SR_11
Function SR_11(a, h, k) returns the thermal resistance associated with spreading between a circular 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_2) while if the conductance approaches infinity then the result limits to the uniform temperature result (SR_1).
Note that the total resistance between the contact and the material far from the half space is
R_total = 1/(h*pi*a^2) + SR_11 (the function SR_11 calculates only the spreading resistance)
The calling protocol is:
R = SR_11(a, h, k)
Inputs:
a = radius of circle [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 R11 units=K/W
a=1 [m]
h=1 [W/m^2-K]
k=1 [W/m-K]
R11=sr_11(a,h,k)
{Solution:
R11 = 0.2675 [K/W]}