**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32019

##### Heat Transfer and Entropy Generation in a Partial Porous Channel Using LTNE and Exothermicity/Endothermicity Features

**Authors:**
Mohsen Torabi,
Nader Karimi,
Kaili Zhang

**Abstract:**

This work aims to provide a comprehensive study on the heat transfer and entropy generation rates of a horizontal channel partially filled with a porous medium which experiences internal heat generation or consumption due to exothermic or endothermic chemical reaction. The focus has been given to the local thermal non-equilibrium (LTNE) model. The LTNE approach helps us to deliver more accurate data regarding temperature distribution within the system and accordingly to provide more accurate Nusselt number and entropy generation rates. Darcy-Brinkman model is used for the momentum equations, and constant heat flux is assumed for boundary conditions for both upper and lower surfaces. Analytical solutions have been provided for both velocity and temperature fields. By incorporating the investigated velocity and temperature formulas into the provided fundamental equations for the entropy generation, both local and total entropy generation rates are plotted for a number of cases. Bifurcation phenomena regarding temperature distribution and interface heat flux ratio are observed. It has been found that the exothermicity or endothermicity characteristic of the channel does have a considerable impact on the temperature fields and entropy generation rates.

**Keywords:**
Entropy generation,
exothermicity,
endothermicity,
forced convection,
local thermal non-equilibrium,
analytical modeling.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1129956

**References:**

[1] T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Introduction to Heat Transfer, 6th ed. John Wiley and Sons, Inc., 2011.

[2] A. Bejan, Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes. CRC Press, 1995.

[3] A. Bejan, Entropy Generation Through Heat and Fluid Flow. New York: Wiley, 1982.

[4] D. A. Nield and A. Bejan, Convection in Porous Media, 4th edition. New York: Springer, 2013.

[5] D. Nield, “Effects of local thermal nonequilibrium in steady convective processes in a saturated porous medium: forced convection in a channel,” J. Porous Media, vol. 1, pp. 181–186, 1998.

[6] B. Alazmi and K. Vafai, “Constant wall heat flux boundary conditions in porous media under local thermal non-equilibrium conditions,” Int. J. Heat Mass Transf., vol. 45, pp. 3071–3087, 2002.

[7] S. A. Khashan, A. M. Al-Amiri, and M. A. Al-Nimr, “Assessment of the local thermal non-equilibrium condition in developing forced convection flows through fluid-saturated porous tubes,” Appl. Therm. Eng., vol. 25, no. 10, pp. 1429–1445, Jul. 2005.

[8] G. M. Chen and C. P. Tso, “A two-equation model for thermally developing forced convection in a porous medium with viscous dissipation,” Int. J. Heat Mass Transf., vol. 54, no. 25–26, pp. 5406–5414, Dec. 2011.

[9] G. M. Chen and C. P. Tso, “Forced convection with viscous dissipation using a two-equation model in a channel filled with a porous medium,” Int. J. Heat Mass Transf., vol. 54, no. 9–10, pp. 1791–1804, Apr. 2011.

[10] X.-L. Ouyang, K. Vafai, and P.-X. Jiang, “Analysis of thermally developing flow in porous media under local thermal non-equilibrium conditions,” Int. J. Heat Mass Transf., vol. 67, pp. 768–775, Dec. 2013.

[11] M. Dehghan, M. S. Valipour, and S. Saedodin, “Perturbation analysis of the local thermal non-equilibrium condition in a fluid-saturated porous medium bounded by an isothermal channel,” Transp. Porous Media, vol. 102, no. 2, pp. 139–152, Jan. 2014.

[12] M. Dehghan, M. T. Jamal-Abad, and S. Rashidi, “Analytical interpretation of the local thermal non-equilibrium condition of porous media embedded in tube heat exchangers,” Energy Convers. Manag., vol. 85, pp. 264–271, Sep. 2014.

[13] J. A. Ochoa-Tapia and S. Whitaker, “Heat transfer at the boundary between a porous medium and a homogeneous fluid,” Int. J. Heat Mass Transf., vol. 40, no. 11, pp. 2691–2707, 1997.

