Convective Heat Transfer Lecture 4 Convective Heat Transfer

Summary of heat transfer by conduction Fourier Law of heat conduction

Temperature Evolution Equations Heat moving in Heat moving out Summing up: With heat generation:

The stationary temperature profile is linear

What happens to the flow reaching the body surface? It will flow into the surrounding fluid, most often air or water!!! If the fluid is at rest, there would be only conduction, as in the solid. This is however physically impossible. Fluid’s density decreases with temperature (except for water between 4ºC and 0ºC). In any case the temperature gradient generates a density gradient, the density gradient generates a pressure gradient and the fluid gets vertical movement: Natural convection. If the flow is laminar, heat transfer remains of Conduction type. As Reynolds Number increases it can get turbulent If the movement of the fluid is forced by any other mechanism (e.g. a fan) then one will get Forced convection. In this case the flow is expected to be turbulent.

Convective heat transfer Convection is the transport associated to the movement of a fluid. When molecules move, they carry heat, momentum, kinetic energy and mass. In Fluid Mechanics Convection is the transport of any property by the movement of the fluid. In some disciplines convection is synonymous of “natural convection” and “forced convection” is designated by “advection” and holds for any property. ΔΤ

The Boundary Layer Momentum boundary layer is the region (layer) close to the surface where the velocity evolves from the undisturbed flow up to the wall velocity (often zero). Thermal boundary layer is the region where the temperature evolves from undisturbed to the wall temperature. They are identical if they have the same length. the surface is not heated/cooled from the leading edge, the thermal boundary layer is thinner.

Where does the heat transferred go? It goes into the fluid, increasing its temperature, if the wall is hotter. It is diffused across the flow, perpendicularly to the velocity. So it is like conduction!!! Why should it be called “convection”? Because in normal conditions the heat is not transferred from molecule to molecule, but through the movement of groups of molecules: eddies. The size of the groups of molecules and their kinetic energy depend on the turbulence intensity and thus on the flow. This is why “h” can vary so much.

Convective heat transfer coefficient v (m/s) V(km/h) h h/u 1 3.6 19.5 2 7.2 22.6 11.3 4 14.4 26.5 6.6 8 28.8 30.8 3.8 16 57.6 34.5 2.2 32 115.2 35.1 1.1

Convective heat transfer between a surface and a fluid This is the simpler case one can think about. It is managed assuming a heat transfer coefficient “h” and assuming that the temperature of the fluid is constant along the wall surface. Is this always realistic?

What Happens to the Heat Transferred to the fluid? Advection It is advected (or convected)!!! i.e. it is transported elsewhere by the flow velocity. Advection transports heat along the flow. If the velocity is vertical and diffusion is horizontal, one gets: Diffusion from the wall Advectiion

How to manage convection in these cases ? Empirical bulk formulations or numerical methods.

What would be the issue in the case of the image?

What happens to your computer when the CPU fan does not work correctly What happens to your computer when the CPU fan does not work correctly? What is the variable that changes in the heat budget?