MHD flow, under the kinetic postulate, of fluids that are initially liquid under thermal radiation effects

2019 ◽  
Vol 97 (6) ◽  
pp. 579-587
Author(s):  
Azad Hussain ◽  
Zainia Muneer ◽  
M.Y. Malik ◽  
Saadia Ghafoor
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Radiation Effects ◽  
Shooting Method ◽  
Porous Plate ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Runge Kutta Method

The present study focuses on the non-Newtonian magnetohydrodynamic flow, under the kinetic postulate, of fluids that are initially liquid past a porous plate in the appearance of thermal radiation effects. Resemblance transfigurations are used to metamorphose the governing equations for temperature and velocity into a system of ordinary differential equations. We then solved these differential equations subject to convenient boundary conditions by using the shooting method along with the Runge–Kutta method. Heat transfer and characteristic flow results are acquired for different compositions of physical parameters. These results are extended graphically to demonstrate interesting attributes of the physics of the problem. Nusselt number and skin friction coefficients are also discussed via graphs and tables for different values of dimensionless parameters. Decline occurs in velocity profile due to escalating values of M. Temperature profile depicts growing behavior due to acceleration in the values of λ and M. Nusselt number and skin friction curves represent rising behavior according to their parameters.

scholarly journals EFFECT OF HEAT AND MASS TRANSFER AND THERMAL RADIATION ON A STEADY MHD CONVECTIVE FLOW WITH VISCOUS DISSIPATION AND SUCTION/INJECTION

2022 ◽  
Vol 52 (1) ◽  
pp. 35-41
Author(s):  
Silpisikha Goswami ◽  
Kamalesh Kumar Pandit ◽  
Dipak Sarma
Keyword(s):  
Nusselt Number ◽  
Thermal Radiation ◽  
Temperature Profile ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Sherwood Number ◽  
Fluid Velocity ◽  
Physical Parameters ◽  
Flow Equations ◽  
The Impact

Our motive is to examine the impact of thermal radiation and suction or injection with viscous dissipation on an MHD boundary layer flow past a vertical porous stretched sheet immersed in a porous medium. The set of the flow equations is converted into a set of non-linear ordinary differential equations by using similarity transformation. We use Runge Kutta method and shooting technique in MATLAB Package to solve the set of equations. The impact of non-dimensional physical parameters on flow profiles is analysed and depicted in graphs. We observe the influence of non-dimensional physical quantities on the Nusselt number, the Sherwood number, and skin friction and presented in tables. A comparison of the obtained numerical results with existing results in a limiting sense is also presented. We enhance radiation to observe the deceleration of fluid velocity and temperature profile for both suction and injection. While enhancing porosity parameter accelerates velocity whereas decelerates temperature profile. As the heat source parameter increases, the temperature of the fluid decreases for both suction and injection, it has been found. With the increasing values of the radiation parameter, the skin friction and heat transfer rate decreases. Increasing magnetic parameter decelerates the skin friction, Nusselt number, and Sherwood number.

scholarly journals Magnetohydrodynamic Time-Dependent Bio-Nanofluid Flow in a Porous Medium with Variable Thermophysical Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
M. Irfan ◽  
M. Asif Farooq ◽  
A. Aslam ◽  
A. Mushtaq ◽  
Z. H. Shamsi
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Local Nusselt Number ◽  
Shooting Method ◽  
Local Density ◽  
Skin Friction Coefficient ◽  
Published Data ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Local Sherwood Number

In this work, a theoretical model with a numerical solution is brought forward for a bio-nanofluid with varying fluid features over a slippery sheet. The partial differential equations (PDEs) involving temperature-dependent quantities have been translated into ordinary differential equations (ODEs) by using similarity variables. Numerical verifications have been done in three different methods: finite difference method, shooting method, and bvp4c. To figure out the influence of parameters on the flows, the graphs are plotted for the velocity, temperature, concentration, and microorganism curves. The boundary layer thickness of the microorganism profile reduces with the Schmidt number and Peclet number. In addition to adding radiative heat flux, we added heat generation, rate of chemical reaction, and first-order slip. Adding these parameters brought new aspects to the underlying profiles. Moreover, the obtained data of the skin friction coefficient, the local Nusselt number, the local Sherwood number, and the local density of motile microorganisms are tabulated against various parameters for the physical parameters. From the results, it is apparent that the local Nusselt number decreases with the Brownian and thermophoretic parameters. The data obtained for physical parameters have a close agreement with the published data. Finally, the graphs for slip conditions are significantly different when the comparison is drawn with no-slip condition.

scholarly journals Numerical Treatment for Darcy-Forchheimer Flow of Sisko Nanomaterial with Nonlinear Thermal Radiation by Lobatto IIIA Technique

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Iftikhar Uddin ◽  
Rizwan Akhtar ◽  
Zhu Zhiyu ◽  
Saeed Islam ◽  
Muhammad Shoaib ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Velocity Profile ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Fluid Model ◽  
Dynamical Analysis ◽  
Physical Parameters ◽  
Nonlinear Thermal Radiation ◽  
Sisko Fluid ◽  
Forchheimer Flow

In this study, the competency of numerical computational framework based on Lobatto IIIA technique is utilized for dynamical analysis of the Darcy-Forchheimer flow of Sisko nanomaterial with nonlinear thermal radiation. The resultant PDEs of the Sisko fluid model expressions are transformed into system of nonlinear ODEs by exploiting the similarity variables. Graphical representations and numerical illustrations are used to envisage the characteristics of various physical parameters of interest on velocity profile, nanoparticles concentration, and temperature distribution of Sisko fluidic system. In addition, skin friction and Nusselt number are numerically examined with observation that the material parameter of Sisko fluid increases the velocity profile as well as Nusselt number while decreasing temperature, concentration profiles, and skin friction coefficient.