[14] F. Arpino, A. Carotenuto, N. Massarotti, and A. Mauro, “New solutions for axial flow convection in porous and partly porous cylindrical domains,” Int. J. Heat Mass Transf., vol. 57, no. 1, pp. 155–170, Jan. 2013.

[15] K. Yang and K. Vafai, “Restrictions on the validity of the thermal conditions at the porous fluid interface—An exact solution,” J. Heat Transfer, vol. 133, no. 11, p. 112601, 2011.

[16] K. Yang and K. Vafai, “Analysis of heat flux bifurcation inside porous media incorporating inertial and dispersion effects – An exact solution,” Int. J. Heat Mass Transf., vol. 54, no. 25–26, pp. 5286–5297, Dec. 2011.

[17] H. J. Xu, Z. G. Qu, T. J. Lu, Y. L. He, and W. Q. Tao, “Thermal modeling of forced convection in a parallel-plate channel partially filled with metallic foams,” J. Heat Transfer, vol. 133, no. 9, p. 092603, 2011.

[18] H. J. Xu, Z. G. Qu, and W. Q. Tao, “Analytical solution of forced convective heat transfer in tubes partially filled with metallic foam using the two-equation model,” Int. J. Heat Mass Transf., vol. 54, no. 17–18, pp. 3846–3855, Aug. 2011.

[19] Y. Mahmoudi and N. Karimi, “Numerical investigation of heat transfer enhancement in a pipe partially filled with a porous material under the local thermal non-equilibrium condition,” Int. J. Heat Mass Transf., vol. 68, pp. 161–173, Jan. 2014.

[20] Y. Mahmoudi, N. Karimi, and K. Mazaheri, “Analytical investigation of heat transfer enhancement in a channel partially filled with a porous material under the local thermal non-equilibrium condition: Effects of different thermal boundary conditions at the porous fluid interface,” Int. J. Heat Mass Transf., vol. 70, pp. 875–891, Mar. 2014.

[21] B. Buonomo, O. Manca, and G. Lauriat, “Forced convection in microchannels filled with porous media in local thermal non-equilibrium conditions,” Int. J. Therm. Sci., vol. 77, pp. 206–222, Mar. 2014.

[22] M. Torabi, K. Zhang, G. Yang, J. Wang, and P. Wu, “Heat transfer and entropy generation analyses in a channel partially filled with porous media using local thermal non-equilibrium model,” Energy, vol. 82, pp. 922–938, 2015.

[23] T. M. Bandhauer, S. Garimella, and T. F. Fuller, “A critical review of thermal issues in lithium-ion batteries,” J. Electrochem. Soc., vol. 158, no. 3, pp. R1–R25, 2011.

[24] K. Zheng, Q. Sun, and M. Ni, “Local non-equilibrium thermal effects in solid oxide fuel cells with various fuels,” Energy Technol., vol. 1, no. 1, pp. 35–41, Jan. 2013.

[25] M. Torabi, K. Zhang, G. Yang, J. Wang, and P. Wu, “Temperature distribution, local and total entropy generation analyses in asymmetric cooling composite geometries with multiple nonlinearities: Effect of imperfect thermal contact,” Energy, vol. 78, pp. 218–234, Dec. 2014.

[26] A. Aziz and W. A. Khan, “Entropy generation in an asymmetrically cooled slab with temperature-dependent internal heat generation,” Heat Transf. Res., vol. 41, no. 3, pp. 260–271, May 2012.

[27] A. Aziz and W. A. Khan, “Classical and minimum entropy generation analyses for steady state conduction with temperature-dependent thermal conductivity and asymmetric thermal boundary conditions: Regular and functionally graded materials,” Energy, vol. 36, no. 10, pp. 6195–6207, Oct. 2011.

[28] M. Torabi and K. Zhang, “Temperature distribution, local and total entropy generation analyses in MHD porous channels with thick walls,” Energy, vol. 87, pp. 540–554, 2015.