The range of applicability of the boundary condition of the first kind at entry into a heat-releasing granular bed has been investigated. It has been shown that in the cases where the heat-transfer process can be described within the framework of a one-temperature (homogeneous) model, it is allowable to use this condition for RePr >> 1. When it is necessary to allow for the phase-temperature difference, the boundary condition of the first kind can be used for the parametric value \( \overset {\smallfrown}{Q} \)≤ 0.02. In the remaining regimes, the generalized Danckwerts condition allowing for the preheating of the heat-transfer agent should be used.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. S. Teplitskii and V. I. Kovenskii, Statement of boundary and conjugation conditions for problems of heat transfer in granular beds on the basis of a two-temperature model, Inzh.-Fiz. Zh., 79, No. 6, 98–106 (2006).
V. A. Borodulya and Yu. P. Gupalo, Mathematical Models of Bubbling-Bed Chemical Reactors [in Russian], Nauka i Tekhnika, Minsk (1976).
V. M. Polyaev, V. A. Maiorov, and L. L. Vasiliev, Hydrodynamics and Heat Transfer in the Porous Elements of the Constructions of Flying Vehicles [in Russian], Mashinostroenie, Moscow (1988).
M. É. Aérov and N. N. Umnik, Thermal-conductivity coefficients in a granular bed, Zh. Tekh. Fiz., 21, Issue 11, 1351–1363 (1951).
V. A. Levin and N. A. Lutsenko, Gas flow through a porous heat-releasing medium with allowance for the temperature dependence of gas viscosity, Inzh.-Fiz. Zh., 79, No. 1, 35–40 (2006).
K. Hooman and A. A. Ranjbar-Kani, Axial conduction effects on thermally developing forced convection in a porous medium: circular tube with uniform wall temperature, Heat Transfer Research, 34, Issues 1–2, 34–40 (2003).
Yu. S. Teplitskii and M. V. Vinogradova, Establishment of boundary conditions for problems of conductiveconvective heat transfer in disperse systems, Inzh.-Fiz. Zh., 80, No. 3, 66–71 (2007).
M. É. Aérov, O. M. Todes, and D. A. Narinskii, Apparatuses with a Stationary Granular Bed [in Russian], Khimiya, Leningrad (1979).
N. I. Gel’perin, V. G. Ainshtein, and V. B. Kvasha, Principles of Fluidization Technique [in Russian], Khimiya, Moscow (1967).
V. I. Kovenskii and Yu. S. Teplitskii, On the thermal conductivity of a blown granular bed, Inzh.-Fiz. Zh., 81, No. 5, 956–962 (2008).
Yu. V. Polezhaev and E. M. Seliverstov, A universal model of heat transfer in systems with penetrating cooling, Teplofiz. Vys. Temp., 40, No. 6, 922–930 (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 6, pp. 1097–1104, November–December, 2009.
Rights and permissions
About this article
Cite this article
Teplitskii, Y.S., Kovenskii, V.I., Lutsenko, N.A. et al. On applicability of the boundary condition of the first kind in problems of heat transfer in heat-releasing granular beds. J Eng Phys Thermophy 82, 1114–1122 (2009). https://doi.org/10.1007/s10891-010-0308-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-010-0308-4