Viscous Dissipation and Thermal Radiation effects in MHD flow of Jeffrey Nanofluid through Impermeable Surface with Heat Generation/Absorption

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Kalpna Sharma ◽  
Sumit Gupta
Keyword(s):  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Radiation Effects ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Homotopy Analysis ◽  
Two Dimensional Flow ◽  
Jeffrey Nanofluid ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

AbstractThis paper investigates steady two dimensional flow of an incompressible magnetohydrodynamic (MHD) boundary layer flow and heat transfer of nanofluid over an impermeable surface in presence of thermal radiation and viscous dissipation. By using similarity transformation, the arising governing equations of momentum, energy and nanoparticle concentration are transformed into coupled nonlinear ordinary differential equations, which are than solved by homotopy analysis method (HAM). The effect of different physical parameters, namely, Prandtl number Pr, Eckert number

scholarly journals MHD Flow of a Micropolar Fluid past a Stretched Permeable Surface with Heat Generation or Absorption

2009 ◽  
Vol 14 (1) ◽  
pp. 27-40 ◽  
Author(s):  
M.-E. M. Khedr ◽  
A. J. Chamkha ◽  
M. Bayomi
Keyword(s):  
Differential Equations ◽  
Heat Generation ◽  
Micropolar Fluid ◽  
Radiation Effects ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Permeable Surface ◽  
Physical Parameters ◽  
Special Cases ◽  
Heat Generation Or Absorption

This work considers steady, laminar, MHD flow of a micropolar fluid past a stretched semi-infinite, vertical and permeable surface in the presence of temperature dependent heat generation or absorption, magnetic field and thermal radiation effects. A set of similarity parameters is employed to convert the governing partial differential equations into ordinary differential equations. The obtained self-similar equations are solved numerically by an efficient implicit, iterative, finite-difference method. The obtained results are checked against previously published work for special cases of the problem in order to access the accuarcy of the numerical method and found to be in excellent agreement. A parametric study illustrating the influence of the various physical parameters on the skin friction coefficient, microrotaion coefficient or wall couple stress as well as the wall heat transfer coefficient or Nusselt number is conducted. The obtained results are presented graphically and in tabular form and the physical aspects of the problem are discussed.

scholarly journals A numerical approach for two-dimensional Sutterby fluid flow bounded at a stagnation point with an inclined magnetic field and thermal radiation impacts

2020 ◽  
pp. 186-186 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Ali Imran ◽  
Muhammad Umar ◽  
Muhammad Zeb ◽  
Muhammad Shoaib ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Velocity Ratio ◽  
Skin Friction Coefficient ◽  
Deborah Number ◽  
Inclined Magnetic Field ◽  
Runge Kutta Method ◽  
Power Law Index

The present study investigates the impacts of thermal radiation and inclined magnetic field on the Sutterby fluid by capitalizing Cattaneo-Christov heat flux system. The suitable transformations from partial differential equations (PDEs) into ordinary differential equations (ODEs) are achieved by capitalizing the strength of similarity conversion system. Well known numerical shooting technique is used along with integrated strength Runge Kutta method of fourth order. The proposed results are compared with Lobatto 111A method which strengthen the convergence and accuracy of present fluidic system. The skin friction coefficients and Nusselt number are numerically exhibited in tabular form, while the parameter of interests in terms of velocity ratio parameter, power law index, the thermal radiation parameter, Prandtl number, Deborah number, magnetic parameter. Here in this contemporary investigation, the phenomenon of thermal radiation on an inclined magnetic field using Sutterby capitalizing Cattaneo-Christov heat flux model has been discussed. The resulting complex nonlinear ODEs are tackled numerically by utilizing a famous shooting technique with the integrated strength of the Runge-Kutta method of fourth order. The obtained numerical results are compared with the MATLbuilt-in solver bvp4c. The numerical values of the skin friction coefficient and reduced Nusselt number are narrated in tabular form, while some proficient parameters like velocity ratio parameter, power-law index, Deborah number, magnetic parameter, inclined magnetic angle, the thermal radiation parameter, Reynolds number and Prandtl number on the velocity and temperature profiles have been discussed numerically as well as graphically. Outcomes of the proposed research show that by increasing the inclined angle, enhancement is seen in the skin-friction coefficient and reduces the Nusselt number. Moreover, by increasing the Reynolds number, the temperature profile declines initially and then moves upward in the channel. The stability and convergence of the proposed methodolgy in validated through residual errors based different tolerances.

