier-Stokes equations, first derived in the nineteenth century using physical approximations and the principles of mass and momentum conservation. The flow of fluids, and the growth of flow instabilities has been the subject of many investigations because fluids have wide uses in engineering and science, including as carriers of heat, solutes and aggregates. Conventional heat transfer fluids used in engineering applications include air, water and oil. However, each of these fluids has an inherently low thermal conductivity that severely limit heat exchange efficiency. Suspension of nanosized solid particles in traditional heat transfer fluids significantly increases the thermophysical properties of such fluids leading to better heat transfer performance. In this study we present theoretical models to investigate the flow of unsteady nanofluids, heat and mass transport in porous media. Different flow configurations are assumed including an inclined cylinder, a moving surface, a stretching cone and the flow of a polymer nanocomposite modeled as an Oldroyd-B fluid. The nanoparticles assumed include copper, silver and titanium dioxide with water as the base fluid. Most recent boundary-layer nanofluid flow studies assume that the nanoparticle volume fraction can be actively controlled at a bounding solid surface, similar to temperature controls. However, in practice, such controls present significant challenges, and may, in practice, not be possible. In this study the nanoparticle flux at the boundary surface is assumed to be zero. Unsteadiness in fluid flows leads to complex system of partial differential equations. These transport equations are often highly nonlinear and cannot be solved to find exact solutions that describe the evolution of the physical phenomena modeled. A large number of numerical or semi-numerical techniques exist in the literature for finding solutions of nonlinear systems of equations. Some of these methods may, however be subject to certain limitations including slow convergence rates and a small radius of convergence. In recent years, innovative linearization techniques used together with spectral methods have been suggested as suitable tools for solving systems of ordinary and partial differential equations. The techniques which include the spectral local linearization method, spectral relaxation method and the spectral quasiliearization method are used in this study to solve the transport equations, and to determine how the flow characteristics are impacted by changes in certain important physical and fluid parameters. The findings show that these methods give accurate solutions and that the speed of convergence of solutions is comparable with methods such as the Keller-box, Galerkin, and other finite difference or finite element methods. The study gives new insights, and result on the influence of certain events, such as internal heat generation, velocity slip, nanoparticle thermophoresis and random motion on the flow structure, heat and mass transfer rates and the fluid properties in the case of a nanofluid

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

In this paper we analyze 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 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. Similarity variable method is applied to the governing non-linear partial differential equations. The transformed into a set of coupled nonlinear ordinary differential equations 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, 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 in special case of the problem shows an excellent agreement

Transient Magnetohydrodynamic Free Convective Heat and Mass Transfer Flow with Thermophoresis past a Radiate Inclined Permeable Plate in the Presence of Variable Chemical Reaction and Temperature Dependent Viscosity

In the present study, an analysis is carried out to investigate the effects of variable chemical reaction, thermophoresis, temperature-dependent viscosity and thermal radiation on an unsteady MHD free convective heat and mass transfer flow of a viscous, incompressible, electrically conducting fluid past an impulsively started infinite inclined porous plate. The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations, which are solved numerically using a sixth-order Runge-Kutta integration scheme with Nachtsheim-Swigert shooting method. Numerical results for the non-dimensional velocity, temperature and concentration profiles as well as the local skin-friction coefficient, the local Nusselt number and the local Stanton number are presented for different physical parameters. The results show that variable viscosity significantly increases viscous drag and rate of heat transfer. The results also show that higher order chemical reaction induces the concentration of the particles for a destructive reaction and reduces for a generative reaction

On the hydrodynamics and heat convection of an impinging external flow upon a cylinder with transpiration and embedded in a porous medium

