Kapitza conductance refers to the heat transfer between a solid surface and a fluid that covers that surface. Fundamentally, it describes the inherent difficulty in transferring energy from a solid to the fluid covering the solid surface. This phenomenon was first observed by P. L. Kapitza in 1941 while studying heat transfer from a solid into He II (superfluid helium).
The circumstances of the discovery are telling. Kapitza conductance as a fundamental mechanism occurs in all cases of heat transfer from a solid surface to fluid. This includes, for example, heat transfer from a solid to water at room temperature. However, Kapitza conductance is very temperature dependent, and its effect is negligible except at liquid helium temperatures. Moreover, due to the very effective heat transfer mechanism found within He II itself, in scenarios involving He II, the effect of Kapitza conductance can be the dominant resistance to heat transfer from a surface to a He II reservoir.
The greatest temperature drop between a heated surface and a He II reservoir connected by a channel of He II will frequently occur right at the solid-liquid interface and be driven by Kapitza conductance. Even in the case of He I (T > 2.2K) the effect of Kapitza conductance is frequently neglected. In cases where the surface heat flux is sufficient to generate boiling, the boiling heat transfer mechanism dominates and Kapitza conductance is negligible.
Kapitza conductance does dominate in cases where the T < 2.2K and where no boiling occurs. This covers a wide range of important technological applications including cooling of superconducting RF cavities and magnets, heat exchanger design and applications below 1K. A significant amount of research on Kapitza conductance has been carried out since the 1941 discovery as a result.
There are theories (acoustic mismatch and phonon radiation limit) that describe the fundamental physics of Kapitza conductance. However, while these theories (particularly the acoustic mismatch) likely describe the physical phenomenon, their predictions tend to bracket the experimental data so practical predictions of Kapitza conductance always rely on empirical data rather than theoretical predictions.
Kapitza conductance depends on the temperature as well as on both the material of the solid (i.e. stainless steel performs differently than copper) and on the surface finish of the solid. Kapitza conductance is independent of any motion of the fluid in contact with the solid.
A detailed discussion of Kapitza conductance may be found in the 2nd edition of “Helium Cryogenics” by S. W. Van Sciver. Other references for Kapitza conductance measurements include: “Kapitza Conductance and Thermal Conductivity of Copper, Niobium and Aluminum in the Range from 1.3 to 2.1 K,” K. Mittag, Cryogenics, Vol. 13, Issue 2 (1973), “High Heat Flux Kapitza Conductance of Technical Copper with Several Different Surface Preparations,” A. Kashani, S.W. Van Sciver, Cryogenics, Vol. 25, Issue 5 (1985), “Kapitza Resistance and Thermal Conductivity of Mylar at Superfluid Helium Temperatures”, G. Hattenberger, S. Carre, F.-P. Juster, B. Baudouy, Cryogenics, Vol. 45, Issue 6 (2005) and “Thermal Conductivity and Kapitza Resistance of Epoxy Resin Fiberglass Tape at Superfluid Helium Temperatures,” B. Boudouy, J. Polinski, Cryogenics, Vol. 49, Issues 3-4 (2009).
Examples of papers discussing the importance of Kapitza Conductance to superconducting RF cavities include: “Thermal Limitations in Superconducting RF Cavities: Improved Heat Transfer at Niobium-Helium Interface,”A. Aizaz and T.L. Grimm, Adv. Cryo. Engr. Vol. 51B (2006) and “Simulation of the Impact of the Kapitza Resistance at Grain-Grain Boundaries on Niobium Superconducting Cavities,” J. Amrit and O. Li., Adv. Cryo. Engr. Vol. 53A (2008).
