Thermal boundary resistance

Experimental data show that the thermal boundary resistance between solids is poorly reproducible [52-53], The experiments in fact demonstrated that the physical and chemical condition of the interfaces is a critical factor determining the thermal boundary resistance. For this reason, the study of the contact resistance has been carried out on evaporated surfaces in order to reduce the irregularities and make Rc more reproducible. 

In 1941, Kapitza [54] reported his measurements of the temperature drop at the boundary between helium and a solid (bronze) when heat flows across the boundary. More than ten years later, Khalatnikov (1952) presented a model, an approximation to what is now known as the acoustic mismatch model , to explain that a thermal resistance Rk (thermal boundary resistance) occurs at boundaries with helium [55],... 

In 1987, Swartz [73] measured the thermal boundary resistance between metal films and the dielectric substrates onto which the films were deposited, in the range 0.6-200 K. A typical example is the measurement of the thermal contact resistance between indium and sapphire [72]. To minimize the dependence on surface irregularities, indium was vacuum deposited onto the sapphire rods the two surfaces were then pressed together and annealed. Analogous measurements have been carried out also with lead and aluminium. In all these cases, it has been clear that the contact resistance was strongly dependent on the sample preparation. In particular, obtained data suggest that the contact between the two materials was not complete. 

E.T. Swartz Solid-solid thermal boundary resistance, Ph.D. Thesis, Cornell University, Ithaca, New York (1987)... 

At low temperatures, Ac, may fall even below that of the matrix. The cause is a thermal boundary resistance between the filler and the matrix, which is a pl enomenon of phonon mismatch. This resistance, the Kapitza resistance, varies as T and is dominant at low temperatures. If the dominant phonon wavelength --T ) becomes larger than the particle diameter, this effect disappears. Whether or not Ac is increased or decreased, depends on the predominance of the Kapitza resistance and the thermal shortcut in the filler particles. At a fixed temperature, this is a function of the filler diameter, as shown in Fig. 12. Small particles can be used to reduce Ac below that of the matrix. Illustrative examples [ are shown in... 

Shenogin Sergei, Xue Liping, Ozisik Rahmi, KebUnski Pawel, and Cahill David G. Role of thermal boundary resistance on the heat flow in carbon-nanotube composites. J. Appl. Phys. 95 (2004) 8136-8144. 

Hida S, Shiga T, Maruyama S, Elliott JA, Shiomi J (2012) Influence of thermal boundary resistance and interfacial phonon scattering on heat conduction of carbon nanotube/polymer composites. Trans Jpn Soc Mech Eng Part B 78(787) 634-643 Hilmi Y, Seyhana TA, Servet T, Metin T, Wolfgang B, Karl S (2010) Electric field effects on CNTs/vinyl ester suspensions and the resulting electrical and thermal composite properties. Compos Sci Technol 70(14) 2102-2110... 

C. F. Carlborg, J. Shiomi and S. Maruyama. Thermal Boundary Resistance between Single-Walled Carbon Nanotubes and Surrounding Matrices. Physical Review B 2008 78 5406. 

If a concentration gradient exists within a fluid flowing over a surface, mass transfer will take place, and the whole of the resistance to transfer can be regarded as lying within a diffusion boundary layer in the vicinity of the surface. If the concentration gradients, and hence the mass transfer rates, are small, variations in physical properties may be neglected and it can be shown that the velocity and thermal boundary layers are unaffected 55. For low concentrations of the diffusing component, the effects of bulk flow will be small and the mass balance equation for component A is ... 

It is difficult to solve the system of Eqs. (39)—(41) for these boundary conditions. However, certain simplifying assumptions can be made, if the Prandtl number approaches large values. In this case, the thermal boundary layer becomes very thin and, therefore, only the fluid layer near the plate contributes significantly to the heat transfer resistance. The velocity components in Eq. (41) can then be approximated by the first term of their Taylor series expansions in terms of y. In addition, because the nonlinear inertial terms are negligible near the wall, one can further assume that the combined forced and free convection velocity is approximately equal to the sum of the velocities that would exist when these effects act independently. Therefore, for assisting flows at large Prandtl numbers (theoretically for Pr -> oo), Eq. (41) can be rewritten in the form ... 

In inert atmospheres the mechanical properties of RBSN are constant up to 1200-1400 °C because of the absence of a glassy grain boundary phase, which is also the reason for the excellent thermal shock and creep behaviour. The thermal shock resistance, hardness and elastic constants depend on the microstructural parameters but are much lower than for dense Si3N4 ceramics [539]. 

The heat transfer coefficient is inversely proportional to the thickness of the thermal boundary layer. The resistance to heat transfer... 

Thermal shock resistance of Cr-Re alloys was sufficient to withstand conditions similar to those imposed by the application. The ability to mechanically twin permitted the accommodation of thermal deformation in the boundary area between the hot and cold zones of the combustion chamber, which is acknowledged to be the its most solicited area. Grain boundary micro cracking on the thermally shocked surface might be overcome by strengthening of the grain boundaries through thermo mechanical treatment. 

The dimensionless shape factor for the isothermal rectangular annulus is derived from the correlation equation of Schneider [89], who obtained accurate numerical values of the thermal constriction resistance of doubly connected rectangular contact areas by means of the boundary integral equation method ... 

K. J. Negus, M. M. Yovanovich, and J. C. Thompson, Thermal Constriction Resistance of Circular Contacts on Coated Surfaces Effect of Contact Boundary Condition, AIAA-85-I014, AIAA 20th Thermophysics Conference, Williamsburg, VA, June 19-21,1985. 

K. A. Martin, Thermal Constriction Resistance of Arbitrary Contacts With the Boundary Condition of the Third Kind, M.A.Sc. Thesis, Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada, 1980. 

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