Hi. Here an article which present a simple method to consider the presence of thermal and hygric resistance in the contact surface of multilayer in building analysis. The values of the resistances were fixed in order to have agreement between simulation and experimental results. Terashima and Mizuhata. 1997. Moisture movement in double layer building materials. http://www.inive.org/members_area/medias/pdf/Inive/clima2000/1997/P236BIS.pdf

In finned heat exchangers, the convective resistance of the inside liquid and the conductive resistance of the wall may be neglected as a first approximation. Then the contact resistance between the tube and the fin could be anywhere from 10% to 50% of the effective convective resistance of air. This takes into account the fin resistance also.

To reduce the contact resistance, several ways are possible. The contact area between the tube and fin is increased by use of "L" footed fins. Further reductions in contact resistance can be achieved by expanding the tube by forcing a steel bullet through the tube. The bullet must be larger in diameter than the tube I.D. But there is an optimum ratio of bullet diameter to tube diameter. Too small ratios will not expand the tube enough and too large ratios can cause deformation and tearing of the foot of the fins that actually worsen the situation.

You have asked a rather bald question. Therefore it is not possible to give you a pointed answer. However, if you wish to have more details, look up the excellent papers by C.V. Madhusudana. You may also look up the papers by Yau Kar Hing and co-workers. 

Prof.Vijay has given a detailed explanation of contact resistance in finned heat exchangers. The determination of contact resistance has to be estimated through experiments.  The details of the problem may be stated if further clarification is needed.  

Prof. Sharma has given a valuable addendum to my explanation. Just wanted to add that Yau Kar Hing et al. have been in successful in predicting the contact resistance by analysis, by first measuring the surface roughness of both mating surfaces (to 0.5 microns) and then applying Monte Carlo methods.

Indeed, the heat transfer coefficient through the gap defined only empirically. If you know the pressing force consisting in heat exchange bodies, the heat transfer coefficient is calculated according to the pressing force.

If not, then the calculated heat radiation in a gap between two parallel surfaces and add terms depending on the conduction through the conductive gap. They are determined from the experiment.

There is a large array of empirical quantitative data on the transfer of heat from one oxidized or polished steel sheet to another. These data obtained in a study of heating and cooling the steel sheet rolls. If it is close to your occasion - please inquire.

You can consider -for your case-only the contact heat transfer between 2 rough surfaces. This contact is not continus since depending on the applied pressure roughness are more or les crushed so that a direct contact occurs. Again depending on the type of roughness the environnement (the fluid)can or cannot fill the remaining cavities. Globally roughness is characterized by the Abbot curve and you can in a first approximation consider that the material is in the crushed zones at his yield strength. This gives a relationship between applied pressure and direct contact zones. In the voids heat is also transferred by conduction since the very thin layers cannot allow a convective circuit. You should look also at the contact electric resistance which is very well analysed because of the problems in connection for high currents. The problems are similar.

This comment is for the 2 gentlemen who mentioned sources which could be of interest but did not give any indication about where the papers can be found and read.

I sincerely think that if we give an answer based on a source we should as well give the links in order to facilitate the direct access to them. I tried to do it but did not succeed. This is the reason why when I give an answer I try to give in it the information in a direct accessible way.