# Question about heat loss from a surface

1. Nov 12, 2008

### nuby

How can I calculate the heat loss from the surface area of a box into air?

Also, how can I calculate the heat/energy loss from a heated gas (into ambient air)?.

2. Nov 12, 2008

### minger

Consequently, if the box were in a forced convection flow region, it would probably be easier. If the air is stagnant, we have whats called Free Convection in that the air is moving due to the natural heating and cooling it experiences with proximity to the box.

Anyways, the general equation for heat convection is:
$$q = hA\Delta T$$
A is the area, dT is the difference in temperature, and q is the heat transfer. The only problem is h, the heat convection coefficient.

We will use experimental results to "guess" the value of h. We can relate the heat transfer coefficient to a non-dimensional number called the Nusselt Number:
$$\bar{Nu_L} = \frac{\bar{h}L}{k}$$
Where L is a characteristic length, k is the thermal conductivity, and h is the heat transfer coefficient that we want. We can get a relation for the Nusselt Number FOR A VERTICAL PLATE as:
$$\bar{Nu_L} = 0.68 + \frac{0.670 {Ra}^{1/4}_L}{\left[1+(0.492/Pr)^{9/16}\right]^{4/9}}$$
The Prandtl Number is easy enough to search for and fine the relation, its easy. The Raylaeigh (sp?) number is then given by:
$$Ra_L = \frac{g\beta(T_s - T_{\infty}L^3}{\nu\alpha}$$
Which has more easy material constants that you can look up.

For a horizontal plate, you can say that:
$$\bar{Nu_L}=0.54Ra^{1/4}_L \mbox{For 10^4<Ra_L<10^7}$$
and
$$\bar{Nu_L}=0.15Ra^{1/3}_L \mbox{For 10^7<Ra_L<10^11}$$

Then just add the effects all 5 sides together. Good luck,

Edit: Figured I'd give you some of those coefficients
Code (Text):
Thermal Conductivity, k*10^3 (W / mK)
100K  9.34
300K 26.3
500K 40.7
Code (Text):
Dynamic Viscosity, v (nu) *10^6
100K 2.00
300K 15.89
500K 38.79
Code (Text):
Thermal Diffusivity, a (alpha)*10^6
100K 2.54
300K 22.5
500K 56.7
For ideal gasses, the volumetric thermal expansion coefficient, $$\beta$$ is simply equal to 1/T (where T is in absolute temperature).

Last edited: Nov 12, 2008