Thermal contact conductance

In physics, thermal contact conductance is the study of heat conduction between solid bodies in thermal contact. The thermal contact conductance coefficient, h c {displaystyle h_{c}} , is a property indicating the thermal conductivity, or ability to conduct heat, between two bodies in contact. The inverse of this property is termed thermal contact resistance. q = − k A d T d x {displaystyle q=-kA{frac {dT}{dx}}}     (1) q = T 1 − T 3 Δ x A / ( k A A ) + 1 / ( h c A ) + Δ x B / ( k B A ) {displaystyle q={frac {T_{1}-T_{3}}{Delta x_{A}/(k_{A}A)+1/(h_{c}A)+Delta x_{B}/(k_{B}A)}}}     (2) In physics, thermal contact conductance is the study of heat conduction between solid bodies in thermal contact. The thermal contact conductance coefficient, h c {displaystyle h_{c}} , is a property indicating the thermal conductivity, or ability to conduct heat, between two bodies in contact. The inverse of this property is termed thermal contact resistance. When two solid bodies come in contact, such as A and B in Figure 1, heat flows from the hotter body to the colder body. From experience, the temperature profile along the two bodies varies, approximately, as shown in the figure. A temperature drop is observed at the interface between the two surfaces in contact. This phenomenon is said to be a result of a thermal contact resistance existing between the contacting surfaces. Thermal contact resistance is defined as the ratio between this temperature drop and the average heat flow across the interface. According to Fourier's law, the heat flow between the bodies is found by the relation: where q {displaystyle q} is the heat flow, k {displaystyle k} is the thermal conductivity, A {displaystyle A} is the cross sectional area and d T / d x {displaystyle dT/dx} is the temperature gradient in the direction of flow. From considerations of energy conservation, the heat flow between the two bodies in contact, bodies A and B, is found as: One may observe that the heat flow is directly related to the thermal conductivities of the bodies in contact, k A {displaystyle k_{A}} and k B {displaystyle k_{B}} , the contact area A {displaystyle A} , and the thermal contact resistance, 1 / h c {displaystyle 1/h_{c}} , which, as previously noted, is the inverse of the thermal conductance coefficient, h c {displaystyle h_{c}} . Most experimentally determined values of the thermal contact resistance fall between0.000005 and 0.0005 m² K/W (the corresponding range of thermal contactconductance is 200,000 to 2000 W/m² K). To know whether the thermal contact resistance is significant or not, magnitudes of the thermal resistances of the layers are compared with typical values of thermal contact resistance. Thermal contact resistance is significant and may dominate for good heat conductors such as metals but can be neglected for poor heat conductors such as insulators.Thermal contact conductance is an important factor in a variety of applications, largely because many physical systems contain a mechanical combination of two materials. Some of the fields where contact conductance is of importance are: