Thermal Convection in a Cylindrical Enclosure with Wavy Sidewall

Abstract

An axisymmetric convection flow within a vertical cylindrical enclosure with adiabatic wavy sidewall was studied. Two important cases of thermal convection 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, dimensionless wavelength, dimensionless amplitude, constant Prandtl number equal to $7$, and Rayleigh numbers between $10^{3}$ and $10^{6}$, were used to characterize the convection 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.

Appendix: Coefficients and Parameters

Table 1 Coefficients of Eqs. 12 and 13

Table 2 Coefficients of Eqs. 16 and 17

where

$$\begin{aligned} \varOmega =2\pi /\varLambda \,\text {and}\,\,\gamma = 1+\varGamma \cos \left( \varOmega \xi \right) . \end{aligned}$$

Table 3 Coefficients of the boundary condition in Eq. 21