
Spreading Resistance of Isoflux Rectangles
and Strips on Compound Flux Channels

Summary
This application calculates two and threedimensional
thermal spreading resistance for isoflux rectangular and strip sources
on a rectangular disk, a semiinfinite rectangular cylinder
or a half space.
Solutions are available for a twolayer system with
different thicknesses and thermal conductivities, and an isotropic medium
with constant properties.
For the finite problem a uniform heat transfer coefficient boundary
condition is applied to the lower surface.
Background
Thermal spreading resistance occurs whenever heat leaves a source of finite
dimensions and enters a larger region. For this particular problem, a
planar rectangular heat source is situated on one end of a compound or
isotropic heat flux channel. The heat flux channel is either semiinfinite
or is cooled along the bottom surface through a uniform film coefficient
(or contact conductance) h. The heat source area can be rectangular,
having dimensions 2a by 2b, or it may be a strip of width
2a. The dimensions of the heat flux channel are 2c by
2d. The lateral boundaries of the heat flux channel are
adiabatic.
The total system thermal resistance R_{total}
is defined by:
R_{total} = ( T_{source}  T_{sink} ) / Q
where: 
T_{source} = 
mean temperature of the heat source
( ^{o}C) 

T_{sink} = 
mean heat sink temperature ( ^{o}C)

 Q = 
heat flow rate through the heat flux channel
(W) 
The total thermal resistance of the system can be determined by:
R_{total} = R_{s} + R_{1D}
where R_{s} is the thermal spreading resistance of the
system and R_{1D} is the onedimesional thermal resistance,
defined as:
R_{1D} =
( t_{1} / k_{1} +
t_{2} / k_{2} +
1 / h ) / A
For the general case of a rectangular source area on a finite, twolayer
rectangular heat flux channel, the spreading resistance will depend on
several geometric and thermophysical parameters:
R_{s} = f ( a, b, c, d,
t_{1} ,
t_{2} ,
k_{1} ,
k_{2} , h )
All calculations based on methods described in M.M. Yovanovich, Y.S.
Muzychka and J.R. Culham, "Spreading Resistance of Isoflux Rectangles and
Strips on Compound Flux Channels," AIAA 980873,
presented at the AIAA 36th Aerospace
Sciences Meeting and Exhibit, Reno, NV, January 12  15, 1998.
Instructions
 Click on the image below that best describes your problem
 When the required tables are loaded, enter
all input values in the table on the left
 Browser will calculate when the Calculate button is clicked
 Depending on the speed of your machine and
the number of terms, the solution may take
a while to compute
Copyright © 2006 Microelectronics Heat Transfer Laboratory