Thermal Ignition in a Reactive Viscous Flow Through a Channel Filled With a Porous Medium

2006 ◽  
Vol 128 (6) ◽  
pp. 601-604 ◽  
Author(s):  
O. D. Makinde
Keyword(s):  
Porous Medium ◽  
Nonlinear Boundary ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Exothermic Reaction ◽  
Thermal Ignition ◽  
Arrhenius Kinetics ◽  
Thermal Criticality ◽  
Flow Through ◽  
Steady State Solutions

This paper examines the steady-state solutions of a strongly exothermic reaction of a viscous combustible material in a channel filled with a saturated porous medium under Arrhenius kinetics, neglecting reactant consumption. The Brinkman model is employed and analytical solutions are constructed for the governing nonlinear boundary-value problem using a perturbation technique together with a special type of Hermite-Padé approximants and important properties of the temperature field including bifurcations and thermal criticality are discussed.

scholarly journals On Steady MHD Thermally Radiating and Reacting Thermosolutal Viscous Flow through a Channel with Porous Medium

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Promise Mebine ◽  
Rhoda H. Gumus
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Boundary Value Problem ◽  
Viscous Flow ◽  
Nonlinear Boundary ◽  
Approximate Solutions ◽  
Nonlinear Boundary Value Problem ◽  
Arrhenius Kinetics ◽  
Flow Through ◽  
Steady State Solutions

This paper investigates steady-state solutions to MHD thermally radiating and reacting thermosolutal viscous flow through a channel with porous medium. The reaction is assumed to be strongly exothermic under generalized Arrhenius kinetics, neglecting the consumption of the material. Approximate solutions are constructed for the governing nonlinear boundary value problem using WKBJ approximations. The results, which are discussed with the aid of the dimensionless parameters entering the problem, are seen to depend sensitively on the parameters.

Linear and non-linear analyses of double-diffusive-Chandrasekhar convection coupled with cross-diffusion in micropolar fluid over saturated porous medium

2020 ◽  
Vol 17 (1) ◽  
pp. 211-236
Author(s):  
Maria Anncy ◽  
Thadathil Varghese Joseph ◽  
Subbarama Pranesh
Keyword(s):  
Porous Medium ◽  
Micropolar Fluid ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Critical Rayleigh Number ◽  
Series Representation ◽  
Content Type ◽  
Cross Diffusion ◽  
Non Linear ◽  
Double Diffusive

PurposeThe problem aims to find the effects of coupled cross-diffusion in micropolar fluid oversaturated porous medium, subjected to Double-Diffusive Chandrasekhar convection.Design/methodology/approachNormal mode and perturbation technique have been employed to determine the critical Rayleigh number. Non-linear analysis is carried out by deriving the Lorenz equations using truncated Fourier series representation. Heat and Mass transport are quantified by Nusselt and Sherwood numbers, respectively.FindingsAnalysis related to the effects of various parameters is plotted, and the results for the same are interpreted. It is observed from the results that the Dufour parameter and Soret parameter have an opposite influence on the system of cross-diffusion.Originality/valueThe effect of the magnetic field on the onset of double-diffusive convection in a porous medium coupled with cross-diffusion in a micropolar fluid is studied for the first time.

scholarly journals Slip Velocity Distribution on MHD Oscillatory Heat and Mass Transfer Flow of a Viscous Fluid in a Parallel Plate Channel

2017 ◽  
Vol 36 ◽  
pp. 91-112
Author(s):  
Venkateswarlu Malapati ◽  
Venkata Lakshmi Dasari
Keyword(s):  
Pulsatile Flow ◽  
Parallel Plate ◽  
Numerical Solutions ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Skin Friction Coefficient ◽  
Flow Problems ◽  
Flow Through ◽  
Plate Channel ◽  
Transfer Flow

