scholarly journals Skin-friction for unsteady free convection MHD flow between two heated vertical parallel plates

2006 ◽  
Vol 33 (4) ◽  
pp. 259-280 ◽  
Author(s):  
Gopal Singha ◽  
P.N. Deka
Keyword(s):  
Free Convection ◽  
Skin Friction ◽  
Mhd Flow ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Convection Flow ◽  
Fluid Temperature ◽  
Parallel Plates ◽  
Electrically Conducting ◽  
Induced Field

Unsteady viscous incompressible free convection flow of an electrically conducting fluid between two heated vertical parallel plates is considered in the presence of a uniform magnetic field applied transversely to the flow. The induce field along the lines of motion varies transversely to the flow and the fluid temperature changing with time. An analytical solution for velocity, induced field and the temperature distributions are obtained for small and large magnetic Reynolds numbers. The skin-friction at the two plates is obtained. Velocity distribution, induced field and skin-friction are plotted against the distance from the plates. It has been observed that with the increase in Rm, the magnetic Reynolds number, at constant M, the Hartmann number, leads to an increase in the skin-friction gradually. But with the increase in M, at constant Rm, the skin-friction decreases.

scholarly journals Unsteady Free Convection Flow between Two Vertical Parallel Plates with Newtonian Heating

MATEMATIKA ◽  
2019 ◽  
Vol 35 (2) ◽  
pp. 117-127
Author(s):  
Fasihah Zulkiflee ◽  
Ahmad Qushairi Mohamad ◽  
Sharidan Shafie ◽  
Arshad Khan
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Skin Friction ◽  
Approximate Solutions ◽  
Convection Flow ◽  
Parallel Plates ◽  
Newtonian Heating ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
Incompressible Viscous Fluids

Free convection flow in a boundary layer region is a motion that results from the interaction of gravity with density differences within a fluid. These differences occur due to temperature or concentration gradients or due to their composition. Studies pertaining free convection flows of incompressible viscous fluids have received much attention in recent years both theoretically (exact or approximate solutions) and experimentally. The situation where the heat be transported to the convective fluid via a bounding surface having finite heat capacity is known as Newtonian heating (or conjugate convective flows). In this paper, the unsteady free convection flow of an incompressible viscous fluid between two parallel plates with Newtonian heating is studied. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutionsfor velocity and temperature are obtained using the Laplace transform technique. The corresponding expressions for skin friction and Nusselt number are also calculated. The graphical results are displayed to illustrate the influence of various embedded parameters such as Newtonian heating parameter and Grashof number. The results show that the effect of Newtonian heating parameter increases the Nusselt number but reduces the skin friction.

scholarly journals Effect of Variable Viscosity on Natural Convection Flow Between Vertical Parallel Plates in the Presence of Heat Generation/Absorption

2019 ◽  
pp. 1-15
Author(s):  
Tada M. Kabir ◽  
Abiodun O. Ajibade
Keyword(s):  
Natural Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Variable Viscosity ◽  
Nonlinear Differential Equations ◽  
Convection Flow ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Parallel Plates ◽  
Natural Convection Flow

The present article was aimed at investigating the effects of variable viscosity on natural convection flow between vertical parallel plates in the presence of heat generation/absorption. The nonlinear differential equations governing the flow were solved using Homotopy perturbation method. The impacts of the several governing parameters on the velocity and temperature profiles are presented graphically and values of skin friction, rate of heat transfer, mass flux and mean temperature for various values of physical parameters are presented through tables. In the course of computation, it was revealed that viscosity  ontributes to decrease velocity and hence reduced resistance to flow. It was also discovered that as the heat generation increases, fluid temperature and velocity increase, while it decrease with the increase in heat absorption. Finally, it was concluded that the skin friction on both plates increase as viscosity increases.

scholarly journals Radiation effect on free convection flow between oscillating parallel plates with mass diffusion

2021 ◽  
Vol 17 (1) ◽  
pp. 1-6
Author(s):  
Fasihah Zulkiflee ◽  
Sharidan Shafie ◽  
Ahmad Qushairi Mohamad
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Skin Friction ◽  
Schmidt Number ◽  
Radiation Effect ◽  
Mass Diffusion ◽  
Convection Flow ◽  
Radiation Parameter ◽  
Parallel Plates ◽  
Transform Method

This study investigates radiation effect on unsteady oscillatory free convection between two parallel plates with mass diffusion. Appropriate non-dimensional variables are used to reduce the dimensional governing equations to dimensionless equation along with imposed initial and boundary conditions. The solutions for velocity, temperature, and concentration profiles are obtained by using Laplace transform method. To illustrate the behavior of the fluid flow, graphical results are presented with influenced of Schmidt number, Prandtl number, radiation parameter, oscillating parameter, Grashof, and mass Grashof number. The corresponding expressions for skin friction, Nusselt number, and Sherwood number are also calculated. It is observed that increasing radiation parameter, Prandtl, and Schmidt number will increase the Nusselt number but the skin friction will be reduced.

