scholarly journals Thermal Diffusion and Diffusion Thermo Effects on the Viscous Fluid Flow with Heat and Mass Transfer through Porous Medium over a Shrinking Sheet

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Nabil Eldabe ◽  
Mahmoud Abu Zeid
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Shear Stress ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Transfer Parameter ◽  
Mass Transfer Parameter ◽  
Permeability Parameter

The motion of the viscous, incompressible fluid through a porous medium with heat and mass transfer over a shrinking sheet is investigated. The cross-diffusion effect between temperature and concentration is considered. This phenomenon is modulated mathematically by a set of partial differential equations which govern the continuity, momentum, heat, and mass. These equations are transformed to a set of ordinary differential equations by using similarity solutions. The analytical solutions of these equations are obtained. The velocity, temperature, and concentration of the fluid as well as the heat and mass transfer with shear stress at the sheet are obtained as a function of the physical parameters of the problem. The effects of Prandtl number, mass transfer parameter, the wall shrinking parameter, the permeability parameter, and Dufour and Soret numbers on temperature and concentration are studied. Also, the effects of mass transfer parameter, permeability parameter, and shrinking strength on the velocity and shear stress are discussed. These effects are illustrated graphically through a set of figures.

scholarly journals The Inclined Factors of Magnetic Field and Shrinking Sheet in Casson Fluid Flow, Heat and Mass Transfer

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 373
Author(s):  
Shahanaz Parvin ◽  
Siti Suzilliana Putri Mohamed Isa ◽  
Norihan Md Arifin ◽  
Fadzilah Md Ali
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Fluid Model ◽  
Casson Fluid ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Flow Heat

The development of the mathematical modeling of Casson fluid flow and heat and mass transfer is presented in this paper. The model is subjected to the following physical parameters: shrinking parameter, mixed convection, concentration buoyancy ratio parameter, Soret number, and Dufour number. This model is also subjected to the inclined magnetic field and shrinking sheet at a certain angle projected from the y- and x-axes, respectively. The MATLAB bvp4c program is the main mathematical program that was used to obtain the final numerical solutions for the reduced ordinary differential equations (ODEs). These ODEs originate from the governing partial differential equations (PDEs), where the transformation can be achieved by applying similarity transformations. The MATLAB bvp4c program was also implemented to develop stability analysis, where this calculation was executed to recognize the most stable numerical solution. Numerical graphics were made for the skin friction coefficient, local Nusselt number, local Sherwood number, velocity profile, temperature profile, and concentration profile for certain values of the physical parameters. It is found that all the governed parameters affected the variations of the Casson fluid flow, heat transfer, mass transfer, and the profiles of velocity, temperature, and concentration. In addition, a stable solution can be applied to predict the impact of physical parameters on the actual fluid model by using a mathematical fluid model.

scholarly journals Numerical Investigation on MHD Marangoni Convective Flow of Nanofluid through a Porous Medium with Heat and Mass Transfer Characteristics

2018 ◽  
Vol 7 (4.10) ◽  
pp. 256
Author(s):  
K. Venkateswara Raju ◽  
P. Durga Prasad ◽  
M. C. Raju` ◽  
R. Sivaraj
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Convective Flow ◽  
Mass Transfer Rate ◽  
Physical Parameters ◽  
Transfer Characteristics ◽  
Similarity Transformations ◽  
Runge Kutta Method

The present study investigates on a steady two-dimensional Marangoni convective flow of nanofluid through a porous medium with heat and mass transfer characteristics. The proposed mathematical model has a tendency to characterize the radiation and chemical reaction effects. The governing equations in the form of partial differential equations have been converted into ordinary differential equations through similarity transformations, which have been solved by using Runge-Kutta method via shooting technique. The characteristics of velocity, temperature and concentration boundary layers are studied for different physical parameters. The local Nusselt and Sherwood numbers are estimated and discussed for aforesaid physical parameters. It is to be noted that the Marangoni ratio parameter is improves the rate of heat transfer and decreases the mass transfer rate.   

scholarly journals Electromagnetic steady motion of Casson fluid with heat and mass transfer through porous medium past a shrinking surface

