## THERMAL SCIENCE

International Scientific Journal

### NUMERICAL STUDY ON LAMINAR FREE CONVECTION HEAT TRANSFER BETWEEN SPHERE PARTICLE AND HIGH PRESSURE WATER IN PSEUDO-CRITICAL ZONE

**ABSTRACT**

Supercritical water fluidized bed reactor (SCWFBR) is a promising new reaction vessel which can effectively gasify wet biomass and efficiently produce hydrogen. Free convection heat transfer from particle in supercritical water (SCW) is a major basic heat transfer mechanism in a fixed bed or fluidized bed with low superficial velocity. In this paper, numerical study on the steady free convection heat transfer around single sphere particle in high pressure water of pseudo-critical zone was carried out. Both the Boussinesq approximation method and real properties model (considering variable specific heat, density, viscosity, and conductivity of SCW) were incorporated to simulate the flow and temperature field. With respect to Boussinesq approximation, real properties model shows higher vorticity and temperature gradients in the vicinity of the sphere surface, which shows variation of thermo-physical property has remarkable effect on the free convection heat transfer process. High local Nusselt number and high heat transfer rate were observed with real properties model.

**KEYWORDS**

PAPER SUBMITTED: 2012-11-13

PAPER REVISED: 2013-03-03

PAPER ACCEPTED: 2013-03-30

PUBLISHED ONLINE: 2013-04-21

**THERMAL SCIENCE** YEAR

**2014**, VOLUME

**18**, ISSUE

**Issue 4**, PAGES [1293 - 1303]

- Lu, Y. J., Jin, H., Guo, L. J., Zhang, X. M., Cao, C. Q., and Guo, X., Hydrogen production by biomass gasification in supercritical water with a fluidized bed reactor, International Journal of Hydrogen Energy, 33 (2008), 21, pp. 6066-6075.
- Wei L.P., Lu Y.J., Wei J.J., Hydrogen production by supercritical water gasification of biomass: Particle and residence time distribution in fluidized bed reactor, International Journal of Hydrogen Energy (2013), dx.doi.org/10.1016/j.ijhydene.2013.01.148
- Raithby, G., and Hollands, K., A general method of obtaining approximate solutions to laminar and turbulent free convection problems, Advances in Heat Transfer, 11( 1975), pp. 265-315.
- Merk, H., and Prins, J., Thermal convection in laminary boundary layers. I, Applied Scientific Research, 4(1953), 1, pp. 11-24.
- Acrivos, A., A theoretical analysis of laminar natural convection heat transfer to non‐Newtonian fluids, AIChE Journal, 6(1960),4, pp. 584-590.
- Fendell, F. E., Laminar natural convection about an isothermally heated sphere at small Grashof number, Journal of Fluid Mechanics, 34(1968), 01, pp. 163-176.
- Potter, J. M., and Riley, N., 1980, "Free convection from a heated sphere at large Grashof number," Journal of Fluid Mechanics, 100(04), pp. 769-783.
- Singh, S., and Hasan, M., Free convection about a sphere at small Grashof number, International Journal of Heat and Mass Transfer, 26(1983), pp. 781-783.
- Churchill, S. W., Comprehensive, theoretically based, correlating equations for free convection from isothermal spheres, Chemical Engineering Communications, 24(1983), 4-6, pp. 339-352.
- Jafarpur, K., and Yovanovich, M. M., Laminar free convective heat transfer from isothermal spheres: A new analytical method, International Journal of Heat and Mass Transfer, 35(1992), 9, pp. 2195-2201.
- Kranse, A., and Schenk, J., Thermal free convection from a solid sphere, Applied Scientific Research, 15(1966), 1, pp. 397-403.
- Schenk, J., and Schenkels, F., Thermal free convection from an ice sphere in water, Applied Scientific Research, 19(1968), 1, pp. 465-476.
- Jaluria, Y., and Gebhart, B., On the buoyancy-induced flow arising from a heated hemisphere, International Journal of Heat and Mass Transfer, 18(1975), 3, pp. 415-431.
- Argyropoulos, S. A., and Mikrovas, A. C., , An experimental investigation on natural and forced convection in liquid metals, International Journal of Heat and Mass Transfer, 39(1996), 3, pp. 547-561.
- Fujii, T., Fujii, M., and Honda, T., A numerical analysis of laminar free convection around an isothermal sphere, Numerical Heat Transfer, 4(1981), 1, pp. 69-84.
- Fujii T, Honda T, and Fujii M., A numerical analysis of laminar free convection around an isothermal sphere: finite-difference solution of the full Navier-Stokes and energy equations between concentric spheres. Numerical Heat Transfer, 7(1984), 1, pp. 103-111.
