the h coefficient may be evaluated classically by empirical correlations for the Nusselt according to the Re and Pr numbers. Then, you have to multiply h by the overall efficiency of the fins obtained classically when considering conduction in the fins. See the book of Bergman et al. and the chapter about conduction in extended surfaces for example.
I have not expertise in this but i will suggest that you can calculate heat flux and from that applying newton's law of colling you can able to find out heat transfer coefficient and from that find out Nu. Same kind of work is done by my friend and he also not able to find out Nu in corrugated plate heat exchanger and he implemented as i suggested