scholarly journals Bayesian Parameter Estimation of Convective Heat Transfer Coefficients of a Roof-Mounted Radiant Barrier System

2005 ◽  
Vol 128 (2) ◽  
pp. 213-225 ◽  
Author(s):  
Philippe Lauret ◽  
Frédéric Miranville ◽  
Harry Boyer ◽  
François Garde ◽  
Laetitia Adelard
Keyword(s):  
Heat Transfer ◽  
Parameter Estimation ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Bayesian Methods ◽  
Thermal Model ◽  
Estimation Method ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Convective Heat Transfer Coefficients

This paper deals with the application of Bayesian methods to the estimation of two convective heat-transfer coefficients of a roof-mounted radiant barrier system. As part of an empirical validation of the thermal model of the roofing complex, a parametric sensitivity analysis highlighted the importance of convective coefficients in the thermal behavior of a roofing complex. A parameter estimation method is then used in order to find the values of the coefficients that lead to an improvement of the thermal model. However, instead of using a classical parameter estimation method, we used a Bayesian inference approach to parameter estimation. The aim of the paper is to introduce the basic concepts of this powerful method in this simple two-parameter case. We show that Bayesian methods introduce an explicit treatment of uncertainty in modeling and a corresponding measure of reliability for the conclusions reached.

Conditions for Equivalency of Countercurrent Vessel Heat Transfer Formulations

1999 ◽  
Vol 121 (5) ◽  
pp. 514-520 ◽  
Author(s):  
R. B. Roemer
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Temperature Difference ◽  
Bulk Temperature ◽  
Transfer Coefficients ◽  
Bulk Fluid ◽  
Heat Transfer Coefficients ◽  
The Difference ◽  
Convective Heat Transfer Coefficients

Previous models of countercurrent blood vessel heat transfer have used one of two, different, equally valid but previously unreconciled formulations, based either on: (1) the difference between the arterial and venous vessels’ average wall temperatures, or (2) the difference between those vessels’ blood bulk fluid temperatures. This paper shows that these two formulations are only equivalent when the four, previously undefined, “convective heat transfer coefficients” that are used in the bulk temperature difference formulation (two coefficients each for the artery and vein) have very specific, problem-dependent relationships to the standard convective heat transfer coefficients. (The average wall temperature formulation uses those standard coefficients correctly.) The correct values of these bulk temperature difference formulation “convective heat transfer coefficients” are shown to be either: (1) specific functions of (a) the tissue conduction resistances, (b) the standard convective heat transfer coefficients, and (c) the independently specified bulk arterial, bulk venous and tissue temperatures, or (2) arbitrary, user defined values. Thus, they are generally not equivalent to the standard convective heat transfer coefficients that are regularly used, and must change values depending on the blood and tissue temperatures. This dependence can significantly limit the convenience and usefulness of the bulk temperature difference formulations.

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