Conjugate heat transfer from a translating drop in an electric field at low Peclet number

Abstract

The conjugate heat exchange with transient interfacial temperature between a translating liquid drop and its host fluid in a uniform electric field is considered. Singular perturbation is developed to obtain the temperature within the domain of the continuous phase whereas regular perturbation is used to obtain the solution inside the drop with the help of the method of weighted residuals. This method proves to be powerful for the solution of problems with time-dependent non-homogeneities arising within the governing equation and/or the boundary conditions. The temperature is computed up to and including the first order in the Peclet number; however, higher order is also performed for the host phase in order to examine the influence of an external field upon the total transport rates. In the first order solution, the effects of an electric field were to alter the temperature inside and outside the droplet as well as the heat flux, but the net heat transfer rate, which is totally controlled by conduction and convection, remains unchanged. Beyond the first order approximation, the contribution to the net heat transfer due to the electric field becomes assessable.