The momentum and energy equations are simplified and using the Boussinesq approximation are cast into two simple second order coupled differential equations. These equations are solved numerically to provide solutions for the temperature and flow distribution which occur between two vertical heated and cooled plates immersed in an infinite sea of fluid. These predictions are shown to agree with existing literature. The analysis is then extended to a different geometry, specifically, a vertical heated (or cooled) vertical pipe acting like a chimney in a sea of fluid, for which there seems to be less information in the literature. Lastly, the work is extended to include the effects of phase change on the walls. This involves solving the energy equation close to the wall where conduction, convection and phase change occurs. It is found that the thickness of the frozen material on the walls has a significant impact on the freezing/melting rates. The analysis and solutions have applications in a number of fields of engineering endeavours including hydrocarbon recovery where wax deposition and hydrate formation on pipe surfaces are known to be a challenge and in the refrigeration industry where evaporator frosting is a problem and where the energy efficiency of ice production is a function of ice thickness on the evaporator walls.
|Translated title of the contribution||Buoyancy dominated convection between heated and cooled vertical plates and open ended pipes with freezing and melting|
|Title of host publication||UKHTC2011, The 12th UK National Heat Transfer Conference, Leeds 30 Aug- 01 Sept|
|Publication status||Published - 2011|
Bibliographical noteMedium/genre: Refereed journal paper and paper presentation
Conference Organiser: UK National Heat Transfer Committee