@article{5bd968d772be465a827b5efe3030bfb0,
title = "A numerical investigation of a buoyancy driven flow in a semi-porous cavity: Comparative effects of ramped and isothermal wall conditions",
abstract = "Steady two-dimensional natural convection taking place in a rectangular cavity, partially filled with an isotropic porous material, has been investigated numerically using an ADI method. It is assumed that one of the vertical walls of the cavity has a ramped temperature distribution. The vorticity-stream function formulation has been used to solve the set of nonlinear partial differential equations governing the flows in the clear region and the adjoining porous region. The effects of Darcy number and Rayleigh number have been discussed in detail.",
keywords = "Brinkman model, Coupled flow, Free convection, Numerical solution, Ramped boundary condition, Rectangular cavity",
author = "Pallath Chandran and Sacheti, {Nirmal C.} and Singh, {Ashok K.}",
note = "Funding Information: This paper deals with a steady two-dimensional free convective coupled flow taking place in the confines of a rectangular vertical cavity with impermeable bounding walls. The cavity space is assumed to consist of a clear fluid region overlying a fluid-saturated porous medium, with Brinkman model governing the flow in the permeable region. It is further assumed that the left vertical wall of the cavity is subjected to ramped temperature distribution. The governing flow equations for each region, allowing for Boussinesq approximation and formulated in terms of vorticity and stream function, have been solved numerically subject to a host of boundary and matching conditions using an ADI method. The influence of two key parameters – Darcy number and the Rayleigh number – on the streamlines, isotherms and fluid temperature, has been discussed in detail. The results for ramped temperature case have been compared with the corresponding results for isothermal temperature profile. Some quantities of interest, arising in a number of applications, have also been computed. Acknowledgements. (a) This research was supported by the Sultan Qaboos University Research Grant No. IG/SCI/DOMS/09/06. (b) The authors thank the referee for the valuable comments and suggestions.",
year = "2013",
month = jun,
doi = "10.2478/johh-2013-0014",
language = "English",
volume = "61",
pages = "103--111",
journal = "Journal of Hydrology and Hydromechanics",
issn = "0042-790X",
publisher = "Slovak Academy of Sciences",
number = "2",
}