Temperature jump

Illustration with a thin gap: The gap width δ is expanded on each side by the temperature jump length g. The solid line does not reflect the actual temperature, but assuming a constant temperature gradient.

The temperature jump is a concept in the thermodynamics of non-equilibrium. Jumps in temperature occur at the interface between gases and solids when gas and solids have different temperatures . Although the temperature is a constant field everywhere , so that physically there can be no question of a "jump", the temperature gradient in the immediate vicinity of the solid is significantly greater than in the gas itself.

Assuming a constant temperature gradient in the gas up to the interface, a point of discontinuity occurs there. The temperature jump length or distance is the length by which the solid body would have to be shifted so that the continuity is given again. ${\displaystyle g}$

Derivation

The heat transfer coefficient for the gas layer without considering the temperature jump is calculated as follows:

${\displaystyle \alpha _{L,G}={\frac {\lambda _{G}}{\delta _{G}}}}$

In order to take the temperature jump into account, the characteristic length within the heat transfer coefficient for the individual sides on which the jump takes place is expanded. In the present case with two walls the following results: ${\displaystyle g}$

${\displaystyle \alpha _{L,G}={\frac {\lambda _{G}}{\delta _{G}+2g}}}$

Kennard gives the following formula to calculate the length : ${\displaystyle g}$

${\displaystyle g\approx \left({\frac {2-\gamma }{\gamma }}\right)\left({\frac {4}{\kappa +1}}\right)\left({\frac {k}{\eta c_{V}}}\right)\Lambda }$

With

• ${\displaystyle \gamma }$: thermal accommodation coefficient as the ratio of the energy that individual molecules on the surface absorb to the energy that they would absorb as a continuum,
• ${\displaystyle \kappa }$: Isentropic exponent
• ${\displaystyle k}$: Thermal conductivity
• ${\displaystyle \eta }$: Viscosity
• ${\displaystyle c_{V}}$: Heat capacity
• ${\displaystyle \Lambda }$: mean free path

literature

• Earle H. Kennard: Kinetic Theory of Gases . 1st edition. McGraw-Hill, New York and London 1938 ( archive.org ).

Individual evidence

1. ↑ ^{a b} R. Kneer: “Heat and substance transfer I / II” (lecture notes) . Ed .: RWTH Aachen University, Chair for Heat and Mass Transfer. Issued September 22, 2017. Aachen September 2017.