Journal of Thermodynamics

Volume 2016, Article ID 8307980, 10 pages

http://dx.doi.org/10.1155/2016/8307980

## Influence of Chemical Reaction on Heat and Mass Transfer Flow of a Micropolar Fluid over a Permeable Channel with Radiation and Heat Generation

Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar, Uttarakhand, India

Received 30 June 2016; Accepted 9 November 2016

Academic Editor: Felix Sharipov

Copyright © 2016 Khilap Singh and Manoj Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The effects of chemical reaction on heat and mass transfer flow of a micropolar fluid in a permeable channel with heat generation and thermal radiation is studied. The Rosseland approximations are used to describe the radiative heat flux in the energy equation. The model contains nonlinear coupled partial differential equations which have been transformed into ordinary differential equation by using the similarity variables*.* The relevant nonlinear equations have been solved by Runge-Kutta-Fehlberg fourth fifth-order method with shooting technique. The physical significance of interesting parameters on the flow and heat transfer characteristics as well as the local skin friction coefficient, wall couple stress, and the heat transfer rate are thoroughly examined.

#### 1. Introduction

The micropolar fluid theory is the one of the most important non-Newtonian fluid models described by Eringen [1]. This theory shows microrotation effects as well as microinertia and has many applications such as polymer fluids, liquid crystals, animal bloods, unusual lubricants, colloidal and suspension solutions, colloidal fluids, liquid crystals, and polymeric suspension. The extensive reviews of the micropolar fluid theory and its applications can be found in Eringen [2] and Lukaszewicz [3]. The unsteady mixed convection flow of a micropolar fluid from a vertical surface in the presence of viscous dissipation and the buoyancy force has been studied by El-Aziz [4]. Ashraf et al. [5] investigated the micropolar fluids flow through a porous channel. Sheikholeslami et al. [6] proposed the flow and heat transfer of micropolar fluid in a permeable channel. Prakash and Muthtamilselvan [7] investigated radiation effect on MHD micropolar fluid flow in porous vertical channel. Darvishi et al. [8] analyzed numerically the micropolar fluid flow from a porous channel. Sherief et al. [9] studied the motion along axis of a circular cylindrical pore in a micropolar fluid of a slip spherical particle. Mosayebidorcheh [10] analyzed the flow of micropolar fluid over a porous channel with changing walls. Recently, many authors [11–14] have studied the micropolar fluid flow for different fluid properties over different geometries. However, the effects of chemical reaction on micropolar fluid flow over a permeable channel in the presence of radiation and heat generation have not been considered in the above investigations.

Combined heat and mass transfer flows in the presence of chemical reaction have numerous applications in engineering and geophysics such as drying, geothermal reservoirs, dehydration at the surface of a water body, drying of porous solids, geothermal pool, thermal insulation, enhanced oil recovery, cooling of nuclear reactors, fibrous insulation, evaporation at the surface of a water body, pollution studies, cooling the polymer production and manufacturing of ceramics, energy transfer in a wet cooling tower, the flow in a desert, and oxidation and synthesis materials. Mohamed and Abo-Dahab [15] studied the effects of chemical reaction and thermal radiation on hydromagnetic free convection heat and mass transfer for a micropolar fluid bounded by a semi-infinite vertical porous plate in the presence of heat generation. In recent years, many researchers have studied and reported the effect of first-order chemical reaction [16–25].

Influence of thermal radiation on flow and heat transfer study has become more important industrially. The heat transfer and temperature profile of a micropolar fluid over different geometries can be affected significantly at high temperature. Bhattacharyya et al. [26] considered thermal radiation effect on micropolar fluid flow and heat transfer over a porous shrinking sheet. Hussain et al. [27] analyzed radiation effects on the thermal boundary layer flow of a micropolar fluid towards a permeable stretching sheet. Oahimire and Olajuwon [28] investigated the influence of Hall current and thermal radiation on heat and mass transfer of a chemically reacting MHD flow of a micropolar fluid through a porous medium. Mabood et al. [29] studied effects of nonuniform heat source/sink and Soret on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation.

The effect of heat generation on heat transfer is an important issue in view of various physical problems. Ziabakhsh et al. [30] analyzed the micropolar fluid flow with heat generation. Singh and Kumar [31] considered the melting effect in stagnation-point flow of micropolar fluid towards a stretching/shrinking surface. Bakr [32] investigated the effects of chemical reaction and heat source magnetoconvection and mass transfer flow of a micropolar fluid in a rotating frame of reference. The heat generation/absorption effects on MHD flow and heat transfer of micropolar fluid through a stretching surface have been proposed by Mahmoud and Waheed [33]. Abbasi et al. [34] examined the flow of Maxwell nanofluid in the presence of heat generation/absorption. Mliki et al. [35] investigated the influence of nanoparticle Brownian motion and heat generation/absorption over linear/sinusoidally heated cavity in the presence of magnetohydrodynamic natural convection. Sheikholeslami and Ganji [36] studied three-dimensional heat and mass transfer flow of nanofluid over a rotating system. Thermal radiation effects on mixed convection flow and heat transfer of a micropolar fluid through an unsteady stretching surface with heat generation/absorption are presented by Singh and Kumar [37].

Motivated by the above studies and applications, the present work explores effects of chemical reaction on heat and mass transfer flow of a micropolar fluid over a permeable channel in the presence of radiation and heat generation. The equations of continuity, momentum, angular momentum, energy, and concentration have been reduced to a system of nonlinear ordinary differential equations by similarity transforms which are solved by Runge-Kutta-Fehlberg method with shooting technique. It is expected that the results obtained from present paper will provide important information to the audience. To the best of our knowledge, such type of study is not investigated before in the scientific literature.

#### 2. Mathematical Formulation

The heat and mass transfer flow of a micropolar fluid in a permeable channel with chemical reaction is considered in the present work. The thermal radiation and heat source are incorporated in the energy equation. The graphical model of the problem has been given along with flow configuration and coordinate system in Figure 1. The assumptions of the problem in detail can be found in [6]. The governing equations of boundary layer are given in the following form:where and indicate the velocity components in the and directions, respectively, is the fluid density, is the dynamic viscosity, is the material parameter, is the angular or microrotation velocity, is the fluid pressure, is the microinertia density, is the microrotation viscosity, is the fluid temperature, is the specific heat at constant pressure, is the fluid concentration, is the thermal conductivity, is the radiative heat flux, is the heat generation coefficient, is the molecular diffusivity, and is the chemical reaction rate coefficient.