Advanced Thermofluids Mechanics - Shape Factor

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ADVANCED THERMOFLUIDS MECHANICS –SHAPE FACTOR
Assignment A: Conduction Theory and Real Life Application and Analysis
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Theory
Shape factor alludes to a value that is influenced by an article's shape however is free
of its measurements. Yovanovich postulated the characteristics of S, the conduction Shape
Factor for a confined three dimensional shaped body dependent on a boundary’s basic
gradient of temperature slope along an outward-facing perpendicular, n projected from the
surface of the body:
For the specific issue of the 3-D fenced in area framed between a warmed internal and cooled
external limit, the boundary is assessed at the inward surface, Ai, where the dimensionless
temperature increment is characterized as:
The general scale length is utilized in making the shape factor dimensionless as shown:
The the total rate of heat transfer, Q and thermal resistance, R relates to shape factor as
follows:
Where the area of the inside surface is choosen as the feature length and is raised by the
power of half, and therefore:

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The figure below shows the various notations used for indicating dimensions of the diffent
shapes of inside bodies
Comparative documentation is utilized for the elements of the external limit shapes.
Hollands and Hassani came up with the conduction shape factor framework for the
dimensionless quantity, S (shape factor) for three dimensional walled in area hole with a
regular hole dividing:
All shapes of bodies are approximated using the sphere’ S∞:
And using the foundations and arguments on 1D heat transfer, the approximation of S0 can
be made:
where δ denotes the least spacing of the gap