Laminar free convection in horizontal annulus filled with glass beads and with annular fins on the inner cylinder

الملخص EN

An experimental and numerical study has been carried out to investigate the heat transfer by natural convection and radiation in a two dimensional annulus enclosure filled with porous media (glass beads) between two horizontal concentric cylinders.

The outer cylinders are of (100, 82 and70mm) outside diameters and the inner cylinder of 27 mm outside diameter with (or without) annular fins attached to it.

Under steady state condition; the inner cylinder surface is maintained at a high temperature by applying a uniform heat flux and the outer cylinder surface at a low temperature inside a freezer.

The experiments were carried out for an annulus filled with glass beads at a range of modified Rayleigh number (4.9 ≤ Ra ≤ 69), radiation parameter (0 < Rd < 10), with fin length of (Hf = 3, 7 and 11mm), with radius ratios of (Rr=(r1 / r2) =0.1405, 0.2045, 0.293 and 0.3649 ), number of fins (n = 0, 12, 23 and 45).

Finite difference method with Boussinesq's approximation is used to solve the continuity, energy and momentum equations.

The numerical solution is capable of calculating the streamline, the temperature field, the velocity field, the local and average Nusselt number.

A computer program in Mat lab has been built to carry out the numerical solution.

The numerical study was done for a range of modified Rayleigh number (4.9 ≤ Ra ≤ 300).

Results show that the average Nusselt number is nearly constant for Ra less than 100 and increased with an increase in modified Rayleigh number.

Nusselt number hardly affected by glass beads size and insignificant affected by Rd for Ra less than 100.

Decreasing Rr cause clearly increase in average Nusselt number and increasing fin length or fin number decrease heat transfer.