ANALYSIS OF LOCAL THERMAL EQUILIBRIUM ASSUMPTION IN TRANSIENT FORCED CONVECTION IN A GRAPHITE FOAM CHANNEL

Year 2020, Volume: 38 Issue: 4, 2057 - 2067, 05.10.2021

Gürşah Gürüf İsmail Solmaz Özgür Bayer

Abstract

In this study, the validity of Local Thermal Equilibrium (LTE) assumption in the transient forced convection of a rectangular channel filled with a block of graphite foam is examined numerically. The governing macroscopic energy conservation equations for solid and gas phases are derived by taking the average of the microscopic one over the averaging volume. Initially, LTE is in existence between the phases and then, the fluid temperature at the channel inlet is suddenly raised. Besides, an appropriate insulation is provided for the wall of the channel. Hence, a transient one-dimensional Local Thermal Non-Equilibrium (LTNE) model is considered in the numerical investigation. Thermo-physical properties of the solid and fluid phases are presumed to be constant. The graphite foam porosity is spatially uniform and constant. The impact of two dimensionless variables such as fluid to solid Nusselt number (Nufs) and Reynolds number (Re) on the LTE assumption is extensively investigated. . It was found that the dimensionless time required to attain LTE between the phases (τLTE) increases with the increasing value of Reynolds number. However, the real-time (σLTE) corresponding to τLTE was found to be nearly 4 sec over the range of Re numbers studied. Additionally, an increase in the Nufs resulted in a decrease in τLTE for a constant value of Re number and σLTE varied from 1.5 to 5 sec. As a result, the obtained findings showed that it is reasonable to assume the LTE between the phases under the investigated conditions.