Free convection flow with chemical reaction effect between oscillating parallel plates

2021 ◽  
Vol 2 (2) ◽  
pp. 52-59
Author(s):  
F. Zulkiflee ◽  
S. Shafie ◽  
A. Ali ◽  
A.Q. Mohamad
Keyword(s):  
Free Convection ◽  
Prandtl Number ◽  
Skin Friction ◽  
Chemical Reaction ◽  
Schmidt Number ◽  
Convection Flow ◽  
Parallel Plates ◽  
Free Convection Flow ◽  
Transform Method ◽  
Grashof Number

This research purpose is to investigate the exact solutions for unsteady free convection flow between oscillating parallel plates with mass diffusion and chemical reaction. The governing equations are modelled and reduced using non-dimensional variables. The method used is Laplace transform method. Solutions for velocity, temperature, and concentration fields as well as skin friction, Nusselt and Sherwood number are obtained. For physical understanding, analytical results for velocity, temperature and concentration profile are plotted graphically with respect to the Schmidt number, Prandtl number, oscillating parameter, Grashof number, mass Grashof number and chemical reaction parameter. Increasing Prandtl number and Schmidt number decreases the concentration, velocity, temperature, and skin friction but increases the Sherwood and Nusselt numbers.

scholarly journals Magnetohydrodynamic Fluctuating Free Convection Flow of Second-Grade Fluid Flow in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Farhad Ali ◽  
Momin Khan ◽  
Madeha Gohar
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Fluid Motion ◽  
Second Grade ◽  
Convection Flow ◽  
Stream Velocity ◽  
Parallel Plates ◽  
Free Convection Flow ◽  
Viscoelastic Parameter ◽  
Electrically Conducting

The article’s objective is to study the magnetohydrodynamic fluctuating free convection flow of incompressible electrically conducting viscoelastic fluid in a porous medium in the presence of a pressure gradient. The flow is between two parallel plates; the lower plate is at rest, while the upper plate moves with a free stream velocity U t . A uniform magnetic field of strength B0 is applied transversely to the fluid motion. The dimensional governing equations and physical initial and boundary conditions are nondimensionalized by inserting appropriate dimensionless variables. Furthermore, Lighthill’s method is used to obtain exact analytical solutions for the velocity, temperature, and concentration distributions. Finally, the influences of inserted parameters are studied through plots and discussed physically. The numerical results are calculated and presented in tabular form for skin friction. It is worth mentioning that when the viscoelastic parameter α 1 tends to zero, the obtained general solution is reduced to Newtonian fluid, which shows the validity and correctness of our obtained exact solutions.

Free convection effects on steady MHD flow past a vertical porous plate

1974 ◽  
Vol 66 (3) ◽  
pp. 541-551 ◽  
Author(s):  
V. M. Soundalgekar
Keyword(s):  
Magnetic Field ◽  
Free Convection ◽  
Porous Plate ◽  
Mhd Flow ◽  
Approximate Solutions ◽  
Magnetic Reynolds Number ◽  
Plate Temperature ◽  
Electrically Conducting ◽  
Vertical Porous Plate ◽  
The Difference

An analysis of two-dimensional steady flow of an incompressible, viscous, electrically conducting fluid past an infinite vertical porous plate is carried out under the following assumptions: (i) that the suction velocity normal to the plate is constant, (ii) that the plate temperature is constant, (iii) that the difference between the temperatures of the plate and the free stream is moderately large, causing free convection currents, (iv) that the transversely applied magnetic field and magnetic Reynolds number are very small and hence the induced magnetic field is negligible.Approximate solutions to the coupled nonlinear equations governing the steady velocity and temperature are derived. They are shown graphically. During the course of discussion, the effects of positive and negative G (the Grashof number: G > 0 implies cooling of the plate, G < 0 heating of the plate), of P (the Prandtl number), of positive and negative E (the Eckert number) and of M (the magnetic field parameter) are presented quantitatively.

scholarly journals Effect of slip condition on viscoelastic mhd oscillatory forced convection flow in a vertical channel with heat radiation

