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.

Homotopy perturbation method for MHD non-Newtonian Williamson fluid over exponentially stretching sheet with viscous dissipation and convective boundary condition

2019 ◽  
Vol 30 (11) ◽  
pp. 1950088 ◽  
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Perturbation Method ◽  
Numerical Method ◽  
Homotopy Perturbation Method ◽  
Stretching Sheet ◽  
Fluid Temperature ◽  
Williamson Fluid ◽  
Homotopy Perturbation ◽  
Exponential Stretching ◽  
Special Cases

This research is aimed at presenting the two-dimensional steady fluid flow, represented by Williamson constitutive model past a nonlinear exponential stretching sheet theoretically. The system of ODEs describing the physical problem is successfully solved numerically with the help of the homotopy perturbation method (HPM). Special attention is given to study the convergence analysis of the proposed method. The influences of the physical governing parameters acting on the fluid velocity and the fluid temperature are explained with the help of the figures and tables. Further, the presented numerical method is employed to calculate both the rate of heat transfer and the drag force for the Williamson fluid flow. In particular, it is observed that both the Eckert number and the dimensionless convective parameter have the effect of enhancing the temperature of the stretching surface, while the inverse was noted for the dimensionless mixed convection parameter. Finally, the comparison with previous numerical investigations of other authors at some special cases which is reported here proves that the results obtained via homotopy perturbation method are accurate and the numerical method is reliable.

scholarly journals MHD 3-dimensional nanofluid flow induced by a power-law stretching sheet with thermal radiation, heat and mass fluxes

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sudipta Ghosh ◽  
Swati Mukhopadhyay ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Two Phase ◽  
Mass Fluxes ◽  
First Case ◽  
Special Cases ◽  
Non Linear ◽  
Mass Transfers

AbstractIn this article, the three-dimensional Magnetohydrodynamics flow of a nanofluid over a horizontal non-linearly stretching sheet in bilateral directions under boundary layer approximation is addressed. A two-phase model has been used for the nanofluid. The influences of thermophoresis, Brownian motion and thermal radiation on heat and mass transfers are considered. Two different cases for the heat and mass transfers are studied. In the first case, uniform wall temperature and zero nanoparticles flux due to thermophoresis are considered. In the second case, prescribed heat and mass fluxes at the boundary are considered. By using the appropriate transformations, a system of non-linear partial differential equations along with the boundary conditions is transformed into coupled non-linear ordinary differential equations. Numerical solutions of the self-similar equations are obtained using a Runge–Kutta method with a shooting technique. Our results for special cases are compared with the available results in the literature, and the results are found to be in good agreement. It is observed that the pertaining parameters have significant effects on the characteristics of flow, heat and mass transfer. The results are presented and discussed in detail through illustrations.

MHD nanofluid flow around a permeable stretching sheet with thermal radiation and viscous dissipation

2021 ◽  
pp. 095440622110230
Author(s):  
Rana MA Muntazir ◽  
Muhammad Mushtaq ◽  
Shamaila Shahzadi ◽  
Kanwali Jabeen
Keyword(s):  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Linear Equations ◽  
Transformation Method ◽  
Nano Particles ◽  
Physical Parameters ◽  
Analytical Technique ◽  
Field Environment

In this research article, we have investigated the unsteady MHD nanofluids flow problem around a permeable linearly stretching sheet under the influence of thermal radiation and viscous dissipation. Transfer of mass and heat analysis is considered for various kinds of nano-particles such as [Formula: see text] , Cu, Ag and TiO2. Many research studies had been concluded that thermal conductivity of traditional fluid accelerates 15–40% as nano-particles are mixed in to a base fluid, this theory however depends upon the adding mechanism of the nano-particles. Although it depends upon volume fraction, agglomeration or size of nano-particles etc. But it can be concluded from this study, in a magnetic field environment not only the fluid flow is more consistent than regular fluid but also the rate of heat transfer increases. We have tabulated the results of the four different types of nanofluid and graphically presented the behavior of [Formula: see text] and Cu nanofluids. These distinct MHD nanofluids are used to explore the parametric features of heat and mass transfer phenomena along a permeable stretching sheet. The impacts of various physical parameters and physical quantities are analyzed. It is observed that from this study that the heat transfers rate of Cu nanofluid is higher than [Formula: see text] nanofluid. The coupled non-linear equations are solved by semi-analytical technique i.e Differential Transformation Method (DTM) along with Pade-approximation and found to be in well agreement with already reported work in literature. The graphical illustration and tabular results represent the physical importance of the work. It was observed and concluded that the temperature profiles in case of Cu nanofluid presents significantly high as compared with [Formula: see text] nanofluid. Also, the thicknesses of velocity, thermal and concentration profile decreases by increasing suction/injection and unsteady parameter. These parameters used to control the flow rate.

scholarly journals Powell-Eyring fluid flow over a stratified sheet through porous medium with thermal radiation and viscous dissipation

2021 ◽  
Vol 6 (12) ◽  
pp. 13464-13479
Author(s):  
W. Abbas ◽  
◽  
Ahmed M. Megahed ◽  
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Numerical Solutions ◽  
Steady Motion ◽  
Physical Parameters ◽  
Newtonian Flows ◽  
Highly Nonlinear ◽  
Dependent Viscosity

<abstract><p>The present study explores the effects of viscous dissipation, the thermal dependent conductivity and the thermal dependent viscosity on the steady motion of a Powell-Eyring fluid over a stratified stretching sheet which embedded in a porous medium. The fact that the nature of non-Newtonian flows problems are highly nonlinear equations has been taken into consideration here and this was the motive objective to determine numerical solutions. So, the emphasis is on the methodology adopted for obtaining numerical solutions that yielded after employing the Chebyshev spectral method. The temperature distributions and the velocity components are evaluated by solving numerically the boundary value problems that correspond to the proposed problem. Then, some figures have been plotted to elucidates the effect of different physical parameters appearing in the problem on both the temperature and the velocity profiles. The presence of the thermal radiation and the viscous dissipation in the fluid flow are shown to have quite a dramatic effect on the temperature profiles. In culmination, cooling process in nuclear reactors and geothermal engineering especially in the presence of thermal stratification phenomenon can be adopted as an application of this study. The theoretical and the observed results provide a fairly good qualitative agreement.</p></abstract>

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