Flow and heat transfer of couple stress fluid in a porous channel with expanding and contracting walls

In this paper, an incompressible laminar flow of a couple stress fluid in a porous channel with expanding or contracting walls is considered. Assuming symmetric injection or suction along the uniformly expanding porous walls and using similarity transformations, the governing equations are reduced to nonlinear ordinary differential equations. The resulting equations are then solved numerically using quasilinearization technique. The graphs for velocity components and temperature distribution are presented for different values of the fluid and geometric parameters.     

Linear stability of convection in a vertical channel filled with nanofluid saturated porous medium

The convection in a vertical channel filled with a porous medium saturated by a nanofluid is studied numerically. The effects of Brownian motion and thermophoresis are incorporated in the model used for nanofluid. Also, the flow within the porous region is governed by Brinkman's equation. The generalized eigenvalue problem for the perturbed state is obtained from a normal mode analysis and solved using the Chebyshev spectral collocation method. The Rayleigh number is expressed as an implicit function of the wavenumber with other parameters. The critical wavenumber and the critical Rayleigh number are calculated for different parameters. The preferred modes under critical conditions are detected.     

Mixed convection of a nanofluid past an inclined wavy surface in the presence of gyrotactic microorganisms

The mixed convection of a nanofluid flow past an inclined wavy surface in the existence of gyrotactic microbes is considered. To convert the wavy surface to a plane surface, a transformation of coordinates is applied. The governing equations that are nonlinear and the accompanying boundary conditions are converted into a dimensionless form using pseudo-similarity variables. Using a local linearization process, the system of nonlinear partial differential equations is linearized. The resulting system is solved using the Bivariate Chebyshev pseudo-spectral collocation method. The influence of different physical and geometrical factors on the parameters of engineering importance of the flow is analyzed and illustrated graphically. It is observed that the skin friction, the density of motile microorganisms, and nanoparticle mass transfer rate are increasing with an increase in the bioconvection Peclet and Schmidt numbers whereas these quantities are decreasing with an increase in Rayleigh number. The local Nusselt number, nanoparticle Sherwood number, and density number of microbes increases with an increase in the Brownian motion and thermophoresis parameter. These physical quantities are increasing when the surface changes from horizontal to vertical.     

Influence of Soret and Dufour on mixed convection flow across a vertical cone

This contribution examines the influence of Soret and Dufour on an incompressible viscous fluid flow across a vertical cone. The flow model is framed in the form of mathematical governing equations and a nondimensionalization is performed on them for ease of the numerical computations' examination; the obtained nonsimilarity equations are solved numerically through the bivariate Chebyshev spectral collocation quasi-linearization method. Outcomes of the flow characteristics, velocity, temperature, concentration, skin friction rate, heat, and mass transfer rates are analyzed with the variations of governing parameters, Prandtl number, buoyancy parameter, Schmidt number, buoyancy ratio, Soret and Dufour parameters at various stream-wise spots of the flow. To certify the exactness of the listed computations, we performed a comparison with prior published computations, which were found with great agreement, and the residual analysis study was also portrayed to reflect the convergence and stability of the adopted numerical technique.     

Mixed convection heat and mass transfer over a vertical plate in a power‐law fluid‐saturated porous medium with radiation and chemical reaction effects

Mixed convection heat and mass transfer from a vertical plate embedded in a power‐law fluid‐saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using the shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21058     

