Usually, the engineer needs the model oh heat and mass tarnsfer for many purposes like: equipement sizing, process efficiency, and so on. In this cas, we need the model for a bubble in a continuous medium. As a result, two cases arise:
case-1: Bubble of air in liquid water.
Case-2: Drop of liquid water in the air.
In the Case 1 is extremely simple and it is described in many students courses of thermodynamics, but about the Case 2 I can only say if I did not want to know how it really happens then there would not be a reason to write an article.
Dear Adel, for a mathematical model of case-1 (gas bubble in liquid medium), see my paper (sorry for autocitation) On a differential equation for a gas bubbles collapse mathematical model, available in RG archive. Gianluca
Dear Gianluca,
Thanks a lot for your reply. I read your paper, it's very good work, but the heat and transfer models are not your paper.
there are several scenarii to be considered such as bubble more hot than the continuous medium or bubble more cold than the medium or the bubble and the medium are in the same temperature condition.
with my best wishes.
Adel
You mention only water and air as fluids but other combinations are also to be considered as for instance the fuel drops in a Diesel engine with a centripedla heat transfer ahd a loss of mass by evaporation.
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