scholarly journals MHD Natural Convection Casson Fluid Flow over a Non-Isothermal Stretching Sheet Embedded in a Porous Medium

2018 ◽  
pp. 1-16 ◽  
Author(s):  
B. O. Falodun ◽  
M. O. Oke ◽  
O. O. Fagbohun
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Natural Convection ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Casson Fluid ◽  
Homotopy Analysis ◽  
Stream Functions ◽  
Spectral Homotopy Analysis Method

In the present study, Magnetohydrodynamics (MHD) natural convection Casson fluid flow over a non-isothermal stretching sheet embedded in a porous medium is considered. The set of governing differential equations are simplified by similarity variables into coupled ordinary differential equations. The defined stream functions satisfied the continuity equation. Roseland approximation is utilized and the present study is therefore limited to an optically thick fluid. The transformed set of coupled nonlinear ordinary differential equations are then solved numerically via spectral homotopy analysis method (SHAM). Results revealed that the Magnetic parameter (M) reduces the velocity profile but produce a significant increase in the temperature profile. Also, it is observed that increasing the thermal radiation parameter increases the thermal condition of the fluid.

scholarly journals Magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abdullah Dawar ◽  
Zahir Shah ◽  
Hashim M. Alshehri ◽  
Saeed Islam ◽  
Poom Kumam
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Lewis Number ◽  
Casson Fluid ◽  
Stretching Cylinder ◽  
Concentration Difference ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Homotopy Analysis

AbstractThis study presents the magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder. The mathematical modeling is presented in the form of partial differential equations and then transformed into ordinary differential equations (ODEs) utilizing suitable similarity transformations. The analytical solution of the transformed ODEs is presented with the help of homotopy analysis method (HAM). The convergence analysis of HAM is also presented by mean of figure. The present analysis consists of five phases. In the first four phases, we have compared our work with previously published investigations while phase five is consists of our new results. The influences of dimensionless factors like a magnetic parameter, thermal radiation, curvature parameter, Prandtl number, Brownian motion parameter, Schmidt number, heat generation, chemical reaction parameter, thermophoresis parameter, Eckert number, and concentration difference parameter on physical quantities of interests and flow profiles are shown through tables and figures. It has been established that with the increasing Casson parameter (i.e. $$\beta \to \infty$$ β → ∞ ), the streamlines become denser which results the increasing behavior in the fluid velocity while on the other hand, the fluid velocity reduces for the existence of Casson parameter (i.e. $$\beta = 1.0$$ β = 1.0 ). Also, the streamlines of stagnation point Casson fluid flow are highly wider for the case of magnetized fluid as equated to non-magnetized fluid. The higher values of bioconvection Lewis number, Peclet number, and microorganisms’ concentration difference parameter reduces the motile density function of microorganisms while an opposite behavior is depicted against density number.

scholarly journals The Consequences of Thermal Radiation and Chemical Reactions on Magneto-hydrodynamics in Two Dimensions Over a Stretching Sheet with Jeffrey Fluid.

2021 ◽  
Author(s):  
Vijay Patel ◽  
Jigisha Pandya
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The Impact

In this research paper, the Homotopy Analysis Method is used to investigate the twodimensional electrical conduction of a magneto-hydrodynamic (MHD) Jeffrey Fluid across a stretching sheet under various conditions, such as when electrical current and temperature are both present, and when heat is added in the presence of a chemical reaction or thermal radiation. Applying similarity transformation, the governing partial differential equation is transformed into terms of nonlinear coupled ordinary differential equations. The Homotopy Analysis Method is used to solve a system of ordinary differential equations. The impact of different numerical values on velocity, concentration, and temperature is examined and presented in tables and graphs. The fluid velocity reduces as the retardation time parameter(2) grows, while the fluid velocity inside the boundary layer increases as the Deborah number () increases. The velocity profiles decrease when the magnetic parameter M is increased. The results of this study are entirely compatible with those of a viscous fluid. The Homotopy Analysis Method calculations have been carried out on the PARAM Shavak high-performance computing (HPC) machine using the BVPh2.0 Mathematica tool.

scholarly journals The Spectral Homotopy Analysis Method Extended to Systems of Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
S. S. Motsa ◽  
F. G. Awad ◽  
Z. G. Makukula ◽  
P. Sibanda
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Analysis Method ◽  
Partial Differential ◽  
Homotopy Analysis ◽  
Spectral Homotopy Analysis Method ◽  
Good Agreement

The spectral homotopy analysis method is extended to solutions of systems of nonlinear partial differential equations. The SHAM has previously been successfully used to find solutions of nonlinear ordinary differential equations. We solve the nonlinear system of partial differential equations that model the unsteady nonlinear convective flow caused by an impulsively stretching sheet. The numerical results generated using the spectral homotopy analysis method were compared with those found using the spectral quasilinearisation method (SQLM) and the two results were in good agreement.

Stagnation-Point Flow and Heat Transfer of a Casson Fluid towards a Stretching Sheet

2012 ◽  
Vol 67 (1-2) ◽  
pp. 70-76 ◽  
Author(s):  
Meraj Mustafa ◽  
Tasawar Hayat ◽  
Pop Ioan ◽  
Awatif Hendi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Analytic Solutions ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Stream Velocity ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

This article reports the flow of a Casson fluid in the region of stagnation-point towards a stretching sheet. The characteristics of heat transfer with viscous dissipation are also analyzed. The partial differential equations representing the flow and heat transfer of the Casson fluid are reduced to ordinary differential equations through suitable transformations. The flow is therefore governed by the Casson fluid parameter β, the ratio of the free stream velocity to the velocity of the stretching sheet a=c, the Prandtl number Pr, and the Eckert number Ec. The analytic solutions in the whole spatial domain have been computed by the homotopy analysis method (HAM). The dimensionless expressions for the skin friction coefficient and the local Nusselt number have been calculated and discussed.

scholarly journals Bioconvection of Nanofluid Past Stretching Sheet in a Porous Medium in Presence of Gyrotactic Microorganisms with Newtonian Heating

2018 ◽  
Vol 220 ◽  
pp. 01004
Author(s):  
Rashid Pourrajab ◽  
Aminreza Noghrehabadi
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Boussinesq Approximation ◽  
Newtonian Heating ◽  
Gyrotactic Microorganisms ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Layer Flow

In this study, the effect of Newtonian heating on the boundary layer flow and heat transfer over a stretching surface in a porous medium in the presence of gyrotactic microorganisms and nanoparticle fractions are analysed. The governing equations are reduced to a system of couple non-linear ordinary differential equations, subjected to the Boussinesq approximation and asymmetric heat conditions. The reduced governing ordinary differential equations are then solved numerically. The solutions obtained are graphically represented. The effects of the controlling parameters on the flow, heat, nanoparticle concentration and the density of motile microorganisms have been examined. The results of the present study show the flow velocity, heat and mass transfer and motile microorganism characteristics on the stretching sheet are strongly influenced by the bioconvection parameters and Newtonian.

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