scholarly journals Caputo Fractional MHD Casson Fluid Flow Over an Oscillating Plate with Thermal Radiation

2021 ◽  
Vol 85 (2) ◽  
pp. 145-158
Author(s):  
Ridhwan Reyaz ◽  
Yeou Jiann Lim ◽  
Ahmad Qushairi Mohamad ◽  
Muhammad Saqib ◽  
Sharidan Shafie
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Numerical Approach ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Fractional Partial Differential Equations ◽  
Governing Equations ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Oscillating Plate

The effect of the thermal radiation on the MHD Casson fluid along with the fractional derivative in an oscillating vertical plate is elucidated. More exactly, the Caputo fractional model is utilized in developing the governing equations. Besides, the influence of the buoyancy force due to the temperature gradient has also been considered. The derived fractional partial differential equations are converted into ordinary differential equations by using the Laplace transform technique and then are solved for analytical solutions via the characteristic method. The inversion of the Laplace transformation is obtained through the numerical approach of Zakian. The effects of various physical parameters on the velocity and temperature profiles, Nusselt number, and skin friction have been analyzed and depicted in graphs and tables. The distribution of the velocity and temperature either in viscous or Casson fluid do enhance by the fractional parameter.

scholarly journals Radiation Effects on Oscillating Vertical Plate with Uniform Heat and Mass Flux

2013 ◽  
Vol 18 (3) ◽  
pp. 643-652
Author(s):  
P. Chandrakala ◽  
P. Narayana Bhaskar
Keyword(s):  
Mass Flux ◽  
Radiation Effects ◽  
Schmidt Number ◽  
Vertical Plate ◽  
Physical Parameters ◽  
Governing Equations ◽  
Uniform Heat ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Oscillating Plate

Abstract Thermal radiation effects on flow past an impulsively started infinite vertical oscillating plate with uniform heat and mass flux is studied. The fluid considered here is a gray, absorbing-emitting radiation but a nonscattering medium. The dimensionless governing equations are solved using the Laplace-transform technique. The velocity, temperature and concentration are studied for different physical parameters such as the radiation parameter, phase angle, Schmidt number and time. The variation of the skin-friction for different values of the parameters is also shown in a table

scholarly journals A new approach for the generalized fractional Casson fluid model with Newtonian heating described by the modified Riemann-Liouville fractional operator

2021 ◽  
Author(s):  
RADHAKRISHNAN BHEEMAN ◽  
Tamilarasi Mathivanan
Keyword(s):  
Fluid Model ◽  
Vertical Direction ◽  
Casson Fluid ◽  
Newtonian Heating ◽  
New Approach ◽  
Laplace Transform Technique ◽  
Casson Fluid Model ◽  
The Laplace Transform ◽  
Liouville Fractional Derivative ◽  
Oscillating Plate

This research is about the transfer of heat of a generalized fractional Casson fluid on an unsteady boundary layer which is passing through an infinite oscillating plate, in vertical direction combined with the Newtonian heating. The results are obtained by using modified Riemann-Liouville fractional derivative. The present fluid model, starts with the governing equations which are then converted to a system of partial differential equations(linear) by using some suitable non-dimensional variables. Using the method of integral balance and the Laplace transform technique, an analytical solution is obtained. The velocity and temperature expressions are derived and the effects of modelling parameters re shown in tables and graphs to validate the obtained theoretical results.

UNSTEADY HEAT TRANSFER FLOW OF A CASSON FLUID WITH NEWTONIAN HEATING AND THERMAL RADIATION

2016 ◽  
Vol 78 (4-4) ◽  
Author(s):  
Abid Hussanan ◽  
Mohd Zuki Salleh ◽  
Ilyas Khan ◽  
Razman Mat Tahar
Keyword(s):  
Heat Transfer ◽  
Thermal Radiation ◽  
Vertical Plate ◽  
Casson Fluid ◽  
Newtonian Heating ◽  
Governing Equations ◽  
Unsteady Heat Transfer ◽  
Laplace Transform Technique ◽  
Limiting Case ◽  
Transfer Flow

This study investigates the unsteady heat transfer flow of a non-Newtonian Casson fluid over an oscillating vertical plate with Newtonian heating on the wall under the effects of thermal radiation. With the help of non-dimensional variables, governing equations are written into dimensionless form and then solved analytically by Laplace transform technique to find the solutions of temperature and velocity. The corresponding solutions of Nusselt number and skin friction are also calculated. The solution in term of viscous fluid is recovered as a limiting case of this work. The effects of the pertinent parameters on temperature and velocity are presented graphically and discussed details in this paper.  

scholarly journals Analytical Solution of Thermal Radiation and Chemical Reaction Effects on Unsteady MHD Convection through Porous Media with Heat Source/Sink

