Local sensitivity analysis for the heat flux-temperature integral relationship in the half-space

Abstract This paper presents insight into the heat flux-temperature ( q ″ −  T ) integral relationship based on constant thermophysical properties. This relationship is often used in one-dimensional, transient heat transfer studies involving null-point calorimetry and heat flux investigations. This study focuses on a 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 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. Good agreement is observed between the fully nonlinear results and locally linearized system. Additionally, a sensitivity study is presented which involves perturbing the average thermophysical properties of thermal conductivity and heat capacity.

[1]  P. Kythe,et al.  Computational Methods for Linear Integral Equations , 2002 .

[2]  F. Lu,et al.  Characterization of Thin-Film Heat-Flux Gauges , 1999 .

[3]  J. L. Lage,et al.  Fractional-Diffusion Solutions for Transient Local Temperature and Heat Flux , 2000 .

[4]  J. L. Lage,et al.  A Fractional-Diffusion Theory for Calculating Thermal Properties of Thin Films From Surface Transient Thermoreflectance Measurements , 2001 .

[5]  Peter Linz,et al.  Analytical and numerical methods for Volterra equations , 1985, SIAM studies in applied and numerical mathematics.

[6]  S. J. Kline,et al.  Describing Uncertainties in Single-Sample Experiments , 1953 .

[7]  W. Cook,et al.  Reduction of data from thin-film heat-transfer gages - A concise numerical technique. , 1966 .

[8]  J. P. Hartnett,et al.  Advances in Heat Transfer , 2003 .

[9]  J. I. Frankel,et al.  A new flux integral relationship for half-space transient heat conduction with arbitrary initial condition , 2008 .

[10]  Jay I. Frankel,et al.  A new multidimensional integral relationship between heat flux and temperature for direct internal assessment of heat flux , 2008 .

[11]  Thomas E. Diller,et al.  Advances in Heat Flux Measurements , 1993 .

[12]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[13]  R. Taylor,et al.  The Numerical Treatment of Integral Equations , 1978 .

[14]  Paul Zarchan,et al.  Advanced Hypersonic Test Facilities , 2002 .

[15]  Jay I. Frankel.  Generalizing the method of Kulish to one-dimensional unsteady heat conducting slabs , 2006 .

[16]  Jay I. Frankel.  Regularization of inverse heat conduction by combination of rate sensor analysis and analytic continuation , 2007 .

[17]  T. Grundy,et al.  Progress in Astronautics and Aeronautics , 2001 .