Analytical and numerical solutions of electro-osmotically driven flow of a third grade fluid between micro-parallel plates

2008 ◽  
Vol 43 (9) ◽  
pp. 985-992 ◽  
Author(s):  
M.B. Akgül ◽  
M. Pakdemirli
Keyword(s):  
Numerical Solutions ◽  
Third Grade ◽  
Parallel Plates ◽  
Third Grade Fluid ◽  
Analytical And Numerical Solutions ◽  
Grade Fluid

Electro-magnetohydrodynamic flow and heat transfer of a third-grade fluid using a Darcy-Brinkman-Forchheimer model

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lijun Zhang ◽  
Muhammad Mubashir Bhatti ◽  
Efstathios E. Michaelides
Keyword(s):  
Temperature Profile ◽  
Fluid Model ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Solution Technique ◽  
Parallel Plates ◽  
Third Grade Fluid ◽  
Transform Method ◽  
Content Type ◽  
Grade Fluid

Purpose The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study. Design/methodology/approach A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme. Findings The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study. Originality/value The obtained results are new and presented for the first time in the literature.

Semi Analytical Solution of Heat Transfer of Magnetohydrodynamic Third-Grade Fluids Flowing Through Parallel Plates With Viscous Dissipation

2018 ◽  
Vol 11 (2) ◽  
Author(s):  
Sumanta Chaudhuri ◽  
Sushil Kumar Rathore
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
Hartmann Number ◽  
Least Square ◽  
Temperature Fields ◽  
Third Grade ◽  
Parallel Plates ◽  
Third Grade Fluid ◽  
Grade Fluid

Abstract This study deals with the heat transfer characteristics of magnetohydrodynamic (MHD) flow of a third-grade fluid through parallel plates, subjected to a uniform wall heat flux, but of different magnitudes. The effect of viscous dissipation has been included for both heating and cooling of the fluid. The least square method (LSM) has been adopted for solving the nonlinear equations. The expressions for the velocity and temperature fields have been derived which, in turn, is utilized to evaluate the Nusselt number. The results indicate an increase in Nusselt number for higher values of the third-grade fluid parameter during heating and indicate a reverse trend for cooling. Nusselt number increases with an increase in Hartmann number during heating, whereas it decreases with increasing values of the Hartmann number while cooling the fluid.

scholarly journals Numerical simulations of heat transfer to a third grade fluid flowing between two parallel plates

2018 ◽  
Vol 96 (5) ◽  
pp. 465-475
Author(s):  
Amer Rasheed ◽  
Fariha Ali ◽  
Muhammad Kamran ◽  
Tanvir Akbar ◽  
Sohail Ahmad Khan
Keyword(s):  
Heat Transfer ◽  
A Priori ◽  
Approximate Solutions ◽  
Third Grade ◽  
Parallel Plates ◽  
Third Grade Fluid ◽  
Flow Parameters ◽  
Heat Transfer Phenomenon ◽  
Grade Fluid ◽  
Flow Configurations

This investigation deals with numerical treatment of heat transfer flow of a third grade fluid between two infinite parallel plates subject to no-slip condition at boundary and no-temperature jump. Three flow configurations, Couette, Poiseuille, and plane Couette–Poiseuille, have been discussed. Approximate solutions using Lagrange–Galerkin method to Couette, Poiseuille, and Couette–Poiseuille flow problems are computed and delineated. It has been substantiated that the fluid rheology and heat transfer phenomenon are greatly influenced by the third grade flow parameters, Brinkman number, and pressure gradient. A rigorous mathematical exposition of the numerical scheme is provided. Because no a priori assumptions are made on pertinent flow parameters, apart from those due to thermodynamic stability, the results presented in this investigation are also valid for their large values.

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