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I'm having a difficult discussion with a colleague because I'm running heat flow simulations for a small heater (5 mm^2 area), and I insist that if we're going to run more electrical power through the heater then we should modify the convective coefficient. However this person claims that even though we are running different powers through the heater and hence obtaining different delta T since we reach a higher temperature, we should keep the same h coefficient, which to me doesn't make sense because every single equation for h that I've seen so far depends on heat flux and temperature in some way or another.

My simulation results match experimental data of the heater if we change the convective coefficient. This person claims that there should be a single h value for all the simulations.

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The convective heat transfer coefficient between the heater and its ambient will depend on the Nusselt number. The Nusselt number in turn is a function of the Reynolds number (forced convection) or the Rayleigh number (free convection), and the Prandtl number of the system. In case of free convection heat transfer the Rayleigh number is indeed a function of the delta_T between the heater and its surrounding, and hence it is expected that the heat transfer coefficient will also be dependent on the temperature difference. To get to know more on this scenario, you could refer to any standard heat transfer textbook like

http://web.mit.edu/lienhard/www/ahttv201.pdf

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