2013 ◽  
Vol 18 (4) ◽  
pp. 1237-1248 ◽  
Author(s):  
K.D. Singh
Keyword(s):  
Magnetic Field ◽  
Oscillatory Flow ◽  
Slip Flow ◽  
Vertical Channel ◽  
Magnetic Reynolds Number ◽  
Slip Condition ◽  
Heat Radiation ◽  
Convection Flow ◽  
Parallel Plates ◽  
Electrically Conducting

Abstract In this paper an oscillatory flow of a viscoelastic, incompressible and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel plates is discussed. One of these plates is subjected to a slip-flow condition and the other to a no-slip condition. The pressure gradient in the channel oscillates with time. A magnetic field of uniform strength is applied in the direction perpendicular to the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature difference of the two plates is also assumed high enough to induce heat transfer due to radiation. A closed form analytical solution to the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters entering into the problem. A number of particular cases have been shown by dotted curves in the figures. During the analysis it is found that the physical and the mathematical formulations of the problems by Makinde and Mhone (2005), Mehmood and Ali (2007), Kumar et al. (2010) and Choudhury and Das (2012) are not correct. The correct solutions to all these important oscillatory flow problems are deduced.

scholarly journals MASS TRANSFER OF FREE CONVECTION FLOW BETWEEN TWO PARALLEL OSCILLATING PLATES.

2019 ◽  
Vol 1 (2) ◽  
pp. 118-121
Author(s):  
Fasihah Zulkiflee ◽  
Sharidan Shafie ◽  
Ahmad Qushairi Mohamad
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Skin Friction ◽  
Schmidt Number ◽  
Convection Flow ◽  
Parallel Plates ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform

This paper investigated unsteady free convection flow between two parallel plates with mass diffusion. One of the plate are considered oscillating. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions. The exact solution for velocity, temperature and concentration profiles are obtained using the Laplace Transform technique. The graphical results of the solutions are presented to illustrate the behavior of the fluid flow with the influenced of Schmidt number, Prandtl number, oscillating parameter, Grashof and mass Grashof number. The corresponding expressions for skin friction, Nusselt number and Sherwood number are also calculated. It is observed that increasing Prandtl and Schmidt number will increased the Nusselt number but decreased the skin friction.

scholarly journals Thermo-diffusion effects on the magnetohydrodynamic natural convection flow of a chemically reactive Brinkman type nanofluid in a porous medium

2019 ◽  
Vol 51 (2) ◽  
pp. 168-179 ◽  
Author(s):  
G. S. Seth ◽  
R. Kumar ◽  
R. Tripathi
Keyword(s):  
Natural Convection ◽  
Skin Friction ◽  
Fluid Velocity ◽  
Surface Concentration ◽  
Convection Flow ◽  
Fluid Temperature ◽  
Species Concentration ◽  
Electrically Conducting ◽  
Laplace Transform Technique ◽  
Mass Transfers

An investigation on the unsteady MHD natural convection heat and mass transfer flow of an electrically conducting, viscous, incompressible, chemically reactive and heat-absorbing nanofluid of Brinkman type past an exponentially accelerated moving vertical plate with ramped wall temperature and ramped surface concentration is carried out. Governing equations are non-dimensionalized and Laplace Transform Technique is used to find the exact solutions for fluid velocity, fluid temperature and species concentration. The quantities of physical interest, i.e. skin friction, rates of heat and mass transfers at the plate are also calculated. Numerical results for the velocity, temperature and species concentration of the fluid are demonstrated with the help of graphs whereas those of skin friction, rate of heat and mass transfers at the plate are displayed in tables for various flow parameters.

scholarly journals Effect of Heat Generation (Absorption) on Unsteady MHD flow over a Truncated Cone Embedded in a Stable Thermally Stratified Environment

2021 ◽  
Vol 8 (S1-Feb) ◽  
pp. 87-96
Author(s):  
Ashwini G
Keyword(s):  
Skin Friction ◽  
Heat Generation ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Stratified Medium ◽  
Convection Flow ◽  
Transfer Coefficients ◽  
Electrically Conducting ◽  
Truncated Cone

This paper examines the effect of heat generation (absorption) on unsteady free convection flow of an incompressible electrically conducting fluid over a truncated cone embedded in a thermally stratified medium in the presence of a transverse magnetic field. The governing nonlinear partial differential equations have been solved numerically, using an efficient implicit finite difference scheme along with quasilinearization technique. The numerical results for skin-friction coefficients and velocity components in x- and y- directions, Nusselt number and temperature profiles are obtained and analyzed for different values of governing parameters. It is observed that, heat generation increases skin friction and decreases heat transfer coefficients, whereas opposite trend is observed during heat absorption. Also it is found that heat generation has a significant effect on temperature profile.

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