## THERMAL SCIENCE

International Scientific Journal

### AN INSPECTION TO THE HYPERBOLIC HEAT CONDUCTION PROBLEM IN PROCESSED MEAT

**ABSTRACT**

This paper analyzes a hyperbolic heat conduction problem in processed meat with the non-homogenous initial temperature. This problem is related to an experimental study for the exploration of thermal wave behavior in biological tissue. Because the fundamental solution of the hyperbolic heat conduction model is difficult to be obtained, a modified numerical scheme is extended to solve the problem. The present results deviate from that in the literature and depict that the reliability of the experimentally measured properties presented in the literature is doubtful.

**KEYWORDS**

PAPER SUBMITTED: 2014-04-04

PAPER REVISED: 2015-03-03

PAPER ACCEPTED: 2015-03-12

PUBLISHED ONLINE: 2015-04-04

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**1**, PAGES [303 - 308]

- Cattaneo, C., Sullaconduzione de Calore., Atti del Semin. Mat. E Fis. Univ. Modena, 3 (1948), pp. 83-101.
- Vernotte, P., Les Paradoxes de la Theorie Continue de L'equation de la Chaleur, Compute Rendus, 246 (1958), pp. 3145-3155.
- Weymann, H.D., Finite Speed of Propagation in Heat Conduction, Diffusion, and Viscous Shear Motion, American J. of Physics., 35 (1967), pp. 488-496.
- Sobolev, S.L., Transport Processes and Traveling Waves in Systems with Local Nonequilibrium, Sov. Phys. Usp., 34 (1991), pp. 217-229.
- O zisik M.N., Tzou, D.Y., On the Wave Theory in Heat Conduction, ASME J. Heat Transfer, 116 (1994), pp. 526-535.
- Arkin, H., Xu, L.X., and Holmes, K.R., Recent Developments in Modeling Heat Transfer in Blood Perfused Tissues, IEEE. Trans. Biomedical Engineering, 41 (1994), pp. 97-107.
- W. Kaminski, Hyperbolic Heat Conduction Equation for Material with a Nonhomogenous Inner Structure, ASME J. Heat Transfer, 112 (1990), pp. 555-560.
- Braznikov, A.M., Karpychev, V.A., and Luikova, A.V., One Engineering Method of Calculating Heat Conduction Process, Inzhenerno Fizicheskij Zhurnal, 28 (1975), pp. 677-680.
- Mitra, K., Kumar, S., Vedavarz, A., and Moallemi, M.K., Experimental Evidence of Hyperbolic Heat Conduction in Processed Meat, ASME J. Heat Transfer, 117 (1995), pp. 568-573.
- Roetzel, W., Putra, N., and Das, S.K., Experiment and Analysis for Non-Fourier Conduction in Materials with non-Homogeneous Inner Structure, Int. J. Thermal Science, 42 (2003), pp. 541-552.
- Bhowmik, A., Singh, R., Repaka, R., Mishra, S.C., Conventional and Newly Developed Bioheat Transport Models in Vascularized Tissues: A Review, Journal of Thermal Biology, 38 (2013), pp. 107-125.
- Ezzat, M. A., AlSowayan, N.S., A-Muhiameed, Z.I.A., Ezzat, S.M., Fractional Modelling of Pennes' Bioheat Transfer Equation, Heat and Mass Transfer, 50(2014), pp. 907-914.
- Liu K.C., Analysis for High-order Effects in Thermal Lagging to Thermal Responses in Biological Tissue, Int. J. Heat and Mass Transfer, 81(2015), pp. 347-354.
- Yang, C.Y., Estimation of the Period Thermal Conditions on the Non-Fourier Fin Problem, Int. J. Heat Mass Transfer, 48 (2005), pp. 3506-3515.
- Özen, Ş., Helhel, S., Çerezci, O., Heat Analysis of Biological Tissue Exposed to Microwave by Using Thermal Wave Model of Bio-Heat Transfer, Burns, 34(2008), pp. 45-49.
- Liu, K.C., Cheng, P.J., Finite Propagation of Heat Transfer in a Multi-Layer Tissue, AIAA J. Thermophys. Heat Transfer, 22 (2008) , pp. 775-782.
- Liu, K.C., Thermal Propagation Analysis for Living Tissue with Surface Heating, Int. J. Thermal Science, 47 (2008) , pp. 507-513.