Asymptotic Model of Free Convection Flow on a Vertical Surface in Porous Media with Newtonian Heating

2015 ◽  
Vol 756 ◽  
pp. 469-475
Author(s):  
Anna A. Bocharova ◽  
Irina V. Plaksina ◽  
Andrey A. Obushnyy
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Free Convection ◽  
Vertical Surface ◽  
Momentum Equation ◽  
Convection Flow ◽  
Asymptotic Model ◽  
Free Convection Flow ◽  
Energy Equations ◽  
The Mathematical Model

The mathematical model based on system of momentum and energy equations for free convection flow along a vertical surface in porous media under boundary conditions of the third sort is solved analytically using the method of matched asymptotic expansions. The region of validity for boundary layer model and expansions for stream function and temperature with parameter of perturbations were defined. The dependence of characteristic flow from governing dimensionless parameters and was analyzed numerically. The influence of viscous and convective terms of momentum equation in the proposed mathematical model significantly increases the rate of heat transfer on plate in porous media in comparison with Darsy flow model.

scholarly journals MODEL MATEMATIKA ALIRAN KONVEKSI BEBAS FLUIDA VISKOELASTIK YANG MELEWATI SILINDER ELIPTIK DENGAN PENGARUH MAGNETOHYDRODYNAMICS (MHD)

WAHANA ◽  
2018 ◽  
Vol 70 (1) ◽  
pp. 1-6
Author(s):  
Annisa Dwi Sulistyaningtyas
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Magnetic Force ◽  
Energy Equation ◽  
Elliptic Cylinder ◽  
Momentum Equation ◽  
Convection Flow ◽  
Free Convection Flow ◽  
The Mathematical Model ◽  
Fluid Characteristics

In fluid case, the mathematical model is the basic for translating a problem into a mathematical language using an equation or function. The governing equation is developed from continuity equation, momentum equation, and energy equation. Fluid characteristics are viscous and elastic result in boundary layer on the surface of elliptic cylinder. Dimensional equations are transformed into non-dimensional form and then classified into the similarity equations using boundary layer theory with influence of magnetic force. The results of this research is mathematical model of free convection flow in viscoelastic fluid passing through the elliptic cylinder with magnetohydrodinamics (MHD). For variation of magnetohydrodinamics (MHD) parameter, velocity and temperature increase when the parameter increases.

EFFECTS OF NEWTONIAN HEATING AND MASS DIFFUSION ON MHD FREE CONVECTION FLOW OVER VERTICAL PLATE WITH SHEAR STRESS AT THE WALL

2016 ◽  
Vol 78 (3-2) ◽  
Author(s):  
Arshad Khan ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Shear Stress ◽  
Free Convection ◽  
Vertical Plate ◽  
Mass Diffusion ◽  
Convection Flow ◽  
Newtonian Heating ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
Set Up ◽  
Energy Equations

Effects of Newtonian heating and mass diffusion on magnetohydrodynamic free convection flow over a vertical plate that applies arbitrary shear stress to the fluid is studied. The fluid is considered electrically conducting and passing through a porous medium. The influence of thermal radiation in the energy equations is also considered. General solutions of the problem are obtained in closed form using the Laplace transform technique. They satisfy the governing equations, initial and boundary conditions and can set up a huge number of exact solutions correlatives to various fluid motions. The effects of various parameters on velocity profiles are shown graphically and discussed in details

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