9 . " AN ATTEMPT TO SOLVE THE HEAT TRANSFER EQUATION IN A MODEL OF PYROLYSIS SPRAY USING 4q-ORDER m-BOUBAKER POLYNOMIALS ", Int.
12.
The steady-state solution of a simplified mass transfer equation that is used to describe the mass exchange over a semi-permeable membrane and models peritoneal dialysis is
13.
For two-and three-dimensional geometries computational fluid dynamics ( CFD ) tools are required to solve simultaneously the fluid flow and heat transfer equations through porous media.
14.
For large excess temperatures, T ^ 4-T _ s ^ 4 \ approx u ^ 4, giving a high-temperature heat-transfer equation of the form
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Which is another statement of Kirchhoff's law, relating two material properties of the medium, and which yields the radiative transfer equation at a point around which the medium is in thermodynamic equilibrium:
16.
26 . " A SOLUTION THE HEAT TRANSFER EQUATION INSIDE HYDROGEN CRYOGENIC VESSELS USING BOUBAKER-ZHAO POLYNOMIALS ", Cryogenics, Paper N?CRYOGENICS-D-08-00142, Accepted ( 2008 ).
17.
If the differences are not large, an accurate formulation of heat transfers in the system may require analysis of heat flow based on the ( transient ) heat transfer equation in nonhomogeneous or poorly conductive media.
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A Biot number greater than 0.1 ( a " thermally thick " substance ) indicates that one cannot make this assumption, and more complicated heat transfer equations for " transient heat conduction " will be required to describe the time-varying and non-spatially-uniform temperature field within the material body.
19.
The opposite is also true : A Biot number greater than 0.1 ( a " thermally thick " substance ) indicates that one cannot make this assumption, and more complicated heat transfer equations for " transient heat conduction " will be required to describe the time-varying and non-spatially-uniform temperature field within the material body.
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