SR_12
The function SR_12(a, h, k) returns the thermal resistance associated with spreading between a square contact area located on the surface of a semi-infinite half-space. The resistance that is calculated is based only on the conduction resistance in the half-space (i.e., the resistance of the interface is not included). The resistance is therefore based on the average temperature on the material-side of the contact. The contact area itself is assumed to be at a uniform temperature. Note that if the conductance approaches zero then the result limits to the uniform heat flux result (SR_5) while if the conductance approaches infinity then the result limits to the uniform temperature result.
Note that the total resistance between the contact and the material far from the half space is
R_total = 1/(h*4*a^2) + SR_12 (function SR_12 calculates only the spreading resistance)
The calling protocol is:
R = SR_12(a, h, k)
Inputs:
a = half width of square [m or ft]
h = conductance [W/m^2-K or Btu/hr-ft^2-R]
k = thermal conductivity of the material [W/m-K or Btu/hr-ft-R]
Outputs:
R = resistance [K/W or R-hr/Btu]
Rohsenow, W.M, J. P. Hartnett, and Y. I. Cho, Handbook of Heat Transfer, 3rd Edition, McGraw Hill, (1998).
Example:
$UnitSystem SI Mass J K Pa Radian
$VarInfo R12 units=K/W
a=1 [m]
h=1 [W/m^2-K]
k=1 [W/m-K]
R12=sr_12(a,h,k)
{Solution:
R12 = 0.2342 [K/W]}