Experimental Evidence of Hyperbolic Heat Conduction in Processed Meat

Abstract

The objective of this paper is to present experimental evidence of the wave nature of heat propagation in processed meat and to demonstrate that the hyperbolic heat conduction model is an accurate representation, on a macroscopic level, of the heat conduction process in such biological material. The value of the characteristic thermal time of a specific material, processed bologna meat, is determined experimentally. As a part of the work different thermophysical properties are also measured. The measured temperature distributions in the samples are compared with the Fourier results and significant deviation between the two is observed, especially during the initial stages of the transient conduction process. The measured values are found to match the theoretical non-Fourier hyperbolic predictions very well. The superposition of waves occurring inside the meat sample due to the hyperbolic nature of heat conduction is also proved experimentally.

Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study

“…Although Mitra et al [13] measured values around 16 s in processed meat, Ali & Zhang's [12] reported a smaller value. Likewise, Kaminski [7] reported a relaxation time between 20 s and 30 s for meat products and Vedavarz et al [27] found an interval between 1 s and 100 s for some biological tissues at room temperature.…”

“…However, Ali & Zhang [12] also point out that these relations are for metals and perfect structures. On the other hand, non-homogeneous materials, such as biological tissues, have very long relaxation times, and consequently would have very low heating speeds [7,13]. Unfortunately, no experimental data have been published to date on the speed of heat propagation in biological tissues.…”

“…This is because in metals, both heat and sound are propagated by mechanisms, such as lattice vibrations, which are all decelerated by the structural imperfections of biological tissues and non-metal materials. In addition, some studies have shown that in many cases the values of C and α imply that the first term of equation (1.3) (secondorder derivative) does not have to be necessarily negligible with respect to the second term (first-order derivative) [12,13]. With the same purpose, Cattaneo [14] and Vernotte [15] proposed a modification of Fourier's linear flux as follows:…”

“…Our objective was therefore to solve the relativistic problem for the concrete case of thermal ablation of biological tissues (including an internal heat source) in order to compare the temperature distributions in the tissue computed theoretically from the three heat equations (Fourier, hyperbolic and relativistic). This case was considered since experimental data have suggested that the thermal relaxation time in biological tissues could be significant [13]. The analytical solutions for the HHE and FHE were previously obtained [19].…”

Solution of a Problem of Generalized Thermoelasticity of an Annular Cylinder with Variable Material Properties by Finite Difference Method

“…Later on, another three new formulations of thermoelasticity based on entropy balance inequality have been proposed by Green and Naghdi [5][6][7]. Several experimental studies [8][9][10] also indicate the actual occurrence of wave type heat transport. Subsequently, several investigations [11][12][13][14][15][16] are carried out on the basis of different generalized theories of thermoelasticity.…”