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Thermal Convection in a Cylindrical
Enclosure with Wavy Sidewall
F.A. Sánchez Cruz, S. Martínez Martínez, H.G. Ramírez Hernández
and S. Méndez Díaz
Abstract
An axisymmetric convection flow within a vertical cylindrical enclosure
with adiabatic wavy sidewall was studied. Two important cases of thermal con-
vection were considered, heating from below and heating from the top, while the
wavy sidewall is adiabatic. An analytical coordinate transformation was used to
obtain a coordinate frame for computation in which the irregular domain fits into a
square. Non-dimensional parameters which include the cavity aspect ratio, dimen-
sionless wavelength, dimensionless amplitude, constant Prandtl number equal to 7,
and Rayleigh numbers between 10
3
and 10
6
, were used to characterize the convec-
tion heat transfer through the cavity. Computational solutions showed that the wavy
wall promotes thermal stratification and low velocity multiple cells patterns. The
effect of the wavy wall was found to restrict the convection fluid flow which yields
low heat transfer through the cavity.
1 Introduction
Thermal convection heat transfer in enclosures has received considerable attention
due to the relevance of the phenomena occurring in many engineering applications
such as cooling of electronic equipment, solidification processes, buildings design,
solar collectors and cooling chambers. Moreover, heat and mass transfer in enclo-
sures are natural common processes found in science fields as geophysics and met-
allurgy. Many real cavities are irregular shaped and the fluid flow and heat transfer
show complicated behaviors, nevertheless, typical analysis are focused on character-
izing enclosures with regular shapes; hexahedral, cylindrical and spherical cavities
being the most studied geometries. Roughness and waviness of walls are parame-
ters scarcely considered when studying transport phenomena in enclosures. Since
the shear stress and heat flux on the walls define the hydrodynamics and heat trans-
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