On Natural Convection Heat Transfer From Three-Dimensional Bodies of Arbitrary Shape

1989 ◽  
Vol 111 (2) ◽  
pp. 363-371 ◽  
Author(s):  
A. V. Hassani ◽  
K. G. T. Hollands
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Arbitrary Shape ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Simple Expression ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Oblate Spheroids ◽  
Body Shapes

A simple expression is developed for the natural convection heat transfer from three-dimensional bodies of arbitrary shape immersed in an extensive fluid. The expression applies to both laminar and turbulent regimes and requires the calculation of purely geometric properties of the bodies. Experiments were performed with air, covering a Rayleigh number (Ra) range of from 10 to 108, on different body shapes oriented in various directions: for example, circular or square disks, a short circular cylinder of height equal to diameter and a similar cylinder but with hemispherical ends, prolate and oblate spheroids of various aspect ratio, and an “apple core” shape. Comparison between the predictions of the expression and the experimental results of this work and those gathered from several other sources ranging up to Ra = 1014 showed very good agreement, with an average rms difference of 3.5 percent for Ra < 108 and 22 percent for 108 < Ra < 1014.

Natural Convection Heat Transfer From Vertical 5×5 Rod Bundles in Liquid Sodium

2016 ◽  
Author(s):  
Koichi Hata ◽  
Katsuya Fukuda ◽  
Tohru Mizuuchi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Heat Fluxes ◽  
Liquid Sodium ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Rod Bundles ◽  
Average Value

Natural convection heat transfer from vertical 5×5 rod bundles in liquid sodium was numerically analyzed for two types of the bundle geometry (equilateral square and triangle arrays, ESA and ETA). The unsteady laminar three dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady-state. The PHOENICS code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 5×5 test rods for diameter (D = 7.6 mm), heated length (L = 200 mm) and L/d (= 26.32) were used in this work. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, (Rf,L)ij and (Rf,L)5×5,S/D, ranging from 3.08 × 104 to 4.19 × 107 (q = 1 × 104∼7 × 106 W/m2) in liquid temperature (TL = 673.15 K). The values of S/D, which are ratios of the diameter of flow channel for bundle geometry to the rod diameter, for vertical 5×5 rod bundles were ranged from 1.8 to 6 on each bundle geometry. The spatial distribution of local and average Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, on vertical rods of a bundle was clarified. The average value of Nusselt number, (Nuav)ij and (Nuav,B)5×5,S/D, for two types of the bundle geometry with various values of S/D were calculated to examine the effect of the bundle geometry, S/D, (Rf,L)ij and (Rf,L)5×5,S/D on heat transfer. The bundle geometry for the higher (Nuav,B)5×5,S/D value under the condition of S/D = constant was examined. The correlations for (Nuav,B)5×5,S/D for two types of bundle geometry above mentioned including the effects of (Rf,L)5×5,S/D and S/D were developed. The correlations can describe the theoretical values of (Nuav,B)5×5,S/D for two types of the bundle geometry for S/D ranging from 1.8 to 6 within −11.77 to 13.34 % difference.

Natural Convection Heat Transfer From Vertical 5 × 5 Rod Bundles in Liquid Sodium

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Koichi Hata ◽  
Katsuya Fukuda ◽  
Tohru Mizuuchi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Heat Fluxes ◽  
Liquid Sodium ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Rod Bundles ◽  
Nusselt Numbers

Natural convection heat transfer from vertical 5 × 5 rod bundles in liquid sodium was numerically analyzed for two types of the bundle geometry (equilateral square array (ESA) and equilateral triangle array (ETA)). The unsteady laminar three-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady-state. The phoenics code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 5 × 5 test rods for diameter (D = 7.6 mm), heated length (L = 200 mm), and L/d (=26.32) were used in this work. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, (Rf,L)ij and (Rf,L)5×5,S/D, ranging from 3.08 × 104 to 4.19 × 107 (q = 1 × 104–7 × 106 W/m2) in liquid temperature (TL = 673.15 K). The values of S/D, which are ratios of the diameter of flow channel for bundle geometry to the rod diameter, for vertical 5 × 5 rod bundles were ranged from 1.8 to 6 on each bundle geometry. The spatial distribution of local and average Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, on vertical rods of a bundle was clarified. The average value of Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, for the two types of the bundle geometry with various values of S/D were calculated to examine the effect of the bundle geometry, S/D, (Rf,L)ij, and (Rf,L)5×5,S/D on heat transfer. The bundle geometry for the higher (Nuav,B)5×5,S/D value under the condition of S/D = constant was examined. The correlations for (Nuav,B)5×5,S/D for two types of bundle geometry above mentioned including the effects of (Rf,L)5×5,S/D and S/D were developed. The correlations can describe the theoretical values of (Nuav,B)5×5,S/D for the two types of the bundle geometry at S/D ranging from 1.8 to 6 within −12.64% to 7.73% difference.

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