A new anisotropic, two‐dimensional, transient heat flux‐temperature integral relationship for half‐space diffusion

Abstract

Fig. 1, m ρ = density, kg/m 3

A new three-dimensional heat flux–temperature integral relationship for half-space transient diffusion

“…Hence, oneand/or two-dimensional experimental studies are commonly performed. As such, Frankel and his colleagues have primarily focused on developing one-and two-dimensional relationships for isotropic, orthotropic and anisotropic materials [7] that account for noisy data [1,4]. A scheme based on Gauss digital filtering the acquired temperature data have been successfully demonstrated and implemented using both numerical data with random noise [1,4] and real experimental data.…”

“…This is possible if the general law (first law of thermodynamics) and constitutive equation for heat flux (Fourier's law) are combined to obtain the classical heat equation in the temperature variable. Frankel and his colleagues [1][2][3][4][5][6][7] have developed a unified mathematical treatment for obtaining these new integral relationships that do not involve any knowledge of spatial gradients. Hence, only time histories of temperature are required.…”

“…This relationship must be discretized in some sense when sensors are used at the in-depth position. Frankel et al [2,7] have developed such a discretization in two-dimensions. The number of sensors required will physically be based on the imposed surface condition.…”