Commerce and Shanti Kumar Gubbi Science College

Dharwad, India

Commerce and Shanti Kumar Gubbi Science College

Dharwad, India

Time filter

Source Type

Patil P.M.,Commerce and Shanti Kumar Gubbi Science College | Patil P.M.,University of Bath | Rees D.A.S.,University of Bath
Transport in Porous Media | Year: 2013

In this paper we investigate the onset of convection in a saturated porous medium where uniform suction into a horizontal and uniformly hot bounding surface induces a stationary thermal boundary layer. Particular attention is paid to how the well-known linear stability characteristics of this boundary layer are modified by the presence of local thermal nonequilibrium effects. The basic conduction state is determined and it is found that the boundary layer forms two distinct regions when the porosity is small or when the conductivity of the fluid is small compared with that of the solid. A linearised stability analysis is performed which results in an ordinary differential eigenvalue problem for the critical Darcy-Rayleigh number as a function of the wave number and the two nondimensional parameters, H and γ, which are associated with local thermal nonequilibrium. This eigenvalue problem is solved numerically by first approximating the equations by fourth order compact finite differences, and then the critical Rayleigh number is computed iteratively using the inverse power method and minimised over the wavenumber. The variation of the critical Rayleigh number and wavenumber with H and γ is presented. One of the unusual effects of local thermal nonequilibrium is that there exists a parameter regime within which the neutral curve is bimodal. © 2013 Springer Science+Business Media Dordrecht.


Patil P.M.,Commerce and Shanti Kumar Gubbi Science College | Patil P.M.,University of Bath | Rees D.A.S.,University of Bath
International Journal of Heat and Mass Transfer | Year: 2014

The principal objective of the present paper is to investigate the onset of convection in a horizontal layer heated from below which consists of distinct porous sublayers which are separated by solid heat-conducting partitions. Each of the porous sublayers are identical as are the solid partitions. The present analysis employs linearised stability theory and a dispersion relation is derived from which neutral curves may be computed. For two-layer configurations the dispersion relation may be written explicitly, but for larger numbers of sublayers a simple systematic numerical procedure is used to compute the dispersion relation which, while it may also be written analytically, rapidly becomes increasingly lengthy as the number of sublayers increases. It is found that neutral curves are always unimodal and each has a well-defined single minimum. We attempt to give a comprehensive physical understanding of the effect of the number of layer, the relative thickness of the partitions and the conductivity ratio on the onset of convection and the form taken by the onset modes. Our results are compared with those of Rees and Genç (2011) [1] who considered the special case where the partitions are infinitesimally thin. © 2013 Published by Elsevier Ltd.


Patil P.M.,Commerce and Shanti Kumar Gubbi Science College | Roy S.,Indian Institute of Technology Madras | Pop I.,Technical University of Cluj Napoca
Chemical Engineering Communications | Year: 2013

An unsteady mixed convection flow over a permeable nonlinearly stretching vertical slender cylinder is considered to investigate the combined effects of thermal and mass diffusion in the presence of surface mass transfer and linear chemical reaction, where the slender cylinder is in line with the flow. The unsteadiness in the flow, temperature, and concentration fields is caused by the continuously nonlinearly stretching vertical slender cylinder. The effect of surface curvature is also taken into account, particularly for the applications of wire and fiber drawing where exact predictions are expected. The governing boundary layer equations are transformed into a nondimensional form by a group of nonsimilar transformations. The resulting system of coupled nonlinear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical computations are performed to understand the physical situations of linearly and nonlinearly stretching surface for various values of the governing parameters to display the effects of velocity, temperature, and concentration profiles graphically. Our main objective in this work is to focus on opposing flow situations. Numerical results for the local skin-friction coefficient, local Nusselt number, and local Sherwood number are also presented. The present results are compared with previously published work, and these comparisons are found to be in excellent agreement. © 2013 Copyright Taylor and Francis Group, LLC.


