View source for Heat transfer coefficient

==Newton’s Law of Cooling==

Newton’s Law of Cooling is:

<math>q = h \cdot A \cdot \Delta T</math>

where q is the heat transfer rate, h is the heat transfer coefficient for the system, A is the area of heat transfer, and ΔT is the temperature difference between the zones of heat transfer.  This description of heat transfer applies to convection.

Generally, for a body at some temperature T<sub>body</sub> in a reservoir of fluid T<sub>fluid</sub>:

ΔT = T<sub>body</sub> - T<sub>fluid</sub>

==Estimating Heat Transfer Coefficient==

In principle h can be calculated from measured data for any given system, but it cannot always be derived from theory.  h can be estimated for systems of known geometry and known materials using empirical methods, however.  

==Nusselt Number==

The Nusselt Number of a thermal interface is a dimensionless analog of the heat transfer coefficient.  For a system than can be bounded by a finite volume, it can be found using the formula:

<math>Nu = \frac{{h \cdot D_h }}{{k_{fluid} }}</math>

where <i>Nu</i> is the Nusselt Number, D<sub>h</sub> is the effective diameter of the interface, and k<sub>fluid</sub> is the [[thermal conductivity]] of the convective fluid.  However, the Nusselt number can be found using empirical relations for the interface’s materials and geometry as well, and then used to derive the heat transfer coefficient.

For example, for a cylinder parallel to the wind:

<math>
Nu = c \cdot {Re} ^n  \cdot \sqrt[3]{{Pr}} 
</math>

where <i>Re</i> and <i>Pr</i> are the fluid Reynolds Number and Prandtl Number of the cylinder-wind system, and c and n are constants for a given range of Reynolds numbers.

<math>Re  = \frac{{\rho  \cdot v \cdot D_h }}{\mu }</math>

and

<math>Pr  = \frac{{c_p  \cdot \mu}}{k }</math>

where ρ is the air density, v is the wind velocity, D<sub>h</sub> is the hydraulic diameter of the cylinder (equal to the diameter for a free floating cylinder, or the diameter of a cylinder with the same surface area in contact with the wind for a half cylinder or buried cylinder), μ is the kinematic viscosity of the air, k is the thermal conductivity of the air, and c<sub>p</sub> is the [[specific heat and heat capacity|specific heat]] of the air.

The values for most of these constants for the Martian air can be found by assuming the air is equivalent to pure carbon dioxide at 7 mb pressure (the average Martian air pressure).  The coefficients for computing the Nusselt number are:

{|
| '''Reynold's Number Range''' || || '''c Value''' || || '''n Value'''
|-
| 1 - 4 || || 0.989 || || 0.330
|-
| 4 - 40 || || 0.911 || || 0.385
|-
| 40 - 4000 || || 0.683 || || 0.466
|-
| 4000 - 40000 || || 0.193 || || 0.618
|-
| 40000 - 250000 || || 0.0266 || || 0.805
|-
|}

Note that the form of the equation used to find the Nusselt number is empirical.  Nusselt Number equations for various systems are simply fitted to experimental data, and there is not necessarily any correspondence between them.  If the wind flow is parallel to the cylinder, the Nusselt number is obtained by an entirely different empirical equation:

<math>Nu = 0.648 \cdot \sqrt {{Re}}  \cdot \sqrt[3]{{Pr }}</math>


Then, once the Nusselt number of the system is known, the heat transfer coefficient of the wind-cylinder heat transfer surface can be computed.

<math>h = \frac{{Nu \cdot k_{fluid} }}{{D_h }}</math>


* See Also: [[Thermodynamics of the greenhouse]]

==External Links==

[http://en.wikipedia.org/wiki/Heat_transfer_coefficient Wikipedia Article: Heat Transfer Coefficient]

{{MainArticle|[[Heat transfer|Heat Transfer]]}}