scholarly journals Effect of Thermal Radiation, Chemical Reaction and Viscous Dissipation on MHD Flow

2018 ◽  
Vol 23 (3) ◽  
pp. 787-801
Author(s):  
B. Zigta
Keyword(s):  
Kinetic Energy ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Energy Equation ◽  
Eckert Number ◽  
Radiation Chemical ◽  
Thermal Buoyancy ◽  
Molecular Diffusivity

Abstract This study examines the effect of thermal radiation, chemical reaction and viscous dissipation on a magnetohydro- dynamic flow in between a pair of infinite vertical Couette channel walls. The momentum equation accounts the effects of both the thermal and the concentration buoyancy forces of the flow. The energy equation addresses the effects of the thermal radiation and viscous dissipation of the flow. Also, the concentration equation includes the effects of molecular diffusivity and chemical reaction parameters. The gray colored fluid considered in this study is a non-scattering medium and has the property of absorbing and emitting radiation. The Roseland approximation is used to describe the radiative heat flux in the energy equation. The velocity of flow transforms kinetic energy into heat energy. The increment of the velocity due to internal energy results in heating up of the fluid and consequently it causes increment of the thermal buoyancy force. The Eckert number being the ratio of the kinetic energy of the flow to the temperature difference of the channel walls is directly proportional to the thermal energy dissipation. It can be observed that increasing the Eckert number results in increasing velocity. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall is high enough due to the presence of thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. These techniques help to convert partial differential equations to a set of ordinary differential equations in dimensionless form and thus they are solved analytically. The following results are obtained: from the simulation study it is observed that the flow pattern of the fluid is affected due to the influence of the thermal radiation, the chemical reaction and viscous dissipation. The increment in the Hartmann number results in the increment of the Lorentz force but a decrement in velocity of the flow. An increment in the radiative parameter results in a decrement in temperature. An increment in the Prandtl number results in a decrement in thermal diffusivity. An increment in both the chemical reaction parameter and molecular diffusivity results in a decrement in concentration.

scholarly journals Thermal Radiation, Chemical Reaction, Viscous and Joule Dissipation Effects on MHD Flow Embedded in a Porous Medium

2019 ◽  
Vol 24 (3) ◽  
pp. 725-737
Author(s):  
B. Zigta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Mhd Flow ◽  
Magnetic Reynolds Number ◽  
Convection Flow ◽  
Joule Dissipation ◽  
Radiation Chemical

Abstract An analysis is presented to study the effects of thermal radiation, chemical reaction, viscous and Joule dissipation on MHD free convection flow between a pair of infinite vertical Couette channel walls embedded in a porous medium. The fluid flows by a strong transverse magnetic field imposed perpendicularly to the channel wall on the assumption of a small magnetic Reynolds number. The governing non linear partial differential equations are transformed in to ordinary differential equations and are solved analytically. The effect of various parameters viz., Eckert number, electric conductivity, dynamic viscosity and strength of magnetic field on temperature profile has been discussed and presented graphically.

EFFECT OF CHEMICAL REACTION AND THERMAL RADIATION ON AXISYMMETRIC MHD FLOW OF JEFFREY NANOFLUID THROUGH A CILIATED CHANNEL FILLED WITH POROUS MEDIUM

2021 ◽  
pp. 2150025
Author(s):  
Sidra Shaheen ◽  
Khadija Maqbool ◽  
Farah Gul ◽  
Ayesha Sohail
Keyword(s):  
Magnetic Field ◽  
Drug Delivery ◽  
Porous Medium ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Partial Differential ◽  
Radiation Chemical ◽  
Jeffrey Nanofluid

