# What is the thermal conductivity across two materials of differing thermal conductivity?

Thermal conductivity measures the speed of heat transfer across a single material, but how do you model heat transfer from one material to another? If you have hot water (0.58 W/(m K)) running across a cold copper plate (401), is the thermal conductivity across the contact surface a mean of the two materials (200)? Or is it limited to the thermal conductivity of the water (0.58)?

In essence, I'm wondering if the material used to construct a heatsink or water cooling block really matters if the block material options (copper, aluminum, titanium) all have a thermal conductivity two orders of magnitude greater than the coolant (water, air) flowing over them. My gut instinct is "yes", but I would like to have a more complete and rational understanding.

• I don't understand ...don't we just transfer heat through water then copper and water surface should get same temp and after which we use k of copper – Utkarsh futous Mar 30 '17 at 17:24
• You should draw a sketch explaining the situation. But heat transfer from one solid to a fluid is complicated. In engineering applications the heat transfer coefficient is calculated from given correlations for the Nusselt number. – MrYouMath Mar 30 '17 at 17:26
• You can analyze the flow of thermal energy through multiple materials in series by using the thermal resistance (en.wikipedia.org/wiki/Thermal_resistance). However, you need to identify the dominant mode of heat transfer. In copper, it's conduction; with a water flow, however, it's likely not conduction but convection. The total resistance could be modeled as $L/k+1/h$, where $h$ is the convection coefficient of the water, as MrYouMath notes. The resulting composite coefficient would be the reciprocal of the total resistance. – Chemomechanics Mar 30 '17 at 18:25