Radiation effect on free convection laminar flow along a vertical flat plate with streamwise sinusoidal surface temperature (original) (raw)
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RADIATION EFFECT ON NATURAL CONVECTION LAMINAR FLOW ALONG A VERTICAL WAVY SURFACE
The effect of thermal radiation on a steady two-dimensional natural convection laminar flow of viscous incompressible optically thick fluid along a vertical wavy surface has been investigated. Using the appropriate variables; the basic equations are transformed into the local non-similarity boundary layer form and then solved employing the Keller-box scheme of finite difference method. Numerical results are presented by streamline, isotherms, velocity and temperature distribution of the fluid as well as the local heat transfer rate in terms of local Nusselt number and average rate of heat transfer for a wide range of Planck number R d and the surface heating parameter θ w . The present numerical result shows excellent agreement with the published results when the effect of thermal radiation was passed over.
Radiation effect on mixed convection laminar flow along a vertical wavy surface
The effect of thermal radiation on a steady two-dimensional mixed convection laminar flow of viscous incompressible optically thick fluid along a vertical wavy surface has been investigated. We consider the boundary layer regime when the Reynolds number Re is large. Using the appropriate variables; the basic equations are transformed to convenient form, and then solved numerically employing two efficient method, namely (i) Keller box method (KBM) and (ii) straightforward finite difference (SFFD) method. Numerical results are presented by streamline and isotherms, velocity and temperature distribution of the fluid as well as the, shearing stress, local, average and total heat transfer rate in terms of the skin-friction coefficient, local, average and total Nusselt number respectively for a wide range of the radiation–conduction parameter or Planck number Rd , surface heating parameter θw, amplitude of the wavy surface α and the Richardson number Ri(= Gr/Re2).
International Journal of Heat and Mass Transfer, 2015
Heat transfer by simultaneous radiation and natural convection through an optically thick fluid over a heated vertical plate has been studied with first-order momentum and thermal non-continuum boundary conditions. The radiant heat flux was treated using the Rosseland diffusion approximation. By solving the local non-similarity two-equation model, numerical solutions were obtained to examine the slip effects on the interaction between radiation and natural convection for a range of rarefied conditions and radiation effects. Results including slip velocity, temperature jump, skin friction, and heat transfer rate are presented graphically and discussed. In addition, an integral correlation is presented for the average Nusselt number as a function of the non-continuum conditions, radiation-conduction parameter, and flow properties.
Effect of thermal radiation on free convection boundary layer flow over a vertical wavy cone
IOSR Journal of Applied Physics, 2013
Effect of thermal radiation on a steady two-dimensional free convection laminar boundary layer flow of a viscous incompressible optically thick fluid over a vertical wavy cone has been investigated. Using appropriate transformations, the basic governing equations are transformed into non-dimensional boundarylayer equations. These equations are then solved numerically by using Mathematica technique. The effect of the radiation parameter on velocity, temperature, skin friction and local Nusselt number has been discussed with graphical representation.
Radiation Effects on Unsteady Free Convection Flow Past a Vertical Plate with Newtonian Heating
2012
A numerical solution of the unsteady radiative, free convection flow with heat and mass transfer of an incompressible viscoelastic fluid past an impulsively started vertical plate is presented here. The Walters-B liquid model is employed to simulate medical cream manufacturing, chemical engineering, and medical biotechnological applications. This rheological model introduces a supplementary terms into the momentum conservation equation. The dimensionless unsteady, coupled and non-linear partial differential conservation equations for the boundary layer regime are solved by an efficient and accurate finite difference scheme of the Crank-Nicolson type. The velocity ,temperature and concentration fields have been studied for the effect of Prandtl number (Pr), Viscoelasticity parameter (Γ), Schmidt number (Sc), Buoyancy ratio parameter (N), Radiation parameter (F). The local skin-friction., Nusselt number and Sherwood number are also presented and analysed graphically. It is also observed that, when the viscoelasticity parameter (Γ) increases, the velocity increases close to the plate surface. An increase in Schmidt number, observed significantly to decrease both velocity and concentration. The present results are compared with available results in literature and are found to be in good agreement.
Natural convection flow with surface radiation along a vertical wavy surface
Accepted in Numerical Heat Transfer: Part A
In this study, natural convection boundary layer flow of thermally radiating fluid along a heated vertical wavy surface is analyzed. Here the radiative component of heat flux emulates the surface temperature. Governing equations are reduced to dimensionless form subject to the appropriate transformation. Resulting dimensionless equations are transformed to a set of parabolic partial differential equations by using primitive variable formulation, which are then integrated numerically via iterative finite difference scheme. Emphasis has been given to low Prandtl number fluid. The numerical results obtained for the physical parameter, such as, surface radiation parameter, R, and radiative length parameter, ξ, are discussed in terms of local skin friction and Nusselt number coefficients. Comprehensive interpretation of velocity distribution is also given in the form of streamlines."
Radiation effect on natural convection boundary layer flow over a vertical wavy frustum of a cone
The effect of thermal radiation on a steady two-dimensional natural convection laminar boundary layer flow of a viscous incompressible optically thick fluid over a vertical wavy frustum of a cone has been investigated. The boundary layer regime when the Grashof number Gr is large is considered. Using appropriate transformations, the basic governing equations are transformed into a dimensionless form and then solved numerically employing two efficient methods, namely: (a) implicit finite difference method together with Keller-box scheme and (b) direct numerical scheme. Numerical results are presented by streamline, isotherms, velocity and temperature distribution of the fluid, as well as the local shearing stress in terms of the local skin-friction coefficient, the local heat transfer rate in terms of local Nusselt number, and the average rate of heat transfer for a wide range of the radiation–conduction parameter or Planck number Rd and the surface heating parameter θw.
Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface
PLoS ONE, 2014
This article addresses the boundary layer flow and heat transfer in third grade fluid over an unsteady permeable stretching sheet. The transverse magnetic and electric fields in the momentum equations are considered. Thermal boundary layer equation includes both viscous and Ohmic dissipations. The related nonlinear partial differential system is reduced first into ordinary differential system and then solved for the series solutions. The dependence of velocity and temperature profiles on the various parameters are shown and discussed by sketching graphs. Expressions of skin friction coefficient and local Nusselt number are calculated and analyzed. Numerical values of skin friction coefficient and Nusselt number are tabulated and examined. It is observed that both velocity and temperature increases in presence of electric field. Further the temperature is increased due to the radiation parameter. Thermal boundary layer thickness increases by increasing Eckert number.
Effect of radiation and mass transfer on the transient free convection flow of a dissipative past semi-infinite vertical plate with uniform heat and mass flux is analyzed, by taking into account the effect of viscous dissipation. This type of problems finds application in many technological and engineering fields such as plasma studies, petroleum industries, MHD energy generators, cooling of nuclear reactors, the boundary layer control in aerodynamics, crystal growth and furnace engineering. The Rosseland approximation is used to describe the radiative heat transfer in the limit of the optically thick fluid. The non-linear, coupled equations are solved using an implicit finite difference scheme of Crank-Nicolson type. Transient temperature, concentration and velocity profiles, local and average skinfriction coefficient, Nusselt number and Sherwood number are presented graphically and discussed. It is observed that, when the radiation parameter increases the velocity and temperature decrease accompanied by simultaneous reduction in both momentum and thermal boundary layers.