To prevent the respiratory diseases in an air ways, a defense mechanism based on mucus transport by the moving cilia plays an important role. The mucus transport is affected by the thermal radiation, chemical reaction that changes the physics of fluid due to nanoparticles and thickness of mucus, also different problems in respiratory tract may occur due to the mucus efficacy. In this study, it is observed that the mucus transport can be controlled by the magnetic field that is produced by the drug delivery of nanoparticles, thermal radiation due to temperature difference, porous medium due to respiratory infection, and diffusion of the nanoparticles (chemical reaction) due to the magnetic drug delivery. In this model, flow of Jeffrey nanofluid through the ciliated tube resembles with the mucus flow in a wind pipe. The movement of the mucus is observed by the momentum, energy and concentration equation in the presence of body forces due to magnetic field, heat source due to radiation, Darcy’s resistance due to infection and chemical reaction due to the concentration of nanoparticles. Mathematical model of this study forms a complex system of partial differential equations under the low Reynolds number and long wavelength approximation. The nonlinear set of partial differential equations is solved by the Homotopy perturbation method and software “Mathematica,” results are found for velocity, temperature and concentration profiles and concluded that the mucus flow decelerates due to magnetic field produced by the drug delivery of the nanoparticles but accelerates due to the viscoelastic parameter of Jeffrey fluid and Darcy’s resistance parameter due to infection. The heat transfer rate in the mucus flow rises by increasing the random motion and reduces by the radiation and energy loss. The diffusion of the nanoparticles in the mucus rises by the growing values of thermophoresis and chemical reaction parameter and reduces by the growing values of viscoelastic and Brownian motion parameter.

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

2019 ◽  
Vol 1 (3) ◽  
pp. 35-57
Author(s):  
Binyam Zigta
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Channel Wall ◽  
Schmidt Number ◽  
Hartmann Number ◽  
Eckert Number ◽  
Viscoelastic Parameter ◽  
Grashof Number

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.

Finite Element Solution for MHD Flow of Nanofluids with Heat and Mass Transfer through a Porous Media with Thermal Radiation, Viscous Dissipation and Chemical Reaction Effects

2017 ◽  
Vol 9 (4) ◽  
pp. 904-923 ◽  
Author(s):  
Shafqat Hussain
Keyword(s):  
Mass Transfer ◽  
Finite Element ◽  
Porous Media ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Finite Element Solution ◽  
Element Solution

AbstractIn this paper, the problem of magnetohydrodynamics (MHD) boundary layer flow of nanofluid with heat and mass transfer through a porous media in the presence of thermal radiation, viscous dissipation and chemical reaction is studied. Three types of nanofluids, namely Copper (Cu)-water, Alumina (Al2O3)-water and Titanium Oxide (TiO2)-water are considered. The governing set of partial differential equations of the problem is reduced into the coupled nonlinear system of ordinary differential equations (ODEs) by means of similarity transformations. Finite element solution of the resulting system of nonlinear differential equations is obtained using continuous Galerkin-Petrov discretization together with the well-known shooting technique. The obtained results are validated using MATLAB “bvp4c” function and with the existing results in the literature. Numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and the impact of various physical parameters such as the magnetic parameterM, solid volume fraction of nanoparticles 𝜙 and type of nanofluid on the flow is discussed. The results obtained in this study confirm the idea that the finite element method (FEM) is a powerful mathematical technique which can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.

EFFECTS OF CHEMICAL REACTION AND THERMAL RADIATION ON MHD FLOW OVER AN INCLINED PERMEABLE STRETCHING SURFACE WITH NON-UNIFORM HEAT SOURCE/SINK: AN APPLICATION TO THE DYNAMICS OF BLOOD FLOW

2014 ◽  
Vol 14 (05) ◽  
pp. 1450067 ◽  
Author(s):  
S. SRINIVAS ◽  
P. B. A. REDDY ◽  
B. S. R. V. PRASAD
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Surface Concentration ◽  
Time Dependent ◽  
Stretching Surface ◽  
Radiation Chemical ◽  
Non Linear

An analysis is performed to study the unsteady hydromagnetic heat and mass transfer of blood in a time-dependent porous narrow blood vessel over a permeable inclined stretching surface under slip conditions. The unsteadiness in the flow, temperature and concentration fields is caused by the time dependence of the stretching velocity, surface temperature and the surface concentration. Thermal radiation, chemical reaction, velocity slip, thermal slip and concentration slips are considered. Similarity transformations are used to convert the governing time-dependent non-linear boundary layer equations for momentum, heat equation and species equations into a system of ordinary differential equations. The resulting non-linear coupled differential equations are solved numerically by using fourth order Runge–Kutta scheme together with shooting method. The influence of pertinent parameters on velocity, temperature, concentration, skin-friction coefficient, Nusselt number and Sherwood number has been studied and numerical results are presented graphically and in tabular form. Comparisons with previously published work are performed and the results are found to be in excellent agreement.