Keywords

Foam, forced convection, graphite, LTE, LTNE, porous media, transient

References

• [1] Lin W., Sunden B., Yuan J., A performance analysis of porous graphite foam heat exchangers in vehicles, Applied Thermal Engineering, 50, 2013, pp.1201-1210.
• [2] Abu-Hıjleh B.A., Al-Nımr M.A., Hader M.A., Thermal equilibrium in transient forced convection porous channel flow, Transport in Porous Media, 57, 2004, pp.49-58.
• [3] Al-Nımr M.A., Abu-Hıjleh B.A., Validation of thermal equilibrium assumption in transient forced convection flow in porous channel, Transport in Porous Media, 49, 2002, pp.127-138.
• [4] Rees D.A.S., Bassom A.P., Sıddheshwar P.G., Local thermal non-equilibrium effects arising from the injection of a hot fluid into a porous medium, Journal of Fluid Mechanics, 594, 2008, pp.379-398.
• [5] Kim S.J., Kim D., Lee D.Y., On the local thermal equilibrium in microchannel heat sinks, International Journal of Heat and Mass Transfer, 43, 2000, pp.1735-1748.
• [6] Kim S. J., Jang S. P., Effects of the darcy number, the prandtl number, and the reynolds number on local thermal non-equilibrium, International Journal of Heat And Mass Transfer, 45, 2002, pp. 3885-3896.
• [7] Khashani S.A., Al-Nimr M.A., Validation of the Local Thermal Equilibrium Assumption in Forced Convection of Non-Newtonian Fluids through Porous Channels, Transport in Porous Media, 61, 2005, pp. 291-305.
• [8] Haddad O.M., Al-NimrA M.A., Al-Khateeb N., Validation of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium: non-Darcian model, International Journal of Heat And Mass Transfer, 47, 2004, pp.2037-2042.
• [9] Zhang X., Liu W., New criterion for local thermal equlibrium in porous media, Journal of Thermophysics and Heat Transfer,22,2008.
• [10] Leong K.C., Li H.Y., Jin L.W., Chai J.C., Numerical and experimental study of forced convection in graphite foams of different configurations, Applied Thermal Engineering, 30, 2010, pp.520-532.
• [11] Solmuş İ., Numerical investigation of heat transfer and fluid flow behaviors of block type graphite foam heat sink inserted in a rectangular channel, Applied Thermal Engineering, 78, 2015, pp.605-615.
• [12] Gürüf G., Solmuş İ., Bilen K., Bayer Ö., Experimental based numerical approach for determination of volumetric heat transfer coefficients of modified graphite foams, Applied Thermal Engineering, 174, 2020, 115310.
• [13] Mahjoob S., Vafai K., A synthesis of fluid and thermal transport models for metal foam heat exchangers, International Journal of Heat And Mass Transfer, 51, 2008, pp. 3701-3711.
• [14] Lu W., Zhao C.Y., Tassou S.A., Thermal analysis on metal-foam filled heat exchangers. Part I: Metal-foam filled pipes, International Journal of Heat And Mass Transfer, 49, 2006, pp. 2751-2761.
• [15] Teamah M. A., El-Maghlany W.M., Dawood M.M.K., Numerical simulation of laminar forced convection in horizontal pipe partially or completely filled with porous material, International Journal of Thermal Sciences, 50, 2011, pp.1512-1522.
• [16] Hetsroni G., Gurevich M., Rozenblit R., Sintered porous medium heat sink for cooling of high-power mini-devices, International Journal of Heat and Fluid Flow, 27, 2006, pp.259-266.
• [17] Dukhan N., Quin˜ones-Ramos P.D., Cruz-Ruiz E., Ve´lez-Reyes M., Scott E.P., One-dimensional heat transfer analysis in open-cell 10-ppi metal foam, International Journal of Heat and Mass Transfer, 48, 2005, pp. 5112-5120.
• [18] Dukhan N., Chen K.C., Heat transfer measurements in metal foam subjected to constant heat flux, Experimental Thermal and Fluid Science, 32, 2007, pp.624-631.
• [19] Hsieh W.H., Wu J.Y., Shih W.H., Chiu W.C., Experimental investigation of heat-transfer characteristics of aluminum-foam heat sinks, International Journal of Heat and Mass Transfer, 47, 2004, pp.5149-5157.
• [20] Izadpanah M.R., Muller-Steinhagen H., Jamialahmadi M., Experimental and theoretical studies of convective heat transfer in a cylindrical porous medium, International Journal of Heat and Fluid Flow, 19, 1998, pp. 629-635.
• [21] Xu H., Gong L., Huang S., Xu M., Non-equilibrium heat transfer in metal-foam solar collector with no-slip boundary condition, International Journal of Heat and Mass Transfer, 76, 2014, pp.357-365. [22] Feng S.S., Kuang J.J., Wen T., Lu T.J., Ichimiya K., An experimental and numerical study of finned metal foam heat sinks under impinging air jet cooling, International Journal of Heat and Mass Transfer, 77, 2014, pp.1063-1074.
• [23] Lua W., Zhao C.Y., Tassou S.A., Thermal analysis on metal-foam filled heat exchangers. Part I: metal-foam filled pipes, International Journal of Heat and Mass Transfer, 49, 2006, 2751-2761.
• [24] Yang Y.T., Hwang M.L., Numerical simulation of turbulent fluid flow and heat transfer characteristics in heat exchangers fitted with porous media, International Journal of Heat and Mass Transfer, 52, 2009, 2956-2965.
• [25] Ando K., Hirai H., Sano Y., An accurate experimental determination of interstitial heat transfer coefficients of ceramic foams using the single blow method, The Open Transport Phenomena Journal, 5, 2013, pp.7-12.
• [26] Dukhan N., Chen K.C., Heat transfer measurements in metal foam subjected to constant heat flux, Experimental Thermal and Fluid Science, 32, 2007, pp.624-631.
• [27] Hwang J.J., Hwang G.J., Yeh R.H., Chao C.H., Measurment of interstitial convective heat transfer and frictional drag for flow across metal foams, Journal of Heat Transfer, 124, 2002, pp.120-129.
• [28] Calmidi V.V., Mahajan R.L., Forced convection in high porosity metal foams, ASME Journal of Heat Transfer, 122, 2000, pp.557-565.
• [29] Tee C.C., Yu N., Li H., Modeling the overall heat conductive and convective properties of open-cell graphite foam, Modeling Simulation Materials Science Engineering, 16, 2008, 075006.