B. V. Rathish Kumar

NATURAL CONVECTION HEAT TRANSFER FROM A HORIZONTAL WAVY SURFACE IN A POROUS ENCLOSURE

Abstract The effect of surface undulations on the natural convection heat transfer from an isothermal surface in a Darcian fluid-saturated porous enclosure has been numerically analyzed using the finite element method on a graded nonuniform mesh system. The flow-driving Rayleigh number Ra together with the geometrical parameters of wave amplitude a, wave phase φ, and the number of waves N considered in the horizontal dimension of the cavity are found to influence the flow and heat transfer process in the enclosure. For Ra around 50 and above, the phenomenon of flow separation and reattachment is noticed on the waits of the enclosure. A periodic shift,n the reattachment point from the bottom wall to the adjacent walls in the clockwise direction, leading to the manifestation of cycles of unicellular and bicellular clockwise and counterclockwise flows, is observed, with the phase varying between 0° and 350°. The counterflow in the secondary circulation zone is intensified with the increase in the value of Ra...

A Study of Free Convection Induced by a Vertical Wavy Surface with Heat Flux in a Porous Enclosure

Free convection induced by a vertical wavy surface with uniform heat flux in a porous enclosure has been analyzed numerically using the finite element method (FEM). The flow and the convection process in the cavity is found to be sensitive to the flow parameter Rayleigh number (Ra), and geometrical parameters like wave amplitude (a), wave phase (φ), and number of waves (N) in the vertical dimension of the cavity. The study reveals that small sinusoidal drifts from the smoothness of a vertical wall with a phase angle of 60o and high frequency enhances the free convection from a vertical wall with uniform heat flux.

NATURAL CONVECTION IN A THERMALLY STRATIFIED WAVY VERTICAL POROUS ENCLOSURE

The effect of surface undulations on natural convection in a thermally stratified vertical porous enclosure has been analyzed numerically by the finite-element method. The influence of increasing number of surface undulations ( N ) with different wave phases (φ) and different wave amplitudes ( a ) has been analyzed. Increasing either number of waves per unit length ( N ) or wave amplitudes ( a ) or thermal stratification ( S ) is seen to decrease Nusselt number (Nu). Interestingly, the periodic variation in Nu with wave phase in the presence of thermal stratification is seen to be sensitive to the number of waves ( N ) per unit length. Maximum heat flux is obtained when the wave phase 210° h φ h 240° for 0 h S h 1. Features such as secondary circulations near the wavy wall and multicellular circulations in the core of the flow field have been noticed.

Free convection in a non-Darcian wavy porous enclosure

A numerical study of non-Darcian natural convection in a wavy vertical enclosure filled with a porous medium is performed. The flow is modelled using Forchheimer extended Darcy model. The governing equations are solved by finite element method. Numerical results demonstrate the importance of non-Darcian effect. Cumulative heat flux and Nusselt number together with flow and temperature distributions in the form of streamlines and isotherms are presented for a wide range of governing parameters like Grashof number, Rayleigh number, wave amplitude, wave phase and roughness parameter.

ON THE INFLUENCE OF WALL PROPERTIES IN THE PERISTALTIC MOTION OF MICROPOLAR FLUID

We carry out a study of the peristaltic motion of an incompressible micropolar fluid in a two-dimensional channel. The effects of viscoelastic wall properties and micropolar fluid parameters on the flow are investigated using the equations of the fluid as well as of the deformable boundaries. A perturbation technique is used to determine flow characteristics. The velocity profile is presented and discussed briefly. We find the critical values of the parameters involving wall characteristics, which cause mean flow reversal.

Effect of thermal stratification on double-diffusive natural convection in a vertical porous enclosure

A numerical study on combined heat and mass transfer by natural convection adjacent to a vertical surface in a thermally stratified fluid saturated square porous enclosure is reported. The Galerkin finite element method on a graded grid system has been employed in the numerical computations. When thermal and species diffusion coefficients are equal, increasing levels of thermal stratification significantly influence both the aiding and opposing flow structures and their concomitant temperature fields. For unequal species and thermal diffusion coefficients changes in the concentration field structure are seen to be more prominent. The Nusselt (Nu) and Sherwood (Sh) number data have been presented for various values of Lewis number (Le), buoyancy ratio (B), and Rayleigh number ( Ra ) at various levels of stratification (S).