Patil P.M.,Commerce and Shanti Kumar Gubbi Science College | Roy S.,Indian Institute of Technology Madras | Pop I.,Technical University of Cluj Napoca
Chemical Engineering Communications | Year: 2012

In this article, a numerical investigation on a steady two-dimensional mixed convection boundary layer flow along a moving semi-infinite vertical plate is presented. The plate is assumed to move with a constant velocity in the direction of the flow. The influence of internal heat generation or absorption is also included in the analysis. The nonlinear partial differential equations governing the flow and thermal fields are written in nondimensional form using a suitable group of transformations. The final nondimensional set of coupled nonlinear partial differential equations is solved using an implicit finite difference scheme in combination with the quasi-linearization technique. The effects of various parameters on the velocity and temperature profiles are reported. In addition, numerical results are presented for the skin friction coefficient and the Nusselt number. The present results are compared with previously published work and are found to be in excellent agreement. © 2012 Taylor and Francis Group, LLC.


Patil P.M.,Commerce and Shanti Kumar Gubbi Science College | Roy S.,Indian Institute of Technology Madras | Pop I.,Technical University of Cluj Napoca
Computers and Fluids | Year: 2012

An unsteady mixed convection boundary layer flow over a permeable non-linearly stretching vertical slender cylinder is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of surface mass transfer, where the slender cylinder is in line with the flow. The unsteadiness in the flow and temperature fields is caused by the continuously non-linearly stretching vertical slender cylinder. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical computations are performed to understand the physical situations of linear and non-linearly stretching surface for different values of parameters to display the velocity and temperature profiles graphically. The obtained results show that the buoyancy parameter λ and the Prandtl number Pr enhance the skin friction coefficient and the local Nusselt number. It is also shown that the suction parameter A (>0) is to decrease the velocity and temperature profiles, but injection parameter A (<0) does the reverse. Results are compared with previously published work and are found to be in excellent agreement. © 2011 Elsevier Ltd.


Patil P.M.,Commerce and Shanti Kumar Gubbi Science College | Chamkha A.J.,Public Authority for Applied Education and Training | Roy S.,Indian Institute of Technology Madras
Meccanica | Year: 2012

This paper reports a detailed numerical investigation on mixed convection flow of a polar fluid through a porous medium due to the combined effects of thermal and mass diffusion. The energy equation accounts for heat generation or absorption, while the nth order homogeneous chemical reaction between the fluid and the diffusing species is included in the mass diffusion equation. The governing equations of the linear momentum, angular momentum, energy and concentration are obtained in a non-similar form by introducing a suitable group of transformations. The final set of non-similar coupled non-linear partial differential equations is solved using an implicit finite-difference scheme in combination with quasi-linearization technique. The effects of various parameters on the velocity, angular velocity, temperature and concentration fields are investigated. Numerical results for the skin friction coefficient, wall stress of angular velocity, Nusselt number and Sherwood number are also presented. © 2011 Springer Science+Business Media B.V.


Patil P.M.,Commerce and Shanti Kumar Gubbi Science College | Anilkumar D.,Albany State University | Roy S.,Indian Institute of Technology Madras
International Journal of Heat and Mass Transfer | Year: 2013

An unsteady mixed convection flow over a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of Newtonian heating in which heat transfer rate from the surface is proportional to the local temperature and thermal radiation effects. It is assumed that the unsteadiness is caused by the time dependent free stream velocity as well as by the moving plate velocity. The governing boundary layer equations with boundary conditions are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Computations are performed and representative set is displayed graphically to illustrate the influence of the mixed convection parameter (λ), Prandtl number (Pr), the ratio of free stream velocity to the composite reference velocity (ε), stream wise co ordinate (ξ) and thermal radiation parameter (R) on the velocity and temperature profiles. The numerical results for the local skin-friction coefficient (ReL1/2Cf) and wall temperature (GW(ξ,0)) are also presented. The numerical results are presented in graphs revealing some interesting features of flow and heat transfer phenomena in this study. Present results are also compared with previously published works and are found to be in excellent agreement. © 2013 Elsevier Ltd. All rights reserved.

Loading Commerce and Shanti Kumar Gubbi Science College collaborators
Loading Commerce and Shanti Kumar Gubbi Science College collaborators