Grashof Number For Heat Transfer Research Articles

Thermal Radiation, Chemical Reaction and Viscous Dissipation Effects on Unsteady MHD Flow of Viscoelastic Fluid Embedded in a Porous Medium

In this paper the effect of unsteady, incompressible, magneto hydrodynamics filled with electrically conducting viscoelastic fluid in an infinite vertical Couette porous channel wall embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel wall. The temperature of the moving channel wall varies periodically and the temperature difference between the two infinite vertical channel walls is high due to thermal radiation. The Eckert number is the ratio of the kinetic energy of the flow to the temperature difference of the channel walls. The solution of the governing equations is obtained using regular perturbation techniques. These techniques are used to transform partial differential equations that are difficult to solve in closed form. These equations are reduced to a set of ordinary differential equations in dimensionless form so can be solved analytically. The effects of physical parameters Viz. Hartmann number, Viscoelastic parameter, Eckert number, Permeability of porous medium, Chemical reaction parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter and Schmidt number on flow parameters Viz., velocity, temperature and concentration has been discussed and shown graphically. The theoretical results have been supported by MATLAB code simulation study. The results show that velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter but reverse effect is observed with temperature, thermal Grashof number, modified Grashof number and permeability of porous medium. Furthermore, The result shows that an increment in both thermal radiation parameter and Eckert number results in decrement of temperature near the moving porous channel wall while it approaches to a zero in the region close to the boundary layer of the stationary channel wall,. An increment in both chemical reaction and Schmidt number results in decreasing concentration. The velocity of fluid increases as Grashof number and modified Grashof number increases.

Effects of Heat and Mass Flux on MHD Free Convection Flow Through a Porous Medium with Radiation and First Order Chemical Reaction

The study of a magneto hydrodynamic (MHD) free convection flow of an incompressible viscous fluid flow past a vertical surface is analyzed by taking into account viscous dissipation under the influence of radiation effect and chemical reaction with constant heat and mass fluxes. The governing partial differential equations have been converted into a set of ordinary differential equations using non dimensional quantities. The perturbation technique has been applied to solve the system of partial differential equations. The velocity, temperature and concentration fields have been studied for the effect of the permeability parameter (α), Grashof number for heat transfer (Gr), Grashof number for mass transfer (Gm), Prandtl number (Pr), magnetic parameter (<i>M</i>), chemical reaction parameter (<i>Kr</i>), Schmidt number (Sc), Eckert number (E), radiation parameter (<i>F</i>) etc. The expressions for the skin-friction, rate of heat transfer and rate of mass transfer are also derived. It is observed that when the radiation parameter increases, the velocity increases near the vertical surface. It is also seen that the concentration decreases with an increase in the chemical reaction parameter (<i>Kr</i>).

The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid

In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.

Numerical Treatment of Casson Fluid Free Convective Flow Past An Infinite Vertical Plate Filled in Magnetic Field in Presence Of Thermal Radiation: A Finite Element Technique

The combined effects of hall current, thermal radiation on an unsteady MHD free convection casson fluid flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical plate are investigated in presence of heat transfer. Numerical solutions of the non-linear coupled governing equations is obtained by finite element technique. The expressions for primary fluid velocity, secondary fluid velocity and fluid temperature, skin friction due to primary and secondary velocity fields and rate of heat transfer coefficient due to temperature at the plate are obtained and discussed with the help of different material parameters like Grashof number for heat transfer, Casson fluid parameter, Magnetic field parameter, hall parameter, thermal radiation parameter, Prandtl number. Finally, it is seen that the numerical results of the present study conform very well to those of previous studies reported in available scientific literatures.

Effects of Mass Transfer on Unsteady Hydromagnetic Convective Flow Past an Infinite Vertical Rotating Porous Plate with Heat Source

The effect of mass transfer on unsteady Hydromagnetic convective flow, of an incompressible electrically conducting fluid, past an infinite vertical rotating porous plate in presence of constant injection and heat source has been investigated. The non-linear partial differential equations governing the flow are solved numerically using the finite differences method. The effect of Hartmann's number, Grashof number for heat transfer, Grashof number for mass transfer, permeability parameter, Schmidt number, Heat source parameter, Prandtl number, Eckert number and rotational parameter on the flow field are presented graphically. A change on the parameters is observed to either increase, decrease or to have no effect on the profiles. The study has some useful information to engineers in the field of oil exploration, geothermal reservoirs, in petroleum and mineral industries, MHD generators, among many other areas.

