Thermal Convection in a Cylindrical Enclosure withWavy Sidewall - Selected Topics of Computational and Experimental Fluid Mechanics - page 381

(Elgazery andAbd 2009 ). Frequently, natural processes involve transport phenomena
from wavy walls through porous media in both, confined and unconfined flows.
For combined heat and mass transfer processes by natural convection along a
vertical wavy surface in a fluid saturated porous enclosure, thermal and mass strati-
fications diminish the Nusselt and Sherwood numbers. Rathish-Kumar and Murthy
( 2010 ) analyzed the Soret and Dufour effects to estimate the combined heat and
mass transfer processes by natural convection from a wavy vertical surface in a
fluid-saturated semi-infinite porous medium. Numerical solutions have been devel-
oped to study natural convection inside an inclined wavy cavity filled with a porous
medium (Misirlioglu et al. 1999 ). The fluid flow and thermal structures were found
to be highly dependent on the surface waviness when the inclination angle is lower
than 45 ⓦ , specially for high Rayleigh numbers. Rostami ( 1999 ) studied the two-
dimensional transient heat transfer and fluid flow in a laterally heated enclosure with
vertical wavy walls, while the horizontal ones were flat and adiabatic. Dalal and
Das ( 2006 ) studied the natural convection inside a two-dimensional cavity with a
wavy vertical wall. The enclosure was heated through the bottom wall by varying
the temperature spatially, while the other three walls were kept at constant temper-
ature. Local and average Nusselt numbers were computed for both conduction- and
convection-dominated regimes.
Transport phenomena in cylindrical enclosures result of practical interest. Nev-
ertheless, the effect of a wavy-side wall on thermal convection is not reported in
literature. The present study considers an axisymmetric flow inside a vertical cylin-
drical enclosure with adiabatic wavy sidewall. Two important cases are studied,
heating from below and heating from the top. Under such conditions the adiabatic
wavy sidewall affects the transport phenomena giving rise to different convection
patterns which modify the heat transfer rate even for conditions where convection
dominates.

2 Problem Statement

Consider the thermal convection within the cylindrical enclosure shown in Fig. 1 a.
The top and bottom walls are kept at constant temperature T 1 and T 2 , respectively,
while the wavy sidewall is thermally insulated. The cylinder has an average radius R
and height L , the wavy wall generatrix curve is a sinusoidal function with wavelength
ʻ

and amplitude a , see the Fig. 1 b. The enclosure is filled with a Newtonian fluid and
the properties are assumed to be constant except the density for which the Boussi-
nesq approximation is applied. The temperature difference between the bottom and
top walls, T 2 − T 1 , is either positive or negative and the gravity acts parallel to the

cylindrical axis.