# Heat Transfer Coefficient to Air Flow Rate

Hey all,
I'm trying to simulate a simple chip-heatsink situation in SolidWorks using their thermal modeling suite. I have found an ideal set of parametric values for the chip to work at a reasonable temperature, but I need to figure out what the convection coefficient means in terms of air flow rates across the chip. Honestly, if someone could give me a simple breakdown in how to do this calculation, I would be very grateful!

The bulk temperature on the chip side is set to 1500 K with a convection of 20 W/m^2-K. I went with 20 rather than 30 (which I was told was a good approximation for standing air) because a colleague thought that the convective coefficient would vary based on the power flux going into the chip (30,000 W/m^2) by about 10% divided by the temperature yielding 20 W/m^2-K. I'm not sure if this procedure is correct, so any input on that would be helpful as well.

So I guess, succinctly, my two questions are 1) what is the convective coefficient for still and moving air at 1500 K and 2) how can I derive airflow from the heat transfer coefficient?

SteamKing
Staff Emeritus
Homework Helper
1500 K? What is this thing running in, a blast furnace?

Are you taking into account the heat generated by the chip when its running? Is the 1500k the chip surface temperature as a result of its operation?

Calculating the convective coefficient depends on a number of parameters and is generally quite complicated to determine analytically. Hence, the abundance of correlations in the literature to evaluate the coefficient based on empirical measurements. Anyway, the convective coefficient is primarily a function of the flow rate and geometry. So if you define your geometry as a series of rectangular channels (assuming its a finned heat sink), and know your flow rate, you should be able to find some correlation for finned heat sinks to calculate the Nusselt number, from which you can calculate the convective coefficient.

Increasing air flow, increases convective coefficient and vice versa. That value of 20W/m2K for still air is probably a reasonable approximation for still air but at the temperatures you are looking at, my guess is that you will have significant circulation due to natural convection (induced by density differences due to the high temp). This will increase your coefficient

Hey everyone! Thank for the responses! 1) Yes, this chip is a thermoelectric chip absorbing IR off an emitter heated by natural gas. 2) The 1500 K is the temperature the emitter will cause the chamber to heat up to--depending on the convection coefficients I use, I can get the chip temperature down to 500 K. 3) I understand what the coefficient means in theory, and I'm familiar with the equations with heat transfer, but SolidWorks does its simulations by using the coefficient as a parameter--I want to equate these coefficients with an airflow velocity, and I can't find any literature or methodology to do so :-\ Is there anyway to go from coefficient to air flow rate?

256bits
Gold Member
Hello SuperP,
Well,this is what http://physics.info/convection/ says,
There is currently no general theoretical model for analyzing forced convection problems. The heat-transfer coefficients h are can only be described by equations based on empirical analysis. For example, the h of air is approximately equal to …

h = 10.45 − v + 10√v

where v is the relative speed of the object through the air; that is, the speed of the object through the air or the speed of the air around the object. This equation is valid for speed from 2 to 20 m/s. Outside of this range h is … ?
I do not know how well that equation models reality.

And here is a course on the subject, with examples, so you can see the difficulty involved
http://s3.amazonaws.com/suncam/npdocs/119.pdf

And a guide on how to
http://www.mikrocontroller.net/attachment/2415/convection_coeff.pdf

Have fun!

Last edited by a moderator:
Hey everyone! Thank for the responses! 1) Yes, this chip is a thermoelectric chip absorbing IR off an emitter heated by natural gas. 2) The 1500 K is the temperature the emitter will cause the chamber to heat up to--depending on the convection coefficients I use, I can get the chip temperature down to 500 K. 3) I understand what the coefficient means in theory, and I'm familiar with the equations with heat transfer, but SolidWorks does its simulations by using the coefficient as a parameter--I want to equate these coefficients with an airflow velocity, and I can't find any literature or methodology to do so :-\ Is there anyway to go from coefficient to air flow rate?

Yes, there are plenty of ways. HTC(heat-transfer coefficient) is almost always presented in terms of flow rate. It is normally presented non-dimensionally in terms of Reynolds Number so you have a plot of Nusselt no. (dimensionless HTC) on the y-axis versus Reynolds no. on the x-axis. So if you define your HTC, you can evaluate the flow rate.

You are going to have to use some correlation to find HTC though, appropriate to your set-up (heat sink geometry). My advice is to refer to Holmans Heat Transfer book. There are plenty of papers on the topic too. Use Google Scholar and try "convection modelling of plate fin heat sinks" or something similar.

Thanks everyone for your responses especially 256bits for his links on the course work and the guide that really helped me figure out how to the do calculations. I managed to get an excel sheet built to help me with the calculations based on the links and some research papers to get values for air!