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This paper presents unsteady as well as steady-state free convection Couette flow of reactive viscous fluid in a vertical channel formed by two infinite vertical parallel porous plates. The motion of the fluid is induced due to free convection caused by the reactive nature of viscous fluid as well as the impulsive motion of one of the porous plates. The Boussinesq assumption is applied, and the nonlinear governing equations of motion and energy are developed. The time-dependent problem is solved using implicit finite difference method, and steady-state problem is solved by applying regular perturbation technique. During the course of computation, an excellent agreement was found between the well-known steady-state solutions and transient solutions at large value of time.

The study of convection processes in porous channels is a well-developed field of investigation because of its importance to a variety of situations. For example, thermal insulations, geothermal system, surface catalysis of chemical reactions, solid matrix heat exchanger, microelectronic heat transfer equipment, porous flat collectors, coal and grain storage, petroleum industries, dispersion of chemical contaminants in various processes, nuclear waste material, and catalytic beds. Some of the examples mentioned above involve two or more fluids, multidimensional and unsteady flows [

The literature on the topic of unsteady as well as steady-state free convection flow problems is well surveyed by Singh et al. [

In all previous studies the working fluid is considered as nonreactive viscous incompressible fluid. However, unsteady as well as steady-state free convection Couette flow of a reactive viscous fluid in a vertical channel formed by two vertical porous plates can be of importance for the design of equipment used in several types of engineering systems. There are many chemical reactions with important practical applications. A common configuration for such reactions is for the reactants to be made to flow over solid catalyst, with the reaction taking place on the surface of the catalyst. A full discussion of catalysis and description of many of its practical applications is given by Chaudhary and Merkin [

The objective of the present work is to analyze the effect of suction/injection on time dependent unsteady as well as steady-state free convection Couette flow of viscous reactive fluid in a vertical channel formed by two infinite vertical parallel porous plates.

Consider the transient free convective Couette flow of viscous reactive fluid in a vertical channel formed by two infinite vertical parallel porous plates. The system under consideration is sketched in Figure

Schematic diagram of the problem.

The fluid is assumed to be Newtonian and obeys the Boussinesq’s approximation. Under the previous assumptions the energy and momentum equations in dimensional form are

The initial and boundary conditions to be satisfied are

Using the expressions (

The governing equations (

To solve the time-dependent equation (

In each time step, firstly the temperature field has been solved and then the velocity field is evaluated using the already known values of the temperature field. The process of computation is advanced until a solution is approached by satisfying the following convergence criterion:

The basic parameters that governed this flow are the reactant consumption parameter

Velocity profile

Velocity profile

Velocity profile

Temperature profile

Temperature profile

Temperature profile for

Temperature profile

Variation of skin friction

Variation of skin friction

Variation of skin friction

Variation of Nusselt number

Variation of Nusselt number

Variation of Nusselt number

Variation of Nusselt number

Variation of Nusselt number

Variation of Nusselt number

The problem of unsteady as well as steady-state natural convection Couette flow of reactive viscous fluid in a vertical channel formed by two vertical porous plates has been presented. The velocity field and temperature field are obtained analytically by perturbation series method for steady free convective Couette flow of viscous reactive fluid in a vertical channel formed by two vertical porous plates and numerically by implicit finite difference technique for unsteady free convective Couette flow of viscous reactive fluid in a vertical channel formed by two vertical porous plates. Graphical results for the velocity, temperature, skin friction, and the Nusselt number variations were presented and discussed for various physical parametric values.

The main findings are as follows.

Skin friction is always higher in the case of air

It is also seen that increase in

The heat transfer is higher at left porous plate

The introduction of suction/injection has distorted the symmetric nature of the flow.

During the course of computation it is observed that at steady state the effect of

Consider

Specific heat of the fluid at constant pressure

Activation energy

Acceleration due to gravity

Gap between the channels

Nusselt number at

Nusselt number at

Prandtl number

Heat reaction parameter

Universal gas constant

Suction/injection parameter

Dimensional time

Dimensionless time

Dimensional temperature of the fluid

Initial temperature of the fluid

Dimensional velocity of the fluid

Dimensionless velocity of the fluid

Dimensional coordinate parallel to channel

Dimensional coordinate perpendicular to channel

Dimensionless coordinate.

Volumetric coefficient of thermal expansion

Density of the fluid

Dimensionless skinfriction at

Dimensionless skin friction at

Thermal diffusivity

Dimensionless temperature

Reactant consumption parameter

Kinematic viscosity

Activation energy parameter

Grashof number.

The author A. K. Samaila is thankful to Usmanu Danfodiyo University, Sokoto, for financial support.