Effects of Cross Diffusion and Radiation on Magneto Mixed Convective Stagnation Flow from a Vertical Surface in Porous Media with Gyrotactic Microorganisms

Review Article

Austin Chem Eng. 2019; 6(1): 1065.

Effects of Cross Diffusion and Radiation on Magneto Mixed Convective Stagnation Flow from a Vertical Surface in Porous Media with Gyrotactic Microorganisms

Nima NI1,2, Ferdows M2,3*, Ardekani MM4 and Alzahrani F3

1Department of Applied Mathematics, University of Dhaka, Bangladesh

2Department of Quantitative Sciences, International University of Business Agriculture and Technology, Dhaka, Bangladesh

3Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia

4Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa

*Corresponding author: Mohammad Ferdows, Department of Applied Mathematics, University of Dhaka, Bangladesh

Received: March 07, 2019; Accepted: April 16, 2019; Published: April 23, 2019


In this paper the Soret and Dufour effects on steady mixed convective boundary layer flow on a vertical surface embedded in porous medium subjected to a magnetic field containing gyrotactic microorganism is studied. The governing momentum, energy, concentration and microorganism equations are transformed into a set of coupled differential equations. The obtaining equations are solved by MAPLE 14.0 algorithm and the numerical result for different values of Soret number Sr, Dufour number Df, Lewis number Le, bioconvection Lewis number Lb, bioconvection peclet number Pb, Hartmann number Ha2, thermal radiation parameter Rd and buoyancy numbers    is presented graphically for both assisting and opposing flow. Comparisons are made with available published results as special cases to validate numerical data and excellent compatibility is found. The effects of physical parameters on nusselt number, Sherwood number and density of motile microorganism are also presented. It is observed that diffusion thermo and thermal diffusion effects on temperature, concentration and microorganisms profile distributions are quite opposite.

Keywords: Boundary Layer Flow; Double Diffusive; Sacling Analysis; Nonliner ODE; Flow Solutions; Physical Parameters.

Subject Classification: 76Dxx


The mixed  convection (combined free and forced) boundary layer flow has attracted considerable attention in recent years because of  their wide applications in nuclear reactor technology  transpiration cooling, separation process in aquifer, ground water pollution, oil recovery processes, food processing, drawing of plastic films, hot rolling and continuous casting of metals and spinning of fibers, glass-fiber and paper productions. Sakiadis [1,2] studied the boundary layer flow through a moving surface. Grubka and Bobba [3], Elbashbeshy [4] observed temperature field in the boundary layer flow over a stretching surface. Cheng [5] studied the mixed convection flow on inclined surfaces in a porous medium. The mixed convection along a nonisothermal wedge in a porous medium was studied by Kumari and Gorla [6]. The Neild and Bejan [7], Ingham and Pop [8,9] , Vafai [10] have reported the detailed review of the  convection through porous media. Now a days the large number of publications, Lai [11], Postelnicu [12], Chamka and Khaled [13],Bansod and Ambedkar [14], Srinivasachary and Surender [15], Garg [16], Swamy [17],  of the mixed convective heat and mass transfer in porous media have been studied for vertical surfaces.

The study of microorganism is called microbiology. Great attentions are paid to biological fluid mechanism particular in the field of microbiology where developments of microorganisms (e.g. motile species of bacteria and algae) in bioconvection are studied. It is commonly observed that in fluid mechanics solid particles are either carried by the fluid flow or pushed by external forces. Bio-convection patterns are inspected in cultures of swimming micro-organisms which are heavier than water and tend to propel themselves toward the upper surface of their environment in response to external stimuli such as gravity, light, and chemical gradient. Bioconvection can also be classified as the macroscopic fluid motion because of the density gradient associated with swimming micro-organisms [18–22] which intensify the density of base fluid in a specific direction that causes bioconvection flow.

Scientists formulate models to observe the fluid motions associated with aquatic microorganisms. A large number of mechanisms are developed that force microorganisms to swim in specific directions depending on the ambient condition. There are different types of motile micro-organisms such as oxytactic or chemotaxis, negative gravitaxis and gyrotactic micro-organisms according to their impelling behavior. Neild and Bejan [7] defined bioconvection as “Pattern formation in suspensions of microorganisms such as bacteria and algae due to up swimming of the microorganisms”. Gyrotactic microorganisms such as Cnivalis swim upward in still water due to the fact that their center of mass is located behind their center of buoyancy. The behavior of mixed convection in suspensions of gyrotactic/oxytactic microorganisms is discussed widely in [23-27].