- Geoola, F., and Cornish, A. R. H., Numerical solution of steady-state free convective heat transfer from a solid sphere, International Journal of Heat and Mass Transfer, 24(1981), 8, pp. 1369-1379.
- Geoola, F., and Cornish, A. R. H., Numerical simulation of free convective heat transfer from a sphere, International Journal of Heat and Mass Transfer, 25(1982), 11, pp. 1677-1687.
- Farouk, B., Natural convection heat transfer from an isothermal sphere, Proc. Thermal Sci. 16-proc. 16th Southeastern Sem., (1983), pp. 347-364.
- Riley, N., The heat transfer from a sphere in free convective flow, Computers & Fluids, 14(1986), 3, pp. 225-237.
- Dudek, D. R., Fletcher, T. H., Longwell, J. P., and Sarofim, A. F., Natural convection induced drag forces on spheres at low Grashof numbers: comparison of theory with experiment, International Journal of Heat and Mass Transfer, 31(1988), 4,pp. 863-873.
- Takamatsu, H., Fujii, M., and Fujii, T., A Numerical Analysis of Free Convection Around an Isothermal Sphere (Effects of Space and Prandtl Number)," JSME International Journal. Ser. 2, Fluids Engineering, Heat Transfer, Power, Combustion, Thermophysical Properties, 31(1988), 1, pp. 66-72.
- Jia, H., and Gogos, G., Laminar natural convection heat transfer from isothermal spheres, International Journal of Heat and Mass Transfer, 39(1996), 8, pp. 1603-1615.
- Kurdyumov, V. N., and Liñán, A., Free convection from a point source of heat, and heat transfer from spheres at small Grashof numbers, International Journal of Heat and Mass Transfer, 42(1999), 20, pp. 3849-3860.
- Nazar, R., and Amin, N., Free convection boundary layer on an isothermal sphere in a micropolar fluid, International Communications in Heat and Mass Transfer, 29(2002), 3, pp. 377-386.
- Bég, O. A., Ramachandra Prasad, V., Vasu, B., Bhaskar Reddy, N., Li, Q., and Bhargava, R., , Free convection heat and mass transfer from an isothermal sphere to a micropolar regime with Soret/Dufour effects, International Journal of Heat and Mass Transfer, 54(2011), 1-3, pp. 9-18.
- Yang, S., Raghavan, V., and Gogos, G., Numerical study of transient laminar natural convection over an isothermal sphere, International Journal of Heat and Fluid Flow, 28(2007), 4, pp. 821-837.
- Prhashanna, A., and Chhabra, R. P., 2010, Free convection in power-law fluids from a heated sphere, Chemical Engineering Science, 65(2010), 23, pp. 6190-6205.
- Molla, M. M., Taher, M., Chowdhury, M. M. K., and Hossain, M. A., Magnetohydrodynamic natural convection flow on a sphere in presence of heat generation, Nonlinear Analysis: Modelling and Control, 10(2005), 4, pp. 349-363.
- Molla, M., Hossain, M., and Taher, M., Magnetohydrodynamic natural convection flow on a sphere with uniform heat flux in presence of heat generation, Acta Mechanica, 186(2006), 1, pp. 75-86.
- Alam, M. M., Alim, M., and Chowdhury, M. M. K., Viscous dissipation effects on MHD natural convection flow over a sphere in the presence of heat generation, Nonlinear Analysis: Modell. and Cont, 12(2007), 4, pp. 447-459.
- Alam, M. M., Alim, M., and Chowdhury, M. M. K., Viscous dissipation effects on MHD natural convection flow along a sphere, Journal of Mechanical Engineering, 36(2008), 0, pp. 44-48.
- Polyakov, A., Heat transfer under supercritical pressures," Advances in Heat Transfer, 21(1991), pp. 1-53.
- Hall, W., Heat transfer near the critical point, Advances in Heat Transfer, 7(1971), pp. 1-86.
- Wagner, W., and Kretzschmar, H. J., International steam tables: properties of water and steam based on the industrial formulation IAPWS-IF97: tables, algorithms, diagrams, and CD-ROM electronic steam tables: all of the equations of IAPWS-IF97 including a complete set of supplementary backward equations for fast calculations of heat cycles, boilers, and steam turbines, Springer Verlag. Berlin, Germany, 2008
- Bejan, A., and Kraus, A. D., Heat transfer handbook, John Wiley & Sons, Inc., New York, USA ,2003.
- Wen, Y., and Jog, M. A., Variable property, steady, axi-symmetric, laminar, continuum plasma flow over spheroidal particles, International Journal of Heat and Fluid Flow, 26(2005), 5, pp. 780-791.