MHD FLOW OF AN EYRING-POWELL FLUID WITH THE EFFECT OF THERMAL RADIATION, JOULE HEATING AND VISCOUS DISSIPATION

2020 ◽  
Vol 9 (11) ◽  
pp. 9259-9271
Author(s):  
K.R. Babu ◽  
G. Narender ◽  
K. Govardhan
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
The Magnetic Field

A two-dimensional stream of an magnetohydrodynamics (MHD) Eyring-Powell fluid on a stretching surface in the presence of thermal radiation, viscous dissipation and the Joule heating is analyzed. The flow model in the form of the Partial Differential Equations (PDEs) is transformed into a system of non-linear and coupled Ordinary Differential Equations (ODEs) by implementing appropriate similarity transformations. The resulting ordinary differential equations are solved numerically by the shooting technique with Adams-Moulton Method of fourth order. The numerical solution obtained for the velocity and temperature profiles has been presented through graphs for different choice of the physical parameters. The magnetic field is found to have a direct relation with the temperature profile and an inverse with the velocity profile. Increasing the thermal radiation, the temperature tends to rise.

scholarly journals Unsteady MHD Bionanofluid Flow in a Porous Medium with Thermal Radiation near a Stretching/Shrinking Sheet

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
M. Irfan ◽  
M. Asif Farooq ◽  
A. Mushtaq ◽  
Z. H. Shamsi
Keyword(s):  
Porous Medium ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Internal Heat ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
The Impact

This research aims at providing the theoretical effects of the unsteady MHD stagnation point flow of heat and mass transfer across a stretching and shrinking surface in a porous medium including internal heat generation/absorption, thermal radiation, and chemical reaction. The fundamental principles of the similarity transformations are applied to the governing partial differential equations (PDEs) that lead to ordinary differential equations (ODEs). The transformed ODEs are numerically solved by the shooting algorithm implemented in MATLAB, and verification is done from MATLAB built-in solver bvp4c. The numerical data produced for the skin friction coefficient, the local Nusselt number, and the local Sherwood number are compared with the available result and found to be in a close agreement. The impact of involved physical parameters on velocity, temperature, concentration, and density of motile microorganisms profiles is scrutinized through graphs. It is analyzed that the skin friction coefficient enhances with increasing values of an unsteady parameter A , magnetic parameter M , and porosity parameter Kp . In addition, we observe that the density of a motile microorganisms profile enhances larger values of the bioconvection Lewis number Lb and Peclet number Pe and decreases with the increasing values of an unsteady parameter A .

Double Stratification in Flow by Curved Stretching Sheet With Thermal Radiation and Joule Heating

2017 ◽  
Vol 10 (2) ◽  
Author(s):  
Tasawar Hayat ◽  
Sumaira Qayyum ◽  
Maria Imtiaz ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Joule Heating ◽  
Radiation Effects ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Curvilinear Coordinates ◽  
Double Stratification ◽  
Curvature Parameter ◽  
Basic Equations

Magnetohydrodynamic (MHD) flow of viscous fluid by curved stretching surface is presented in this paper. Heat and mass transfer analysis is studied with double stratification and thermal radiation effects. Joule heating is also taken into consideration. Basic equations of flow problem are obtained using curvilinear coordinates. The partial differential equations are reduced to the nonlinear ordinary differential equations using suitable transformations. Graphical results are shown and analyzed for the effect of different parameters on fluid characteristics. It is noted that thermal and solutal stratification parameters have opposite effect on temperature and concentration distributions. Magnitude of pressure, skin friction coefficient, and Nusselt number decreases for larger curvature parameter.

scholarly journals Effects of Inclination of the Plate Embedded in Porous Media on Radiative and Chemically Reactive MHD Convection

2019 ◽  
Vol 8 (4) ◽  
pp. 10239-10245
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Chemical Reaction ◽  
Radiation Effects ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Petroleum Engineering ◽  
Physical Parameters

This work is focused on the numerical study of thermodiffusion, inclination of the plate, order of chemical reaction, Diffusion-thermo and thermal radiation effects on a steady magnetohydrodynamic convective flow over an inclined plate in a porous medium under the influence of viscous dissipation along with the application of heat generation/ absorption effects. The partial differential equations governing the fluid flow are transformed into coupled non dimensional ordinary differential equations with the help of similarity transformations. Suitable codes in MATLAB’s built in solver bvp4c, which is a highly accurate and efficient solver of MATLAB, are developed to solve these coupled ordinary differential equations numerically. The behaviour of the fluid velocity, temperature and species concentration for variations in the various thermo-physical parameters are illustrated via graphs. From the numerical results it is evident that the heat and mass transfer of the fluid are significantly influenced by the order of chemical reaction, thermal radiation, inclination of the plate, Soret and Dufour effects. Results obtained in this paper may be useful in the field of chemical industries, chemical engineering, petroleum engineering. Gas separating instruments can be installed in big cities as an engineering application so that harmful pollutants can be removed which are present in small quantities mixed with air.

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