scholarly journals Similarity Solution of Heat and Mass Transfer for Natural Convection over a Moving Vertical Plate with Internal Heat Generation and a Convective Boundary Condition in the Presence of Thermal Radiation, Viscous Dissipation, and Chemical Reaction

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. Mohammed Ibrahim ◽  
N. Bhashar Reddy
Keyword(s):  
Boundary Condition ◽  
Natural Convection ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Vertical Plate ◽  
Internal Heat ◽  
Internal Heat Generation

Steady laminar natural convection flow over a semi-infinite moving vertical plate with internal heat generation and convective surface boundary condition in the presence of thermal radiation, viscous dissipation, and chemical reaction is examined in this paper. In the analysis, we assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface of the plate contains a heat source that decays exponentially with the classical similarity variable. We utilized similarity variable to transform the governing nonlinear partial differential equations into a system of ordinary differential equations, which are solved numerically by applying shooting iteration technique along fourth-order Runge-Kutta method. The effects of the local Biot number, Prandtl number, buoyancy forces, the internal heat generation, the thermal radiation, Eckert number, viscous dissipation, and chemical reaction on the velocity, temperature, and concentration profiles are illustrated and interpreted in physical terms. A comparison with previously published results on the similar special cases showed an excellent agreement. Finally, numerical values of physical quantities, such as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number, are presented in tabular form.

Dissipative effects on a chemically and thermally radiative heat fluid flow past a shrinking porous sheet

2020 ◽  
pp. 1-14
Author(s):  
A. Shahid ◽  
M. Ali Abbas ◽  
H.L. Huang ◽  
S.R. Mishra ◽  
M.M. Bhatti
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Linearization Method ◽  
Surface Drag ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Dissipative Effects ◽  
Successive Linearization Method

The present study analyses the dissipative influence into an unsteady electrically conducting fluid flow embedded in a pervious medium over a shrinkable sheet. The behavior of thermal radiation and chemical reactions are also contemplated. The governing partial differential equations are reformed to ordinary differential equations by operating similarity transformations. The numerical outcomes for the arising non-linear boundary value problem are determined by implementing the Successive linearization method (SLM) via Matlab software. The velocity, temperature, and concentration magnitudes for distant values of the governing parametric quantities are conferred, and their conduct is debated via graphical curves. The surface drag coefficient increases, whereas the local Nusselt number and Sherwood number decreases for enhancing unsteadiness parameter across suction parameter. Moreover, the magnetic and suction parameters accelerate velocity magnitudes while by raising porosity parameter, velocity decelerates. Larger numeric of thermal radiation parameter and Eckert number accelerates the temperature profile while by enhancing Prandtl number it decelerates. Schmidt number and chemical reaction parameters slowdowns the concentration distribution, and the chemical reaction parameter influences on the point of chemical reaction that benefits the interface mass transfer. It is expected that the current achieved results will furnish fruitful knowledge in industrious utilities.

MHD STAGNATION POINT FLOW OF HYPERBOLIC TANGENT FLUID WITH VISCOUS DISSIPATION AND CHEMICAL REACTION

2021 ◽  
Vol 21 (2) ◽  
pp. 569-588
Author(s):  
KINZA ARSHAD ◽  
MUHAMMAD ASHRAF
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Normal Velocity ◽  
Hyperbolic Tangent ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In the present work, two dimensional flow of a hyperbolic tangent fluid with chemical reaction and viscous dissipation near a stagnation point is discussed numerically. The analysis is performed in the presence of magnetic field. The governing partial differential equations are converted into non-linear ordinary differential equations by using appropriate transformation. The resulting higher order non-linear ordinary differential equations are discretized by finite difference method and then solved by SOR (Successive over Relaxation parameter) method. The impact of the relevant parameters is scrutinized by plotting graphs and discussed in details. The main conclusion is that the large value of magnetic field parameter and wiessenberg numbers decrease the streamwise and normal velocity while increase the temperature distribution. Also higher value of the Eckert number Ec results in increases in temperature profile.

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