Spreading Resistance of Isoflux Rectangles
and Strips on Compound Flux Channels

Summary

This application calculates two- and three-dimensional thermal spreading resistance for isoflux rectangular and strip sources on a rectangular disk, a semi-infinite rectangular cylinder or a half space. Solutions are available for a two-layer 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 semi-infinite 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 Rtotal is defined by:

Rtotal = ( Tsource - Tsink ) / Q

where: Tsource = mean temperature of the heat source ( oC)
Tsink = mean heat sink temperature ( oC)
Q = heat flow rate through the heat flux channel (W)

The total thermal resistance of the system can be determined by:

Rtotal = Rs + R1D

where Rs is the thermal spreading resistance of the system and R1D is the one-dimesional thermal resistance, defined as:

R1D = ( t1 / k1 + t2 / k2 + 1 / h ) / A

For the general case of a rectangular source area on a finite, two-layer rectangular heat flux channel, the spreading resistance will depend on several geometric and thermophysical parameters:

Rs = f ( a, b, c, d, t1 , t2 , k1 , k2 , 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 98-0873, presented at the AIAA 36th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 12 - 15, 1998.


Instructions

  1. Click on the image below that best describes your problem
  2. When the required tables are loaded, enter all input values in the table on the left
  3. Browser will calculate when the Calculate button is clicked
  4. Depending on the speed of your machine and the number of terms, the solution may take a while to compute


Finite Compound Channel with
Rectangular Heat Source

Finite Isotropic Channel with
Rectangular Heat Source

Finite Compound Channel with
Strip Heat Source

Finite Isotropic Channel with
Strip Heat Source

Semi-Infinite Compound Channel With
Rectangular Heat Source

Semi-Infinite Isotropic Channel With
Rectangular Heat Source

Semi-Infinite Compound Channel With
Strip Heat Source

Semi-Infinite Isotropic Channel With
Strip Heat Source

Compound Half Space With
Rectangular Heat Source

Isotropic Half Space With
Rectangular Heat Source



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Last Updated February, 1998