Analysis of Heat and Mass Transfer in a Vertical Annular Porous Cylinder Using FEM

Abstract

The present study is intended to study heat and mass transfer in a vertical annular cylinder embedded with saturated porous medium. The inner surface of cylinder is maintained at uniform wall temperature and uniform wall concentration. The governing partial differential equations are non-dimensionalised and solved by using finite element method (FEM). The porous medium is discritised using triangular elements with uneven element size. Large number of smaller-sized elements are placed near the walls of the annulus to capture the smallest variation in solution parameters. The results are reported for both aiding and opposing flows. The effects of various non-dimensional numbers such as buoyancy ratio, Lewis number, Rayleigh number, aspect ratio, etc on heat and mass transfer are discussed. The temperature and concentration profiles are presented.123 698 I. A. Badruddin et al.

Double diffusion in square porous cavity subjected to conjugate heat transfer

“…draws the conclusion of Lewis number (Le) As observed in case of heat and mass transfer[12], Lewis number influences the mass transfer substantially. This is obvious from present case (figure 4), that shows highly distorted iso-concentration lines as compared to isotherms, when Lewis number (Le) is increased from 1 to 25.…”

“…The literature reveals that various heat transfer characteristics of porous cavities have been investigated and reported by many researchers. For instance, the heat transfer has been investigated in porous cavities and porous annulus by applying hot temperature at left vertical wall and maintaining cold temperature at the right wall [7][8][9][10][11][12][13]. This included the investigation of heat transfer along with difficult boundary conditions or various other phenomenon such as viscous irregular cavity [7], viscous dissipation [8][9][10], Soret and Dufor effect [11], heat and mass transfer [12] , the effect of heat generating strip placed inside the porous cavity [13], wavy tube heat exchanger [14], flow of nanofluid inside the porous media [15][16][17] etc.…”

Investigation of heat transfer in irregular porous cavity subjected to various boundary conditions

“…Investigation of heat transfer in regular porous cavity (Jecl and Kerget, 2003; Bahloul, 2006; Saeid and Pop, 2004; Badruddin et al , 2006a, 2007a; Sharif and Mohammad, 2005; Nazari et al , 2015) has been the best choice of research for many researchers, probably because of its applications as well as simple geometry and boundary conditions involved, making it relatively easy to analyze. It is also notable that porous medium confined in the cylindrical geometry with axisymmetric boundary condition can also be treated as cavity (Rajamani et al , 1995; Prasad and Kulacki, 1984; Badruddin et al , 2012a, 2012b, 2012c; Ahmed et al , 2011, 2014) with proper care of governing equations. The increased complexity either in porous geometry or the boundary conditions is somewhat involved process.…”

“…The literature suggests that there has been renewed interest to study the uncommon or irregular shapes of cavity containing the porous medium. For instance, there have been studies conducted with respect to the square porous annulus (Badruddin et al , 2012a, 2012b; Nik-Ghazali et al , 2014; Ebaid and Bataresh, 2017). It was found that the temperature in such cavities exhibits peculiar behavior with Nusselt number showing dependence on the length of internal boundary.…”

Simplified finite element algorithm to solve conjugate heat and mass transfer in porous medium

“…In this process, one must be aware of two fundamental points: first, it does not calculate exact solutions but approximate ones; second, it discretizes the problem by representing functions by a finite number of values, that is, to move from the “continuous” to the “discrete”. There are numerous methods for the numerical approximation of PDEs, among them, popularly adopted are finite element method (Lewis and Garner, 1972; Strada and Lewis, 1980; Morgan et al , 1984; Tadayon et al ,1987; Ahmed et al , 2011; Ahmed et al , 2009; Badruddin et al , 2006a, 2006b, 2007a, 2007b, 2012a, 2012b, 2012c; Li and Rui, 2015; Sajid et al , 2008; Balla and Kishan, 2015; Wansophark et al , 2005) finite difference method (Achemlal and Sriti, 2015; del Teso, 2014; Oka et al , 1994; Rui and Liu, 2015; Liu and Yuan, 2008; Sheremet and Pop, 2014; Chamkha and Muneer, 2013; Sheremet, 2015) and finite volume method (Dotlić, 2014; Kumar, 2012). These finite element, finite difference and finite volume methods require that each PDE be converted into its equivalent set of algebraic equations that depends on the number of elements into which the physical domain is divided.…”