## THERMAL SCIENCE

International Scientific Journal

### A THEORETICAL ANALYSIS OF LOCAL THERMAL EQUILIBRIUM IN FIBROUS MATERIALS

**ABSTRACT**

The internal heat exchange between each phase and the Local Thermal Equilibrium (LTE) scenarios in multi-phase fibrous materials are considered in this paper. Based on the two-phase heat transfer model, a criterion is proposed to evaluate the LTE condition, using derived characteristic parameters. Furthermore, the LTE situations in isothermal/adiabatic boundary cases with two different heat sources (constant heat flux and constant temperature) are assessed as special transient cases to test the proposed criterion system, and the influence of such different cases on their LTE status are elucidated. In addition, it is demonstrated that even the convective boundary problems can be generally estimated using this approach. Finally, effects on LTE of the material properties (thermal conductivity, volumetric heat capacity of each phase, sample porosity and pore hydraulic radius) are investigated, illustrated and discussed in our study.

**KEYWORDS**

PAPER SUBMITTED: 2012-06-07

PAPER REVISED: 2013-01-07

PAPER ACCEPTED: 2013-03-05

PUBLISHED ONLINE: 2013-04-13

**THERMAL SCIENCE** YEAR

**2015**, VOLUME

**19**, ISSUE

**Issue 1**, PAGES [69 - 82]

- Cattaneo, C., Sulla Conduzione Del Calore, Atti Semin. Mat. Fis. Univ. Modena, 3(1948),83-101.
- Vernotte, P., Paradoxes in the Continuous Theory of the Heat Equation, C. R. Acad. Bulg. Sci., 246(1958),3154-3155.
- Tzou, D.Y., A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales, Journal of Heat Transfer, 117(1995),1,PP. 8-16.
- Amiri, A., et al., Analysis of dispersion effects and non-thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media, International Journal of Heat and Mass Transfer, 37(1994),6,PP. 939-954.
- Nield, D.A., et al., Effect of local thermal non-equilibrium on thermally developing forced convection in a porous medium, International Journal of Heat and Mass Transfer, 45(2002),25,PP. 4949-4955.
- Kuznetsov, A.V., An investigation of a wave of temperature difference between solid and fluid phases in a porous packed bed, International Journal of Heat and Mass Transfer, 37(1994),18,PP. 3030-3033.
- Minkowycz, W.J., et al., On departure from local thermal equilibrium in porous media due to a rapidly changing heat source: the Sparrow number, International Journal of Heat and Mass Transfer, 42(1999),18,PP. 3373-3385.
- Lee, D.Y., et al., Analytical characterization and conceptual assessment of solid and fluid temperature differentials in porous media, International Journal of Heat and Mass Transfer, 42(1999),3,PP. 423-435.
- Yang, K., et al., Analysis of temperature gradient bifurcation in porous media - An exact solution, International Journal of Heat and Mass Transfer, 53(2010),19-20,PP. 4316-4325.
- Vadasz, P., On the paradox of heat conduction in porous media subject to lack of local thermal equilibrium, International Journal of Heat and Mass Transfer, 50(2007),21-22,PP. 4131-4140.
- Zhao, L., et al., Fractal Approach to Flow through Porous Material, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2009),7,PP.
- Shi, X.-J., et al., Fractal Phenomenon in Micro-Flow through a Fiber Bundle, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2009),7,PP.
- Li, Z.-b., et al., Fractional Complex Transform For Fractional Differential Equations, Mathematical and Computational Application, 15(2010),5,PP.
- Li, Z.-B., An Extended Fractional Complex Transform, International Journal of Nonlinear Sciences and Numerical Simulation, 11(2010),
- He, J.-H., A New Fractal Derivation, Thermal Science, 15(2011),5,PP.
- Fan, J., et al., Hierarchy of Wool Fibers and Fractal Dimensions, International Journal of Nonlinear Sciences and Numerical Simulation, 9(2008),3,PP. 293-296.
- Yang, X.-j., et al., Fractal heat conduction problem solved by local fractional variation iteration method, Thermal Science, In press(2012),
- Lee, J., et al., Effect of Thermal Non-Equilibrium on Convective Instability in a Ferromagnetic Fluid-Saturated Porous Medium, Transport In Porous Media, 86(2011),1,PP. 103-124.
- Nouri-Borujerdi, A., et al., The effect of local thermal non-equilibrium on conduction in porous channels with a uniform heat source, Transport In Porous Media, 69(2007),2,PP. 281-288.
- Hayes, A.M., et al., The thermal modeling of a matrix heat exchanger using a porous medium and the thermal non-equilibrium model, International Journal of Thermal Sciences, 47(2008),10,PP. 1306-1315.
- Tian, M., et al., Measuring the thermophysical properties of porous fibrous materials with a new unsteady-state method, Journal of Thermal Analysis and Calorimetry, 107(2012),1,PP. 395-405.
- Xu, F., et al., Modeling skin thermal pain sensation: Role of non-Fourier thermal behavior in transduction process of nociceptor, Computers in Biology and Medicine, 40(2010),5,PP. 478-486.
- Tian, M., et al., Skin thermal stimulation on touching cool fabric from the transient stage to steady-state stage, International Journal of Thermal Sciences, 53(2012),0,PP. 80-88.
- Pan, N., et al., Fibrous Materials as Soft Matter, Textile Res. J., 77(2007),4,PP. 205-213.
- Wang, X.Y., et al., Abrasion resistance of thermally bonded 3D nonwoven fabrics, Wear, 262(2007),3-4,PP. 424-431.
- Amiri, A., et al., Transient analysis of incompressible flow through a packed bed, International Journal of Heat and Mass Transfer, 41(1998),24,PP. 4259-4279.
- Wang, L., et al., Equivalence between dual-phase-lagging and two-phase-system heat conduction processes, International Journal of Heat and Mass Transfer, 51(2008),7-8,PP. 1751-1756.
- Kim, K.J., et al., Thermal conduction between a heated microcantilever and a surrounding air environment, Applied Thermal Engineering, 29(2009),8-9,PP. 1631-1641.
- Tian, M., et al., Effects of layer stacking sequence on temperature response of multi-layer composite materials under dynamic conditions, Applied Thermal Engineering, 33-34(2012),219-226.
- Hammerschmidt, U., A Quasi-Steady State Technique to Measure the Thermal Conductivity, International Journal of Thermophysics, 24(2003),5,PP. 1291-1312.
- Farnworth, B., Mechanisms of Heat Flow Through Clothing Insulation Textile Research Journal, 53(1983),12,PP. 8.
- Tian, M., et al., Effects of layering sequence on thermal response of multilayer fibrous materials: Unsteady-state cases, Experimental Thermal and Fluid Science, 41(2012),0,PP. 143-148.