2019 ◽  
pp. 416-416
Author(s):  
Nabil El-Dabe ◽  
Mohamed Abou-Zeid ◽  
Omar El-Kalaawy ◽  
Salah Moawad ◽  
Ola Ahmed
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Fluid Velocity ◽  
Steady Motion ◽  
Physical Parameters ◽  
Physical Situation ◽  
Fluid Temperature ◽  
Electric Parameter

The motion of non-Newtonian fluid with heat and mass transfer through porous medium past a shrinking plate is discussed. The fluid obeys Casion model, heat generation, viscous dissipation, thermal diffusion and chemical reaction are taken in our considered. The motion is modulated mathematically by a system of non liner partial differential equations which describe the continuity, momentum, heat and mass equations. These system of non linear equations are transformed into ordinary differential equations by using a suitable transformations. These equations are solved numerically by using Mathematica package. The numerical distributions of the velocity, temperature and concentration are obtained as a functions of the physical parameters of the problem. Moreover the effects of these parameters on these solutions are discussed numerically and illustrated graphically through some figures. It is clear that these parameters play an important role to control the velocity, temperature and concentration of the fluid motion. It?s found that the fluid velocity deceases with the increasing of electric parameter while it increases as the magnetic hartman parameter increases, these results is good agreement with the physical situation. Also, the fluid temperature decreases and increases as the Prandtl number and Eckert number increases respectively. At least the fluid concentration decreases with both of soret and schimdt numbers.

scholarly journals Peristaltic Motion of Non-Newtonian Fluid with Heat and Mass Transfer through a Porous Medium in Channel under Uniform Magnetic Field

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Nabil T. M. Eldabe ◽  
Bothaina M. Agoor ◽  
Heba Alame
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Newtonian Fluid ◽  
Pressure Rise ◽  
Perturbation Series ◽  
Peristaltic Motion ◽  
Method Of Solution ◽  
Permeability Parameter

This paper is devoted to the study of the peristaltic motion of non-Newtonian fluid with heat and mass transfer through a porous medium in the channel under the effect of magnetic field. A modified Casson non-Newtonian constitutive model is employed for the transport fluid. A perturbation series’ method of solution of the stream function is discussed. The effects of various parameters of interest such as the magnetic parameter, Casson parameter, and permeability parameter on the velocity, pressure rise, temperature, and concentration are discussed and illustrated graphically through a set of figures.

scholarly journals Heat and Mass Transfer on MHD Flow of a Viscoelastic Fluid through Porous Media over a Shrinking Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
D. Bhukta ◽  
G. C. Dash ◽  
S. R. Mishra
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Temperature Field ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Viscoelastic Fluid ◽  
Power Law ◽  
Nonlinear Partial Differential Equations ◽  
Shrinking Sheet ◽  
Mass Transfer Effect

An attempt has been made to study the heat and mass transfer effect in a boundary layer flow through porous medium of an electrically conducting viscoelastic fluid over a shrinking sheet subject to transverse magnetic field in the presence of heat source. Effects of radiation, viscous dissipation, and uniform heat sink on the heat transfer have been considered. The method of solution involves similarity transformation. The coupled nonlinear partial differential equations representing momentum, concentration, and nonhomogenous heat equation are reduced into a set of nonlinear ordinary differential equations. The transformed equations are solved by applying Kummer’s function. The exact solution of temperature field is obtained for power-law surface temperature (PST) as well as power-law heat flux (PHF) boundary condition. The interaction of magnetic field is proved to be counterproductive in enhancing velocity and concentration distribution, whereas presence of porous matrix reduces the temperature field at all points.

Heat and Mass Transfer of a MHD Flows of An Oldroyd 8-Constant Nano-Fluid Through a Non-Darcy Porous Medium

2017 ◽  
Vol 14 (1) ◽  
pp. 321-329
Author(s):  
Abeer A Shaaban
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat And Mass Transfer ◽  
Induced Magnetic Field ◽  
Linear Ordinary Differential Equations ◽  
Nano Fluid ◽  
Non Linear

