zbMATH — the first resource for mathematics

Natural convection near $$4^ oC$$ in a horizontal water layer heated from below. (English) Zbl 0548.76069
A numerical study of two-dimensional natural convection in a horizontal water layer heated from below is reported. The density maximum associated with water at $$3.98^ oC$$ and atmospheric pressure occurs inside the layer, as the top surface is maintained at $$0^ oC$$ while the bottom surface temperature varies in the range $$4^ oC-10^ 0C$$. Three separate series of numerical simulations document the effect of Rayleigh number, bottom wall temperature and layer horizontal length on the flow pattern and on the net heat transfer rate vertically through the layer.

MSC:
 76R10 Free convection 76M99 Basic methods in fluid mechanics
Full Text:
References:
 [1] Goren, Chem. Eng. Sci. 21 pp 515– (1966) [2] Moore, J. Fluid Mech. 61 pp 553– (1973) [3] J. Boussinesq,Theorie Analytique de la Chaleur(Gauthier–Villars, Paris, 1903), pp. 2, 172. [4] Forbes, J. Heat. Transfer 97 pp 47– (1975) · doi:10.1115/1.3450286 [5] Robillard, J. Fluid Mech. 118 pp 123– (1982) [6] Cheng, Numer. Heat Transfer 1 pp 101– (1978) [7] Gebhart, J. Fluid Mech. 89 pp 673– (1978) [8] Z. H. Qureshi and B. Gebhart, inProceedings of the 6th International Heat Transfer Conference, Toronto(Hemisphere, New York, 1978), Vol. 2, p. 217. [9] Robillard, J. Heat Transfer 103 pp 528– (1981) [10] Bénard, Ann. Chim. Phys. 23 pp 62– (1901) [11] S. Chandrasekhar,Hydrodynamic and Hydromagnetic Stability(Dover, New York, 1981), pp. 9–219. [12] Rayleigh, Philos. Mag. 32 pp 529– (1916) · doi:10.1080/14786441608635602 [13] Sparrow, J. Fluid Mech. 18 pp 513– (1964) [14] P. G. Drazin and W. H. Reid,Hydrodynamic Stability(Cambridge U.P., Cambridge, England, 1981), pp. 32–63. [15] Veronis, Astrogeophys. J. 137 pp 641– (1963) [16] Tien, AIChE J. 14 (1968) [17] Sun, AIChE J. 15 pp 910– (1969) [18] Debler, J. Fluid Mech. 24 pp 165– (1966) [19] S. Patankar,Numerical Heat Transfer and Fluid Flow(Hemisphere, New York, 1980), pp. 30–40, 67-68, and 90-100. [20] P. J. Roache,Computational Fluid Dynamics(Hermosa, Albuquerque, NM, 1976), pp. 117–119. [21] Yen, Int. J. Heat Mass Transfer 17 pp 1349– (1974)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.