An Investigation Into Fluid Flow, Heat and Mass Transfer in a Vertical Porous Annular Cylinder with Outer Wall Subjected to Natural Convection

Mukesh Patil Mukesh Patil, TJPRC
2020 International Journal of Mechanical and Production Engineering Research and Development  
Heat and mass transfer along with fluid flow in a vertical annular cylinder embedded with porous medium for the convective boundary condition of the outer wall is analysed in the present work. The fluid flow and heat transfer are assumed to take place by pure natural convection. The inner wall is subjected to uniform temperature. The species concentration is also assumed to be uniform at the inner wall. The fluid is assumed to obey Darcy's law. The governing partial differential equations are
more » ... ial equations are non-dimensionalised using suitable non-dimensional parameters and the solution is obtained by finite element analysis. The porous medium is divided using triangular elements of uneven size. MATLAB is used to solve the coupled energy, species and momentum equations in an iterative manner. The effects of Rayleigh number and Biot number on the fluid flow and heat transfer for different design parameters of the porous annulus are investigated. The design parameters considered for the present study are aspect ratio and radius ratio. The flow patterns and temperature distribution for the varying Rayleigh number and Biot number are also discussed in the present work. Also the effect of Lewis number on the mass transfer for the same design parameters, as mentioned above are investigated. The species concentration distribution for varying Lewis number is also discussed in the present work. The results reveal that the convection increases with the Rayleigh number. Convection also increases with the radius ratio. It is observed that the convection decreases with the increase in Aspect ratio. It is also observed that the convection increases with Biot number, however the increase in convection is not significant for higher values of Biot number. The mass transfer increases substantially with the increase in Lewis number. 14658 Mukesh Patil Impact Factor (JCC): 8.8746 SCOPUS Indexed Journal NAAS Rating: 3.11 problem of heat transfer in saturated porous vertical annulus with combined effect of radiation and convection has been studied by Irfan et al. [7]. Inspired by electric heating elements, Wang [8] has given a set of critical Rayleigh numbers for various size ratios of cylinder at which the convection heat transfer starts. Here the bottom surfaces of the cylinder were subjected to constant heat flux with the side walls being insulated. The problem of heat transfer in a vertical porous annulus requires attention as it has many practical applications such as gas cooled reactor vessels, bio-mass converters, insulated pipe lines, heat exchangers, geophysical applications, etc. Yet, to the best knowledge of the authors there appears to be no study in the literature, concerned with the effect of convection (hT∞) at the outer wall of a saturated vertical porous annular cylinder with uniform temperature ( ̅ ) and uniform concentration boundary conditions ( ̅ ) on the inner wall. The objective of the present work is to study the effect of Rayleigh number, Biot number on the fluid flow and heat transfer and also the effect of Lewis number on mass transfer for different design parameters of the vertical porous annular cylinder with natural convection at the outer wall, while maintaining uniform temperature and concentration boundary condition on the inner wall.
doi:10.24247/ijmperdjun20201394 fatcat:pixvszkqknhi3jl2rrg3go5aty