Analytical Study on Unsteady MHD Free Convection and Mass Transfer Flow Past a Vertical Porous Plate

The unsteady MHD free convection and mass transfer boundary layer flow past a semi-infinite vertical porous plate immersed in a porous medium with heat source is studied. The plate moves with a uniform velocity in the direction of the fluid flow while the free stream velocity is considered to follow the exponentially increasing small perturbation law. The governing equations are solved analytical by using perturbation technique depending on the physical parameters including the Radiation parameter (R), the Magnetic parameter (M), the Prandtl number (Pr), the Grashof number for heat transfer (Gr), the Modified Grashof number for mass transfer (Gc), the Schmidt number (Sc), the soret number (S0), the permeability parameter (K) and the heat source (Q). The influence of these parameters on velocity field, temperature field, concentration field, skin friction, Nusselt number and Sherwood number at the plate are discussed with graphically.

Three-dimensional free convection MHD flow in a vertical channel through a porous medium with heat source and chemical reaction

An analysis is made to study the three-dimensional MHD free convection flow in a vertical channel through a porous medium with heat source and chemical reaction. The flow phenomenon is characterized by magnetic parameters (M), Darcy number (Kp), Reynolds number (Re), source parameter (S), Grashof number for heat transfer (Gr), Grashof number for mass transfer (Gc), Prandtl number (Pr), Schmidt number (Sc), and chemical reaction parameter (Kc). Approximate solutions of the velocity, temperature, and concentration are obtained using a perturbation technique. The effect of these parameters on the velocity, temperature and concentrations distribution is discussed and some interesting results are presented.

Combined Heat and Mass Transfer by Natural Convection from a Semi-Infinite Plate Submitted to a Magnetic Field with Hall Currents

:The present work is concerned with the MHD unsteady free convection flow from a vertical semi-infinite plate of an incompressible electrically conducting fluid. The effects of the viscous dissipation and the Hall currents are analyzed. The unsteady governing equations are reduced to a system of ordinary differential non-dimensional equations and the resulting equation system is solved numerically by using the Network Simulation Method. This numerical method is based on the electrical analogy, where only previous spatial discretization is necessary to obtain a stable and convergent solution with very low computational times. To solve the system of algebraic equations with time as continuous function, an electric circuit simulator is used. Numerical results for velocities, temperature, concentration and current terms are illustrated graphically. We have observed that the Grashof number for heat transfer (Gr) and mass transfer (G*) accelerate the velocity of the flow field at all points. But the increase in velocity of the flow field is more significant in presence of mass transfer. The effect of Schmidt number Sc on mass transfer process is a decrease of concentration distribution as a result of decrease of the concentration boundary layer thickness.

Oscillatory MHD free convective flow through a porous medium with mass transfer, Soret effect and chemical reaction

An attempt is made to investigate the problem of an oscillatory MHD free convective flow through a porous medium with mass transfer, Soret effect and chemical reaction when the temperature as well as concentration at the plate varies periodically with time about a steady mean. Analytical solutions to the coupled non-linear equations governing the flow and heat and mass transfer are obtained by using regular perturbation technique. The influence of the different parameters entering in to the problem viz. the Hartmann number M, the Grashof number for heat transfer G r , the Grashof number for mass transfer G m , Soret number S 0 , the plate velocity U , chemical reaction C h etc. on temperature distribution, species concentration, velocity distribution, skin-friction and the rates of heat and mass transfer at the plate are discussed graphically.

Simultaneous heat and mass transfer on oscillatory free convection boundary layer flow

The problem of simultaneous heat and mass transfer in two-dimensional free convection from a semi-infinite vertical flat plate is investigated. An integral method is used to find a solution for zero wall velocity and for a mass transfer velocity at the wall with small-amplitude oscillatory wall temperature. Low- and high-frequency solutions are developed separately and are discussed graphically with the effects of the parameters Gr (the Grashof number for heat transfer), Gc (the Grashof number for mass transfer) and Sc (the Schmidt number) for Pr = 0–71 representing aid at 20°C.