Is there an equation for convective heat transfer?

Question

Is there an equation I can use to calculate the temperature (as a function of time) of an object which is gaining or losing heat by convection? Or equivalently, the rate of energy transfer from the object to the surrounding fluid (or vice-versa)? It can involve constants representing properties of the object and the surrounding fluid.

I know about the heat equation for conduction and the Stefan-Boltzmann law for radiation, but I can't think of one for convection.

Answer 1

Nothing as easy from basic principles as for conduction or radiation.

You can multiple the mean heat carried by the convecting liquid by it's mass rate of flow

$$ \Delta T = c_p * (T_{in} - T_{out}) * \frac{\Delta V}{\Delta t} \rho \Delta t .$$

Where $T_{in}$ is the mean temperature of the liquid moving toward the sink (cool side) and $T_{out}$ is the temperature of the liquid moving the other way.

The problem is that you can't get the temperature(s) of the convecting liquid or the flow rate without detailed calculations or measurements.

For the generaly case you pretty much have to go to CFD.

Answer 2

http://www.egr.msu.edu/~somerton/Nusselt/

here you can find some formulas for calculating Nusselt, Prandtl, Reynolds, Rayleigh and Grasshoff numbers. Those are important for evaluating conditions in different systems. Numbers will tell you which state of convection is around your geometry (natural, forced, laminar, turbulent, external, internal). For each case there exist some correlation.

More info about Nusselt number and others you can find eg. on Wikipaedia.

After calculating convenient numbers, you can calculate heat transfer coefficient zumbeispiel from Nusselt nuber.

Answer 3

For convection, you have a similar formula as conduction for heat transfer. http://en.wikipedia.org/wiki/Nusselt_number

$$\frac{dQ}{dt}=-\frac{N_uk_fA\Delta T}{L}$$

Answer 4

There are some formulas (for example, for cylinders, such as pipes) in the following book: Bosworth R.C.L. Heat transfer phenomena. The flow of heat in physical systems. – Associated general publications, PTY. LTD. – Sydney. – 1952, 211 p. Both heat conduction (in the so called stagnant film near the pipe) and convection are important for pipe cooling in the air. It is interesting that the relevant coefficients depend on the orientation of the pipes (vertical/horizontal).