Mixed Convection Heat Transfer in the Annulus Between Two Concentric Vertical Cylinders Using Porous Layers

Abstract

A numerical investigation of the steady-state, laminar, axi-symmetric, mixed convection heat transfer in the annulus between two concentric vertical cylinders using porous inserts is carried out. The inner cylinder is subjected to constant heat flux and the outer cylinder is insulated. A finite volume code is used to numerically solve the sets of governing equations. The Darcy-Brinkman-Forchheimer model along with Boussinesq approximation is used to solve the flow in the porous region. The Navier-Stokes equation is used to describe the flow in the clear flow region. The dependence of the average Nusselt number on several flow and geometric parameters is investigated. These include: convective parameter, λ, Darcy number, Da, thermal conductivity ratio, K r , and porous-insert thickness to gap ratio (H/D). It is found that, in general, the heat transfer enhances by the presence of porous layers of high thermal conductivity ratios. It is also found that there is a critical thermal conductivity ratio on which if the values of Kr are higher than the critical value the average Nusselt number starts to decrease. Also, it found that at low thermal conductivity ratio (K r ≈ 1) and for all values of λ the porous material acts as thermal insulation.Keywords Mixed convection · Porous media · Darcy-Brinkman-Forchheimer model · Heat transfer · Critical thermal conductivity ratio Nomenclature C F Forchheimer coefficient , C F = 1.75/ 150φ 5 C p Specific heat (J kg −1 K −1 ) D Gap between the two concentric cylinders (r o − r i ) [m] Da Darcy number (K /D 2 )

Numerical study of natural convection in a vertical porous annulus with discrete heating

“…Three porous inserts are attached at the inner cylinder of the annulus in the form of porous rings and the flow equations are solved by considering two different set of equations for fluid and porous domains. Later, Al-Zahrani and Kiwan [23] numerically analyzed the mixed convection in an open-ended vertical annulus with a porous layer attached to the outer surface of the inner cylinder. They considered the Darcy-Brinkman-Forchheimer model for the porous region and the Navier-Stokes equation for the clear fluid region, and found that the heat transfer can be enhanced by using porous layers of high thermal conductivity ratios.…”

“…Relative to a large volume of investigations in the porous annulus, we noticed that the preceding works on natural convection in a vertical porous annulus are limited to uniform heating of the inner wall by either isothermal or isoflux wall-heating conditions [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. However, in many practical applications, heating takes place over a portion of one of the vertical walls, where the size and location of the heating segment may significantly affect the heat transport process in the annular enclosure filled with a fluid-saturated porous media.…”

Double-Diffusive Convection from a Discrete Heat and Solute Source in a Vertical Porous Annulus

“…Among the finite porous enclosures, free convective heat transfer in a differentially heated vertical porous annulus has received considerable attention owing to its importance in high performance insulation for buildings and porous heat exchangers (Hickox and Gartling 1985;Char and Lee 1998;Al-Zahrani and Kiwan 2009;Shivakumara et al 2003;Prasad 1986). Natural convection in square and rectangular porous enclosures subject to discrete heating has drawn much attention in recent years.…”

Numerical investigation of transient mixed convection of nanofluid in a cavity with non-Darcy porous inner block and rotating cylinders with harmonic motion

“…They found that for a low thermal conductivity ratio, the difference between fluid and solid temperatures was at its highest level. Al Zahrani et al 4 performed an analysis of the mixed convection in the porous space between twain concentric cylinders. The obtained results show that if the thermal conductivity ratio is further than its critical value, the average Nusselt number decreases.…”