Bioconvection in a squeezing flow of a micropolar fluid in a horizontal channel

The bioconvection flow of an incompressible micropolar fluid containing microorganisms between two infinite stretchable parallel plates is considered. A mathematical model, with a fully coupled nonlinear system of equations describing the total mass, momentum, thermal energy, mass diffusion, and microorganisms is presented. The governing equations are reduced to a set of nonlinear ordinary differential equations with the help of suitable transformations. The resulting nonlinear ordinary differential equations are linearized using successive linearization method, and the resulting system of linear equations is solved using the Chebyshev collocation method. The detailed analysis illustrating the influences of various physical parameters, such as the micropolar coupling number, squeezing parameter, the bioconvection Schmidt number, Prandtl numbers, Lewis number, and bioconvection Peclet number on the velocity, microrotation, temperature, concentration and motile microorganism distributions, skin friction coefficient, Nusselt number, Sherwood number, and density number of motile microorganism, is examined. The influence of the squeezing parameter is to increase the dimensionless velocities and temperature and to decrease the local Nusselt number and local Sherwood number. The density number of motile microorganism is decreasing with squeezing parameter, bioconvection Lewis number, bioconvection Peclet number, and bioconvection Schmidt number.     

Effects of nonlinear Boussinesq approximation and double dispersion on a micropolar fluid flow under convective thermal condition

This article investigates the effect of double dispersion on the natural convective flow of a micropolar fluid along an inclined plate in the presence of the convective thermal condition. In addition, the nonlinear convection is considered to analyze the heat and mass transfer phenomena of thermal systems, which are performed at moderate‐ and high‐level temperatures. A combination of local nonsimilarity and successive linearization techniques is used to evaluate the associated complicated nondimensional governing equations. This study discusses the impact of relevant factors on the fluid characteristics through graphs. The influence of nonlinear convection parameters on the heat and mass transfer rates seems to be more in Darcy porous media compared with that in non‐Darcy porous media.     

Peristaltic pumping of a micropolar fluid in a tube

Summary.  Peristaltic transport of a micropolar fluid in a circular tube is studied under low Reynolds number and long wavelength approximations. The closed form solutions are obtained for velocity, microrotation components, as well as the stream function and they contain new additional parameters namely, N the coupling number and m the micropolar parameter. In the case of free pumping (pressure difference Δp=0) the difference in pumping flux is observed to be very small for Newtonian and micropolar fluids but in the case of pumping (Δp>0) the characteristics are significantly altered for different N and m. It is observed that the peristalsis in micropolar fluids works as a pump against a greater pressure rise compared with a Newtonian fluid. Streamline patterns which depict trapping phenomena are presented for different parameter ranges. The limit on the trapping of the center streamline is obtained. The effects of N and m on friction force for different Δp are discussed. Received June 20, 2002; revised October 23, 2002 Published online: April 17, 2003 The authors thank the referees for pointing out some mistakes in the governing equations and for the suggestions to improve the presentation of the paper.     

Mixed convection in a doubly stratified micropolar fluid saturated non‐Darcy porous medium

The effects of thermal and solutal stratification on mixed convection along a vertical plate embedded in a micropolar fluid saturated non‐Darcy porous medium are analysed. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms by pseudo‐similarity variables. The resulting system of equations is then solved numerically using the Keller‐box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The velocity, microrotation, temperature and concentration profiles are shown for different values of the coupling number, non‐Darcy parameter, mixed convection parameter, thermal and solutal stratification parameters. The numerical values of the skin friction, wall couple stress, heat and mass transfer rates for different values of governing parameters are also tabulated. © 2011 Canadian Society for Chemical Engineering     

Combined radiation and mixed convection from a vertical wall with suction/injection in a non–Darcy porous medium

Summary. Mixed convection flow of an absorbing fluid up a uniform non–Darcy porous medium supported by a semi-infinite ideally transparent vertical flat plate due to solar radiation is considered. The external flow field is assumed to be uniform, the effect of the radiation parameter in the boundary layer adjacent to the vertical flat plate with fluid suction/injection through it is analyzed in both aiding and opposing flow situations. It is observed that the similarity solution is possible only when the fluid suction/injection velocity profile varies as x^–1/2. The velocity and temperature profiles in the boundary layer and the heat transfer coefficient are presented for selected values of the parameters. It is observed that the Nusselt number increases with the increase in the radiation parameter and also when the value of the surface mass flux parameter moves from the injection to the suction region.