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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.

Thermosolutal or double diffusive convection is a transition process that involves concurrent heat and mass whenever there exist temperature and species concentration differences in a medium or between media, with one dependent on the other. This simultaneous occurrence of heat and mass transfer gradients is considered under conditions of technological and engineering importance. These are usually found in fluid-saturated porous media and are encountered in a wide range of thermal engineering applications such as in geothermal systems, oil extraction, ground water pollution, thermal insulation, heat exchangers, storage of nuclear wastes, packed bed catalytic reactors, atmospheric and oceanic circulation. Buoyancy induced flows are rife with references as provided in the text by Rubin and Atkinson [

The study of an electrically conducting fluid, which influences many natural and man-made flows, has many applications in engineering problems such as magnetohydrodynamics (MHDs) generators, plasma studies, nuclear reactors, geothermal energy extraction, and the boundary layer control in the field of aerodynamics. Sharma and Chaudhary [

Combustion processes are very fast and exothermic reactions. Therefore, once the reaction is ignited the process proceeds very quickly and tends to be very nonisothermal. Hence, combustion processes release large amounts of energy, and they have many applications in the production of power, heat, and in incineration processes. Generally, combustion processes are complex because of the combination of complex kinetics, mass transfer control, and large temperature variations. For example, chemical reactions in high speed turbulent flows are accompanied with high temperatures and are of practical import. These are involved in hypersonic aircraft and re-entry vehicles. For nonisothermal chemical reactors, Schmidt [

The previous investigation on combustible flow of gas in a horizontal pipe in the presence of free convection with radiative heat transfer was carried out by Idowu and Adeoti [

In Section

We consider the buoyancy induced steady flow in a porous medium bounded by two horizontal impermeable parallel walls. The lower wall which is on

Physical model.

The governing boundary conditions associated to (

The radiative flux equation (

The functional form (

In order to facilitate the analysis, the following dimensionless variables and parameters are employed:

Therefore, the dimensionless governing equations are

The posed problem (

Suppose that the constant exponent

For the problem at hand, in applying the WKBJ approximation, only the eikonal and transport terms will be retained. Therefore, the general solution to (

Now, having obtained the solutions for the temperature and concentration, we can proceed to the solution of the velocity. Therefore, the solution to (

The potential function (

An understanding of the factors that control the potential function (

Potential function profiles for variations in the parameters: (a) Exponential constant,

We also considered the effect of the radiation parameter,

Temperature profiles for variations in the radiation parameter,

Now, the ad hoc concentration solution (

Concentration profiles as a function of

In most of combustion calculations, there are several hundreds of reactions that could be considered. However, due to limited computational resources, it is customary to select only important reaction mechanisms, neglecting those that are less important (i.e., those reactions whose rates cannot be measured). Preliminary investigations in this work revealed that for

The WKBJ approximate concentration solution (

Concentration profiles as a function of

Next, we examine the contributions of the temperature and concentration solutions to the velocity solution (

Velocity profiles as a function of

Secondly, we explore the effect of the WKBJ approximate concentration solution (

Comparison of velocity solution (

(1) | (2) | |||||||

Velocity equation ( | Velocity equation ( | Velocity equation ( | Velocity equation ( | Velocity equation ( | Velocity equation ( | |||

0 | 0.0742590085 | 0.0784487847 | 2.5 | 0.0578335848 | 0.0636934325 | 0.0 | 0.0791013367 | 0.0765976954 |

2 | 0.0666834061 | 0.0733996050 | 3.0 | 0.0489935405 | 0.0539958380 | 0.4 | 0.0769449694 | 0.0760755165 |

5 | 0.0591602527 | 0.0688520731 | 3.5 | 0.0414079865 | 0.0456719438 | 0.7 | 0.0727141684 | 0.0750122273 |

10 | 0.0517051176 | 0.0649783577 | 4.0 | 0.0350527304 | 0.0386955124 | 1.0 | 0.0666834061 | 0.0733996049 |

In each of the columns (1–3) in the table, (

It is hoped that the present investigation may serve as toolkits for numerical experimentations. It is noted here that the efficient computation of thermal radiation effect with strongly exothermic reaction under generalized Arrhenius kinetics is essential for the design and analysis of industrial thermal systems, such as furnaces, boilers, burners, nuclear power plants, combustion products (such as