This paper extends the existing studies of heat convection by an external flow impinging upon a flat porous insert to that on a circular cylinder inside a porous medium. The surface of the cylinder is subject to constant temperature and can include uniform or non-uniform transpiration. These cylindrical configurations are introduced in the analyses of stagnation point flows in porous media for the first time. The equations governing steady transport of momentum and thermal energy in porous media are reduced to simpler nonlinear differential equations and subsequently solved numerically. This reveals the dimensionless velocity and temperature fields of the stagnation-point flow, as well as the Nusselt number and shear stress on the surface of the cylinder. The results show that transpiration on the surface of the cylinder and Reynolds number of the external flow dominate the fluid dynamics and heat transfer problems. In particular, non-uniform transpiration is shown to significantly affect the thermal and hydrodynamic responses of the system in the circumferential direction. However, the permeability and porosity of the porous medium are found to have relatively smaller influences

Finite element computation of magnetohydrodynamic nanofluid convection from an oscillating inclined plate with radiative flux, heat source and variable temperature effects

The present work describes finite element computations for radiative magnetohydrodynamic convective Newtonian nanofluid flow from an oscillating inclined porous plate with variable temperature. Heat source/sink and buoyancy effects are included in the mathematical model. The problem is formulated by employing Tiwari-Das nanofluid model and two water - based nanofluids with spherical shaped metal nano particles as copper and alumina are considered. The Brinkman and Maxwell-Garnetts models are used for the dynamic viscosity and effective thermal conductivity of the nanofluids respectively. An algebraic flux model, the Rosseland diffusion approximation is adopted to simulate thermal radiative flux effects. The dimensionless, coupled governing partial differential equations are numerically solved via the finite element method with weak variational formulation by imposing initial and boundary conditions with a weighted residual scheme. A grid independence study is also conducted. The finite element solutions are reduced to known previous solutions in some limiting cases of the present investigation and are found to be in good agreement with published work. This investigation is relevant to electromagnetic nanomaterial manufacturing processes operating at high temperatures where radiation heat transfer is significant

Shooting Method to Study Mixed Convection Past a Vertical Heated Plate with Variable Fluid Properties and Internal Heat Generation

Study of Mixed Convection past a vertical heated plate embedded in a sparsely packed porous medium with internal heat generation and variable fluid properties like permeability, porosity and thermal conductivity has been carried out numerically. In this analysis, the governing highly non-linear coupled partial differential equations are transformed into a system of ordinary differential equations with the help of similarity transformations and solved them numerically by using the shooting algorithm with Runge-Kutta-Fehlberg scheme and Newton Raphson method to obtain velocity, temperature and concentration distributions. The features of fluid flow, heat and mass transfer characteristics are analyzed by plotting the graphs and the physical aspects are discussed in detail to interpret the effect of various significant parameters of the problem. The results obtained show that the impact of buoyancy ratio parameter, Prandtl number Pr, Schmidt number Sc and other parameters plays an important role in the fluid flow through porous medium. The obtained results are compared with previously published work o

Free Convection Along a Vertical Wavy Surface in a Nanofluid

The study of this paper is to introduce a boundary layer analysis for the fluid flow and heat transfer characteristics of an incompressible nanofluid along a vertical wavy surface in a nanofluid. The Resulting transformed governing equations are solved numerically by an implicit finite-difference scheme (Keller-Box method). The results are presented for the major parameters including the wave amplitude , buoyancy ratio parameter , Brownian motion parameter , Thermophoresis parameter and Lewis number. A systematic study on the effects of the various parameters of the local frication factor, surface heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) characteristics is carried out. The Obtained results are presented graphicall

Free Convection Along a Vertical Wavy Surface in a Nanofluid

The study of this paper is to introduce a boundary layer analysis for the fluid flow and heat transfer characteristics of an incompressible nanofluid along a vertical wavy surface in a nanofluid. The Resulting transformed governing equations are solved numerically by an implicit finite-difference scheme (Keller-Box method). The results are presented for the major parameters including the wave amplitude , buoyancy ratio parameter , Brownian motion parameter , Thermophoresis parameter and Lewis number. A systematic study on the effects of the various parameters of the local frication factor, surface heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) characteristics is carried out. The Obtained results are presented graphicall