Local sensitivity analysis for the heat flux-temperature integral relationship in the half-space. (English) Zbl 1205.80018
The paper provides an insight into the heat flux-temperature integral relationship based on locally averaged thermophysical properties. This relationship is often used in one-dimensional, transient heat transfer studies entailing null-point calorimetry and heat flux research and is an extremely useful tool for simplifying analysis and providing reasonable results to many experimental studies. This investigation focuses on short transient studies where energy has not fully penetrated the body as the result of an imposed surface heating condition. A full nonlinear heat transfer model with temperature dependent thermophysical properties is developed involving a half-space planar region. Temperature results are then introduced into the constant property integral relationship and a newly derived Kirchoff integral relationship for retrieving the local heat flux. The fully nonlinear results and locally linearized system are observed to be in good agreement. Also, a sensitivity study is described which involves perturbing the average thermophysical properties of thermal conductivity and heat capacity.
Reviewer: Viktor Shevchuk (Lviv)
MSC:
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 35K05 | Heat equation |
| 35K55 | Nonlinear parabolic equations |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
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