scholarly journals Effect of chemical reaction and radiation on double diffusive flow of a viscous, dissipative fluid through porous medium in a rectangular cavity with heat sources

2013 ◽  
Vol 18 (4) ◽  
pp. 1115-1150
Author(s):  
T.L. Raju ◽  
P. Muralidhar
Keyword(s):  
Porous Medium ◽  
Stream Function ◽  
Rectangular Cavity ◽  
Heat Sources ◽  
Element Analysis ◽  
Coupled Equations ◽  
Stiffness Matrices ◽  
Diffusive Flow ◽  
Transfer Flow ◽  
And Diffusion

Abstract In this paper, an attempt is made to discuss the combined influence of radiation and dissipation on the convective heat and mass transfer flow of a viscous fluid through a porous medium in a rectangular cavity using the Darcy model. Making use of the incompressibility, the governing non-linear coupled equations for the momentum, energy and diffusion are derived in terms of the non-dimensional stream function, temperature and concentration. The Galerkin finite element analysis with linear triangular elements is used to obtain the global stiffness matrices for the values of stream function, temperature and concentration. These coupled matrices are solved using an iterative procedure and expressions for the stream function, temperature and concentration are obtained as linear combinations of the shape functions. The behavior of temperature, concentration, the Nusselt number and Sherwood number is discussed computationally for different values of the governing parameters, such as the Rayleigh Number (Ra), heat source parameter (α), Eckert number (Ec), Schmidt Number (Sc), Soret parameter (S0), buoyancy ratio (N).

scholarly journals Regularity, Asymptotic Solutions and Travelling Waves analysis in a porous medium system to model the interaction between invasive and invaded species

2021 ◽  
Author(s):  
José Díaz ◽  
Antonio Naranjo
Keyword(s):  
Porous Medium ◽  
Travelling Waves ◽  
Stationary Solutions ◽  
Uniqueness Of Solutions ◽  
Linear Diffusion ◽  
Diffusion Parameters ◽  
Medium System ◽  
Topological Argument ◽  
And Diffusion ◽  
Stable Connection

This work provides an analytical approach to characterize and determine solutions to a porous medium system of equations with views in applications to invasive-invaded biological dynamics. Firstly, the existence and uniqueness of solutions are proved. Afterwards, profiles of solutions are obtained making use of the selfsimilar structure that permits to show the existence of a diffusive front. The solutions are then studied within the Travelling Waves (TW) domain showing the existence of potential and exponential profiles in the stable connection that converges to the stationary solutions in which the invasive specie predominates. The TW profiles are shown to exist based on the geometry perturbation theory together with an analytical-topological argument in the phase plane. The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded specie TW is not trivial in the non-linear diffusion case and reflects the existence of a TW trajectory governed by the invaded specie runaway (in the direction of the advection) and the diffusion (acting along a finite speed front or support).

Stokes’ first problem for an electro-conducting micropolar fluid with thermoelectric properties

2010 ◽  
Vol 88 (1) ◽  
pp. 35-48 ◽  
Author(s):  
Magdy A. Ezzat ◽  
Hamdy M. Youssef
Keyword(s):  
Thermoelectric Properties ◽  
Micropolar Fluid ◽  
Inversion Formula ◽  
Figure Of Merit ◽  
Fourier Expansion ◽  
Fourier Transforms ◽  
Heat Sources ◽  
Layer Model ◽  
Thermoelectric Figure ◽  
Coupled Equations

This work is related to the flow of an electro-conducting micropolar fluid presenting thermoelectric properties effect in the presence of a magnetic field. The electro-conducting thermofluid equation of heat transfer with one relaxation time is derived. The flow of an electro-conducting micropolar fluid over a plate that is moved suddenly is considered. The governing coupled equations in the frame of the boundary-layer model are applied to Stokes' first problem with heat sources. Laplace-transform and Fourier-transform techniques are used to obtain the solution. The inverses of the Fourier transforms are obtained analytically. The Laplace transforms are obtained using the complex inversion formula of the transform together with Fourier-expansion techniques. Numerical results for the temperature distribution, the velocity, and the microrotation components are represented graphically. Thermoelectric figure-of-merit, Seebeck and Peltier effects on a micropolar fluid are studied.

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