heat transfer coefficient - backwards

[heaterguy]

If you know the htc from hot metal to cold air, can the same htc be used for hot air to cold metal?

For instance, we know the htc for for air at 100'F with metal at 150'F is 2.9 btu/lb/'F/ft2. Is the htc the same for air at 100'F and the metal at 50'F? Is it even close to the same?

 

[Tremolo]

heaterguy,

Good question. Generally, the heat transfer coefficient will be different whether the metal is being heated or cooled.

To illustrate this dependence, consider one of the most well-known correlations for heat transfer: the Dittus-Boelter equation. This equation is:

hd/k = 0.023Re^0.8Pr^n

h = heat transfer coefficient
d = tube diameter
k = thermal conductivity
Re = Reynolds number
Pr = Prandtl number

The exponent n has different values depending on whether the plate is heated or cooled:
n = 0.3 for cooling and 0.4 for heating

Of course the Dittus-Boelter equation was developed for turbulent flow inside of tubes. However, correlations for heat transfer between air and plates, cylinders, or tube outer surfaces also shows a dependence on heating or cooling. In addition, there is a dependence on the orientation of the plate (horizontal, vertical, inclined, upward facing surface, downward facing surface).

I don’t know off hand how much difference there will be in the heating vs cooling heat transfer coefficient.

TREMOLO

 

[heaterguy]

Tremolo,

Thank you for that quick response. This application is natural convection. We know the htc for heating air with metal (electric heaters), but now we need an htc for heating a metal block.

Does natural vs. forced convection change your answer?

 

[Tremolo]

heaterguy,

Natural convection has a heating/cooling dependence which itself is dependent on the orientation of the metal surface.

I believe I can give you an answer if you can tell me whether the heater surface is vertical or horizontal. Same for the metal block (or perhaps the block has a horizontal top and vertical sides).


TREMOLO.

 

[heaterguy]

The metal-to-air geometry is metal rods. The air-to-metal geometry is a steel box.

 

[BretCahill]

Conductivity, viscosity and density of air change pretty much with temperature. Maybe you could get ball park figures using cold to hot data for hot to cold over 50 degrees but anything much greater than that might give wildly different results.


Bret Cahill

 

[25362]

Holman brings the following HTC approximations for free convection (air at atmospheric pressure and "moderate" temperatures):

Heated plate facing upward or cooled plate facing downward:

laminar: h = 1.32 ([Δ]T/L)[sup]0.25[/sup]
turbulent: h = 1.43 ([Δ]T)[sup]0.33[/sup]

Heated plate facing downward or cooled plate facing upward:

h = 0.61([Δ]T/L[sup]2[/sup])[sup]0.2[/sup]

Vertical plane:

laminar: h = 1.42 ([Δ]T/L)[sup]0.25[/sup]
turbulent: h = 0.95 ([Δ]T)[sup]0.33[/sup]

where

h: W/(m[sup]2[/sup].[sup]o[/sup]C)
L: vertical or horizontal dimension, m
[Δ]T: T[sub]w[/sub] - T[sub][∞][/sub] , [sup]o[/sup]C

I assume one could use the above for the box case.

Turbulent: (Gr.Pr) > 10[sup]9[/sup]
Laminar: 10[sup]4[/sup]< (Gr.Pr) < 10[sup]9[/sup]

 

[heaterguy]

25362,

Good stuff. Thanks.

What is the definition of "moderate". Is 100'F Delta T considered moderate? Is 500'F?

Is top flow the same for laminar and turbulent conditions?

Just as a note: the top flow htc for metal to air is ~20 times higher than air to metal. Also, using these htc equations gives a much lower heat up time than we expect.

Regards,

Craig

 

[heaterguy]

Holman's numbers are way too low. They might make sense with about 10 deg. F temperature difference, but fall way off with 50 deg. F or higher temperature difference.