# Scaling of thermal resistance to air vs oil

For electronic components, thermal resistance from component to ambient(air) is often given, and used with a resistive model of 'thermal resistors' to make temperature rise calculations simple. These values are usually given in some context such as to component to air, to heat sink, etc.

I have been looking for resources for calculating component temperatures when submerged in oil, i would like to know if i can as a rough rule of thumb multiply the thermal resistivity (in air) of an object, with the ratio of thermal conductivity of air to oil for example. In order to derive the thermal resistivity (in oil). Since at glance, it looks like a thermal resistance has thermal conduction as a linear component when calculated.

Can someone elaborate if this rule of thumb is applicable, assuming the object is submerged in an infinite ambient medium of oil, instead of air. Given that we know the thermal resistance in air ?

• The folks over at Electrical Engineering might be the better ones to ask. I've seen data sheets with performance in both air and oil, but can't lay hands on one readily. Sep 8, 2022 at 18:18
• I think the answer if you want to be precise is no. Especially if heat sinks are involved then convection is important. Or if a fan is part of the air cooling. Sep 8, 2022 at 18:20

For example, we usually correlate the convection coefficient with a characteristic length $$L$$, a thermal conductivity $$k$$, and certain combinations of the Reynolds, Rayleigh, and Prandtl numbers. Of these, the geometry (and thus $$L$$) remains unchanged with a fluid switch, and you already propose accounting for differences in $$k$$ (albeit by proportional scaling only).
But $$\text{Re}$$, $$\text{Ra}$$, and $$\text{Pr}$$ also incorporate the fluid density, viscosity, specific heat, and coefficient of thermal expansion, all of which I'd expect to differ substantially between air and oil. Scaling by the ratio of the thermal conductivities does not address these other dependencies.