FREE CONVECTION HEAT TRANSFER FROM AN ISOTHERMAL WAVY SURFACE IN A POROUS ENCLOSURE

The coupled streamfuction–temperature equations governing the Darcian flow and convection process in a fluid-saturated porous enclosure with an isothermal sinusoidal bottom sun face, has been numerically analyzed using a finite element method (FEM). No restrictions have been imposed on the geometrical non-linearity arising from the parameters like wave amplitude (a), number of waves per unit length (N), wave phase (Φ), aspect ratio (A) and also on the flow driving parameter Rayleigh number (Ra). The numerical simulations for varying values of Ra bring about interesting flow features, like the transformation of a unicellular flow to a multicellular flow. Both with increasing amplitude and increasing number of waves per unit length, owing to the shift in the separation and reattachment points, a row–column pattern of multicellular flow transforms to a simple row of multicellular flow. A cycle of n celluar and n+1 cellular flows, with the flow in adjacent cells in the opposite direction, periodically manifest with phase varying between 0 and 360°. The global heat transfer into the system has been found to decrease with increasing amplitude and increasing number of waves per unit length. Only marginal changes in the global heat flux are observed, either with increasing Ra or varying Φ. Effectively, sinusoidal bottom surface undulations of the isothermal wall of a porous enclosure reduces the heat transfer into the system.

Parallel computation of natural convection in trapezoidal porous enclosures

In this study, coupled non-linear partial differential equations governing the natural convection from an isothermal wall of a trapezoidal porous enclosure have been solved numerically by finite element method (FEM) in conjunction with GMRES, a Krylov subspace based solver. In view of the enormous amount of computation, a parallel numerical algorithm for incomplete LU-conjugate gradient (ILU-CG) solver on eight-noded ANUPAM cluster under MIMD paradigm based on ANULIB message passing library has been developed. Parallel computations have been carried out for various values of flow and geometric parameters both under Darcian and non-Darcian assumptions on the porous model. Cumulative heat fluxes and Nusselt number (Nu) associated with convection process are presented through computer generated plots.

Combined Influence of Mass and Thermal Stratification on Double-Diffusion Non-Darcian Natural Convection From a Wavy Vertical Wall to Porous Media

We analyze the combined influence of mass and thermal stratification on non-Darcian double-diffusive natural convection from a wavy vertical wall to a porous media. A finite difference scheme based on the Keller box approach is derived for the boundary layer equations resulting from the use of nonsimilarity transformation on the coupled nonlinear partial differential equations. Extensive numerical simulations are carried out to analyze the influence of wave amplitude a, Grashof number Gr * , thermal stratification parameter S T , concentration stratification parameter S C , buoyancy ratio B, and Lewis number Le on the double-diffusive natural convection process

Double diffusive natural convection in a doubly stratified wavy porous enclosure

Combined heat and mass transfer process by natural convection along a vertical wavy surface in a thermal and mass stratified fluid saturated porous enclosure has been numerically analysed. Finite element method has been used and the influence of varying flow, heat and mass transfer governing parameters has been reported. Presence of thermal and mass stratification terms reduces the Nusselt number and Sherwood number values in all the cases. The flow circulation pattern which is anti-clockwise when the species buoyancy forces are opposing the thermal buoyancy forces, gets clockwise when the forces are aiding. When the two buoyancy forces are equal and opposing, a multi-cellular pattern with alternating circulation orientation manifests. Several other interesting features such as thermal and mass boundary layers, thermal plumes, secondary circulation zones, flow intensification etc. are noticed in the flow, temperature and concentration fields with varying flow, heat and mass transfer governing parameters.