Explicit finite-difference method was used to obtain the solution of the system of the non-linear ordinary differential equations which transform from the non-linear partial differential equations. These equations describe the steady magneto-hydrodynamic flow of an oldroyd 8-constant non-Newtonian nano-fluid through a non-Darcy porous medium with heat and mass transfer. The induced magnetic field was taken into our consideration. The numerical formula of the velocity, the induced magnetic field, the temperature, the concentration, and the nanoparticle concentration distributions of the problem were illustrated graphically. The effect of the material parameters (α1 α2), Darcy number Da, Forchheimer number Fs, Magnetic Pressure number RH, Magnetic Prandtl number Pm, Prandtl number Pr, Radiation parameter Rn, Dufour number Nd, Brownian motion parameter Nb, Thermophoresis parameter Nt, Heat generation Q, Lewis number Le, and Sort number Ld on those formula were discussed specially in the case of pure Coutte flow (U0 = 1, d <inline-formula> <mml:math display="block"> <mml:mrow> <mml:mover accent="true"> <mml:mi>P</mml:mi> <mml:mo stretchy="true">^</mml:mo> </mml:mover> </mml:mrow> </mml:math> </inline-formula> /dx = 0). Also, an estimation of the global error for the numerical values of the solutions is calculated by using Zadunaisky technique.

Effect of Melting on Mixed Convection Heat and Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
R. R. Kairi ◽  
P. V. S. N. Murthy
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Newtonian Fluid ◽  
Power Law ◽  
Soret Effect ◽  
Physical Parameters ◽  
Convection Heat ◽  
Wide Range

In this paper, we investigate the influence of melting on mixed convection heat and mass transfer from vertical flat plate in a non-Newtonian fluid-saturated non-Darcy porous medium including the prominent Soret effect. The wall and the ambient medium are maintained at constant but different levels of temperature and concentration such that the heat and mass transfer occurs from the wall to the medium. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. A similarity solution for the transformed governing equations is obtained. The numerical computation is carried out for various values of the nondimensional physical parameters. The variation of temperature, concentration, and heat and mass transfer coefficients with the power law index, mixed convection parameter, inertia parameter, melting parameter, Soret number, buoyancy ratio, and Lewis number is discussed for a wide range of values of these parameters.

Influence of viscous dissipation and thermo-diffusion on double diffusive convection over a vertical cone in a non-Darcy porous medium saturated by a non-Newtonian fluid with variable heat and mass fluxes

2018 ◽  
Vol 7 (1) ◽  
pp. 65-72
Author(s):  
Rishi Raj Kairi ◽  
Ch. RamReddy ◽  
Santanu Raut
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Newtonian Fluid ◽  
Power Law ◽  
Vertical Cone ◽  
Variable Heat ◽  
Double Diffusive

Abstract This paper emphasizes the thermo-diffusion and viscous dissipation effects on double diffusive natural convection heat and mass transfer characteristics of non-Newtonian power-law fluid over a vertical cone embedded in a non-Darcy porous medium with variable heat and mass flux conditions. The Ostwald–de Waele power-law model is employed to describe the behavior of non-Newtonian fluid. Local non-similarity procedure is applied to transform the set of non-dimensional partial differential equations into set of ordinary differential equations and then the resulting system of equations are solved numerically by Runge-Kutta fourth order method together with a shooting technique. The influence of pertinent parameters on temperature and concentration, heat and mass transfer rates are analyzed in opposing and aiding buoyancy cases through graphical representation and explored in detail.

scholarly journals Exact Solutions of Heat and Mass Transfer with MHD Flow in a Porous Medium under Time Dependent Shear Stress and Temperature

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Arshad Khan ◽  
Ilyas Khan ◽  
Farhad Ali ◽  
Asma Khalid ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Shear Stress ◽  
Heat And Mass Transfer ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Convection Flow ◽  
Closed Form Solutions ◽  
Special Cases ◽  
Laplace Transform Technique

This paper aims to study the influence of thermal radiation on unsteady magnetohyrdodynamic (MHD) natural convection flow of an optically thick fluid over a vertical plate embedded in a porous medium with arbitrary shear stress. Combined phenomenon of heat and mass transfer is considered. Closed-form solutions in general form are obtained by using the Laplace transform technique. They are expressed in terms of exponential and complementary error functions. Velocity is expressed as a sum of thermal and mechanical parts. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Analytical results for the pertinent flow parameters are drawn graphically and discussed in detail. It is found that the velocity profiles of fluid decrease with increasing shear stress. The magnetic parameter develops shear resistance which reduces the fluid motion whereas the inverse permeability parameter increases the fluid flow.

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