Vertical cold plate natural convection 3

[RE]

I am working in natural convection on a vertical plate. The problem is how to calculate the heat transfer coefficient. Invariably text books give correlations bassed on Nusselt, Grashof, and Prandtl numbers for a hot plate in a cold fluid (gas or liquid). What happened with a cold plate in a hot fluid? It is correct to use the same correlations? I suppose the mecanism of heat transfer is quite different. How to calculate in this case the temperature difference for the Grashof number?,...(T fluid - T plate) ?
Thank you.

 

[ardilesd]

Hello,
Try McAdams, Heat transmission, taken by Kern.
The correlations are the same for cold or hot plate when they are vertical !!
Differences arise when horizontal plates are considered.
This is for air as the medium, perhaps for some other fluid.... ?
Regards

 

[Koske]

You should be more specific, and you should pay attention to phase change, because due to the differnce in temperatures, and partial pressures of vater vapor in hot air and bondary layer of the cold plate you can have condensation (which will drasticly change the way of calculting the heat ransfer).

 

[Tunalover]

ardilesd is right about the correlations. Also, Koske is right about the condensation. Phase change heat transfer can dwarf single phase heat transfer. The heat released from the condensate will accelerate cooling in a big way.

 

[25362]

From the previous answers you see the question is not as simple as it appears firsthand. You are right in not mentioning the Reynolds' number among the dimensionless groups since the case is one of free natural convection in gas, or in the laminar regime if the fluid is a liquid.

The one group that is definitely used for gases in these situations is the Grashof number. The Pr value for atmospheric air is about 0.7 for a wide range of temperatures.

If we are speaking of a vertical plate being heated by surrounding air in an open environment, the most probable air downward movements due to density differences would be sufficiently slow as to be considered in the laminar regime.

For such a case books say, the HTC, h = 1.42 (delta T/L)^025.

h is in W/(m^2.K); delta T = Tair-Tplate, K; L= height of plate, m.
If delta T changes with time, so would the value of h. A preliminary value for estimation would be 5 W/(m^s.K)

If the fluid is a liquid there are formulas in specialized books. One of them for a falling film with Re < 400 is:

h = 0.064 k. (Pr^0.344) . (visc bulk/visc wall) / [(visc)^2/(g.dens^2)]^0.33

h = HTC for convection of the fluid
k = thermal conductivity of the fluid. For water @ 100F, 0.63 W/(m.C); @ 200F, 0.68 W/(m.K)
visc.= viscosity of liqid, cP; water @ 100F, 0.68 CP; @200F, 0.31 cP.
dens. = density of liquid, kg/m^3; water 993 kg/m^3 @ 100 F; 963 @ 200 F.
g = local acceleration due to gravity, generally taken as 9.8 m/s^2.
Pr = Prandtl number, for water @ 100F, 4.53; @ 200F, 1.90.

If the liquid temperature is constant, the Pr value wouldn't change.

Apparently you are dealing with an &quot;unsteady state heat transfer&quot; situation, which may require graphics based on analytical solutions suitable for computer programming.

 

[cdvk]

I was asking myself the same question as &quot;RE&quot; above - and found the replies to be helpful. I was wondering if &quot;25362&quot; could tell me where he/she had gotten the equations to approximate h (h=1.42*(deltaT/L)^0.25) ?

Thank you

 

[jb48]

I believe its from the ASHREA Fundamentals handbook. I you take the general equation based on Gr & Pr numbers, and insert fluid properties for air at 14.7 psia, the equation reduces to the above.