V. R. Prasad

Numerical study of heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects

A numerical solution is presented for the natural convective dissipative heat transfer of an incompressible, third grade, non-Newtonian fluid flowing past an infinite porous plate embedded in a Darcy–Forchheimer porous medium. The mathematical model is developed in an (x,y) coordinate system. Using a set of transformations, the momentum equation is rendered one-dimensional and a partly linearized heat conservation equation is derived. The viscoelastic formulation presented by Akyildiz (2001 Int. J. Non-Linear Mechanics 36 349–52) is adopted, which generates lateral mass and viscoelastic terms in the heat conservation equation, as well as in the momentum equation. A number of special cases of the general transformed model are discussed. A finite element method is implemented to solve, with appropriate boundary conditions, the coupled third-order, second degree ordinary differential equation for momentum and the second-order, fourth degree heat conservation equation. We study the influence of the third grade viscoelastic parameter (β3), Darcian parameter (inversely proportional to permeability (kp)), the Forchheimer inertial parameter (b), transpiration velocity (Vo), the transpiration parameter in the heat equation (R) and the thermal conductivity parameter (S) on momentum and heat transfer. Additionally, we study the influence of the Forchheimer inertial parameter (b) on second-order viscoelastic non-Darcy free convection flow and also the effects of the third grade parameter (β3) on Darcian free convection. Velocities increase with rising permeability (Darcian parameter) for both second and third grade viscoelastic free convection regimes and decrease with rising Forchheimer parameter. The effects of the other parameters are described at length. The flow scenario is important in chemical engineering processes.

NUMERICAL STUDY OF MIXED BIOCONVECTION IN POROUS MEDIA SATURATED WITH NANOFLUID CONTAINING OXYTACTIC MICROORGANISMS

A mathematical model has been developed for steady-state boundary layer flow of a nanofluid past an impermeable vertical flat wall in a porous medium saturated with a water-based dilute nanofluid containing oxytactic microorganisms. The nanoparticles were distributed sufficiently to permit bioconvection. The product of chemotaxis constant and maximum cell swimming speed was assumed invariant. Using appropriate transformations, the partial differential conservation equations were non-dimensionalised to yield a quartet of coupled, non-linear ordinary differential equations for momentum, energy, nanoparticle concentration and dimensionless motile microorganism density, with appropriate boundary conditions. The dominant parameters emerging in the normalised model included the bioconvection Lewis number, bioconvection Peclet number, Lewis number, buoyancy ratio parameter, Brownian motion parameter, thermophoresis parameter, local Darcy-Rayleigh number and the local Peclet number. An implicit numerical solution to the well-posed two-point non-linear boundary value problem is developed using the well-tested and highly efficient Keller box method. Computations are validated with the Nakamura tridiagonal implicit finite difference method, demonstrating excellent agreement. Nanoparticle concentration and temperature were found to be generally enhanced through the boundary layer with increasing bioconvection Lewis number, whereas dimensionless motile microorganism density was only increased closer to the wall. Temperature, nanoparticle concentration and dimensionless motile microorganism density were all greatly increased with a rise in Peclet number. Temperature and dimensionless motile microorganism density were reduced with increasing buoyancy parameter, whereas nanoparticle concentration was increased. The present study found applications in the fluid mechanical design of microbial fuel cell and bioconvection nanotechnological devices.

Thermo-Diffusion and Diffusion-Thermo Effects on MHD Free Convective Heat and Mass Transfer from a Sphere Embedded in a Non-Darcian Porous Medium

The problem of combined heat and mass transfer by natural convection over a sphere in a homogenous non-Darcian porous medium subjected to uniform magnetic field is numerically studied, taking Soret/Dufour effects into account. The coupled, steady, and laminar partial differential conservation equations of mass, momentum, energy, and species diffusion are normalized with appropriate transformations. The resulting well-posed two-point boundary value problem is solved using the well-tested, extensively validated Keller-Box implicit finite difference method, with physically realistic boundary conditions. A parametric study of the influence of Soret number (Sr), Dufour number (Du), Forchheimer parameter (Λ), Darcy parameter (Da), buoyancy ratio parameter (𝑁), Prandtl number (Pr), Schmidt number (Sc), magnetohydrodynamic body force parameter (𝑀), wall transpiration (𝑓𝑤) is the blowing/suction parameter, and streamwise variable (ξ) on velocity, temperature, and concentration function evolution in the boundary layer regime is presented. Shear stress, Nusselt number, and Sherwood number distributions are also computed. Applications of the study arise in hydromagnetic flow control of conducting transport in packed beds, magnetic materials processing, geophysical energy systems, and magnetohydrodynamic chromatography technology.

Keller Box and Smoothed Particle Hydrodynamic Numerical Simulation of Two-Phase Transport in Blood Purification Auto- Transfusion Dialysis Hybrid Device with Stokes and Darcy Number Effects

A computational simulation of laminar natural convection fully-developed multi-phase suspension in a porous medium channel is presented. The Darcy model is employed for the porous material which is valid for low velocity, viscous-dominated flows. The Drew-Marble fluid-particle suspension model is employed to simulate both particulate (red blood cell) and fluid (plasma) phases. The transformed two-point nonlinear boundary value problem is shown to be controlled by a number of key dimensionless thermo-physical parameters, namely the Darcy number (Da), momentum inverse Stokes number (Sk m ), particle loading parameter (p L ), inverse thermal Stokes number (Sk T ), particle-phase wall slip parameter (W) and buoyancy parameter (B). Detailed numerical solutions are presented with an optimized K eller B ox implicit finite difference M ethod ( KBM ) for the influence of these parameters on the fluid-phase velocity (U) and particle-phase velocity (Up). Validation is also included using the S moothed P article H ydrodynamic ( SPH ) Lagrangian method and excellent correlation achieved. Increasing Darcy number is observed to significantly accelerate the fluid-phase flow and less dramatically enhance particle-phase velocity field. Magnitudes of fluid phase velocity are also elevated with both increasing viscosity ratio and particle-phase wall slip parameter. Increasing buoyancy effect depresses particle phase velocity. An increase in particle loading parameter is also observed to suppress both fluid and particle phase velocities. No tangible change in fluid or particle phase temperatures is computed with increasing Darcy number. The study is relevant to dialysis devices exploiting thermal and porous media filtration features.