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Abdel-Nasser A. Osman ◽  
S. M. Abo-Dahab ◽  
R. A. Mohamed
Keyword(s):  
Thermal Radiation ◽  
Chemical Reaction ◽  
Energy Equation ◽  
Radiative Heat ◽  
Physical Parameters ◽  
Governing Equations ◽  
Laplace Transform Technique ◽  
Source Sink ◽  
Rosseland Approximation ◽  
Infinite Vertical Plate

This paper analytically studies the thermal radiation and chemical reaction effect on unsteady MHD convection through a porous medium bounded by an infinite vertical plate. The fluid considered here is a gray, absorbing-emitting but nonscattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The dimensionless governing equations are solved using Laplace transform technique. The resulting velocity, temperature and concentration profiles as well as the skin-friction, rate of heat, and mass transfer are shown graphically for different values of physical parameters involved.

scholarly journals Exact solution of thermal radiation on vertical oscillating plate with variable temperature and mass flux

2010 ◽  
Vol 37 (1) ◽  
pp. 1-15
Author(s):  
R. Muthucumaraswamy
Keyword(s):  
Thermal Radiation ◽  
Phase Angle ◽  
Mass Flux ◽  
Radiation Effects ◽  
Variable Temperature ◽  
Physical Parameters ◽  
Plate Temperature ◽  
Grashof Number ◽  
Laplace Transform Technique ◽  
Oscillating Plate

Thermal radiation effects on unsteady flow past an infinite vertical oscillating plate in the presence of variable temperature and uniform mass flux is considered. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised linearly with time and the mass is diffused from the plate to the fluid at an uniform rate. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, concentration and temperature are studied for different physical parameters like the phase angle, radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number and time. It is observed that the velocity increases with decreasing phase angle ?t.

scholarly journals Numerical Simulation of Heat Transfer Flow Subject to MHD of Williamson Nanofluid with Thermal Radiation

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 10
Author(s):  
Muhammad Amer Qureshi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Single Phase ◽  
Physical Parameters ◽  
Fundamental Symmetry ◽  
Box Scheme ◽  
Mhd Boundary Layer ◽  
Slippery Surface ◽  
Transfer Flow

In this paper, heat transfer and entropy of steady Williamson nanofluid flow based on the fundamental symmetry is studied. The fluid is positioned over a stretched flat surface moving non-uniformly. Nanofluid is analyzed for its flow and thermal transport properties by consigning it to a convectively heated slippery surface. Thermal conductivity is assumed to be varied with temperature impacted by thermal radiation along with axisymmetric magnetohydrodynamics (MHD). Boundary layer approximations lead to partial differential equations, which are transformed into ordinary differential equations in light of a single phase model accounting for Cu-water and TiO2-water nanofluids. The resulting ODEs are solved via a finite difference based Keller box scheme. Various formidable physical parameters affecting fluid movement, difference in temperature, system entropy, skin friction and Nusselt number around the boundary are presented graphically and numerically discussed. It has also been observed that the nanofluid based on Cu-water is identified as a superior thermal conductor rather than TiO2-water based nanofluid.

scholarly journals Ohmic and Viscous Dissipation Effect on Free and Forced Convective Flow of Casson Fluid in a Channel

2021 ◽  
Vol 12 (1) ◽  
pp. 132-148
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Convective Flow ◽  
Casson Fluid ◽  
Pictorial Representation ◽  
Physical Parameters ◽  
Partial Differential ◽  
Buoyancy Parameter ◽  
Forced Convective Flow

Analytical study of the free and forced convective flow of Casson fluid in the existence of viscous dissipation, ohmic effect and uniform magnetic field in a porous channel to the physical model. The nonlinear coupled partial differential equations are converted to linear partial differential equations using similarity transformation and the classical perturbation method. The physical parameters such as Prandtl number (Pr), viscous dissipation (Vi), Schmidt number (Sc), Reynolds number (R), thermal buoyancy parameter (λ), Ohmic number (Oh), Casson fluid parameter (β), Darcy number (Da), Hartmann number (M2), the concentration of buoyancy parameter (N), chemical reaction rate (γ) effect on velocity, temperature and concentration have been studied with pictorial representation. For the particular case, the present paper analysis is compared with the previous work and is found good agreement.

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.

Implementation of DTM as a numerical study for the Casson fluid flow past an exponentially variable stretching sheet with thermal radiation

2021 ◽  
pp. 2150111
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Thermal Radiation ◽  
Numerical Method ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Transformation Method ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Special Cases

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement.

scholarly journals Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1238 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stagnation Point ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Three Solutions ◽  
Convective Boundary ◽  
Suction Parameter ◽  
Stretching Surfaces ◽  
The Impact

In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.

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