The present investigation deals with the effect of slip on the hydromagnetic pulsatile flow through a parallel plate channel filled with saturated porous medium. Based on the pulsatile flow nature, the transformed conservation equations are solved analytically subject to physically appropriate boundary conditions by using two term perturbation technique. Exact solutions are obtained for the velocity, temperature and concentration fields. In particular skin friction coefficient, Nusselt number and Sherwood number are found to evolve into their steady state case in the large time limit. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection fluid flow problems. Parametric study of the solutions are conducted and discussed.GANIT J. Bangladesh Math. Soc.Vol. 36 (2016) 91-112

Effect of Boundary Conditions on the Onset of Thermomagnetic Convection in a Ferrofluid Saturated Porous Medium

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
I. S. Shivakumara ◽  
C. E. Nanjundappa ◽  
M. Ravisha
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Porous Layer ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Lower Boundary ◽  
Fluid Viscosity ◽  
Thermomagnetic Convection ◽  
Upper Boundary

The onset of thermomagnetic convection in a ferrofluid saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated for a variety of velocity and temperature boundary conditions. The Brinkman–Lapwood extended Darcy equation, with fluid viscosity different from effective viscosity, is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-ferromagnetic, while the upper boundary is considered to be either rigid-ferromagnetic or stress-free. The thermal conditions include fixed heat flux at the lower boundary, and a general convective-radiative exchange at the upper boundary, which encompasses fixed temperature and heat flux as particular cases. The resulting eigenvalue problem is solved using the Galerkin technique and also by using regular perturbation technique when both boundaries are insulated to temperature perturbations. It is found that the increase in the Biot number and the viscosity ratio, and the decrease in the magnetic as well as in the Darcy number is to delay the onset of ferroconvection. Besides, the nonlinearity of fluid magnetization has no effect on the onset of convection in the case of fixed heat flux boundary conditions.

scholarly journals Radiation Effects on Mass Transfer Flow through a Highly Porous Medium with Heat Generation and Chemical Reaction

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
S. Mohammed Ibrahim
Keyword(s):  
Porous Medium ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Radiation Effects ◽  
Perturbation Technique ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
High Porosity ◽  
Moving Plate ◽  
Flow Through

The present paper is concerned to analyze the influence of the unsteady free convection flow of a viscous incompressible fluid through a porous medium with high porosity bounded by a vertical infinite moving plate in the presence of thermal radiation, heat generation, and chemical reaction. The fluid is considered to be gray, absorbing, and emitting but nonscattering medium, and Rosseland approximation is considered to describe the radiative heat flux in the energy equation. The dimensionless governing equations for this investigation are solved analytically using perturbation technique. The effects of various governing parameters on the velocity, temperature, concentration, skin-friction coefficient, Nusselt number and Sherwood number are shown in figures and tables and analyzed in detail.

Analysis of the Laminar Newtonian Fluid Flow Through a Thin Fracture Modelled as a Fluid-Saturated Sparsely Packed Porous Medium

2017 ◽  
Vol 72 (3) ◽  
pp. 253-259 ◽  
Author(s):  
Igor Pažanin ◽  
Pradeep G. Siddheshwar
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Order Approximation ◽  
Saturated Porous Medium ◽  
Darcy Law ◽  
Brinkman Model ◽  
Order Of Accuracy ◽  
Flow Through ◽  
Fluid Saturated Porous Medium ◽  
Flow Inertia

AbstractIn this article we investigate the fluid flow through a thin fracture modelled as a fluid-saturated porous medium. We assume that the fracture has constrictions and that the flow is governed by the prescribed pressure drop between the edges of the fracture. The problem is described by the Darcy-Lapwood-Brinkman model acknowledging the Brinkman extension of the Darcy law as well as the flow inertia. Using asymptotic analysis with respect to the thickness of the fracture, we derive the explicit higher-order approximation for the velocity distribution. We make an error analysis to comment on the order of accuracy of the method used and also to provide rigorous justification for the model.

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