Is there any relation between Thermodynamics enhancement factor(TEF) and Havens ratio(HR) ? if yes then how to calculate the HR if TEF is given ?
Your question is not very clear, mostly because you are not giving any context. In particular I don't know what you mean by "thermodynamic enhancement factor", which can refer to many things. But taking a clue from the word thermodynamic, my contention would be that the relation you ask for is just not possible.
The Haven ratio is the ratio between a diffusion constant and the ionic conductivity, which makes it a constant that depends on the dynamics of the system. Even though the word thermodynamics suggests otherwise, there is no real dynamics in thermodynamics, it is an equilibrium theory in which there is no place for dynamical constants. This makes it impossible for thermodynamics to make any statement about diffusion constants, conductivities, or similar quantities, which are all related to (integrals over) time correlation functions. Unless you are talking about some enhancement factor in non-equilibrium thermodynamics, this rules out the possibility of a relation you ask for.
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