Boundary Layer Regime for Laminar Free Convection between Horizontal Circular Cylinders

Abstract

The steady, buoyancy-driven, laminar motion induced in the annulus of two horizontal, concentric, circular cylinders by a difference in the boundary temperatures is studied analytically in the large Rayleigh number limit. The flowfield is divided into five physically distinct regions: (1) an inner free convection boundary layer near the inner cylinder, (2) an outer free convection boundary layer near the outer cylinder, (3) a vertical plume above the inner cylinder, (4) a stagnant region below the inner cylinder, and (5) a core region surrounded by the other four regions. Zeroth-order solutions which account for the coupling of those five regions are obtained in the high Prandtl number limit using a boundary-layer approximation and integral methods. Comparisons of the calculated heat transfer and temperature fields with experiment and numerical finite-difference results are favorable.

Heat Transfer by Natural Convection from a Horizontal Isothermal Circular Cylinder in Air

“…In experiments on coaxial cylinders, Beckman [65] found that the ratio should be > 56 for negligible error; Jische and Farschi [66] suggested a value much greater than 10; Hessami et al [67] proposed that the ratio should be 100 for 1% error; and Mahony et al [68] suggested that the ratio should be > 10 for Ra > 10 3 . Clemes et al [3] found negligible difference between the heat transfer with a ratio of 15, compared with a ratio of 30. In studies of the effect of confining vertical walls on the natural convective heat transfer from heat transfer engineering horizontal cylinders, the following values of the ratio s /D were proposed for negligible error, where s is the spacing between the walls: »20 [28], > 30 [34], > 20 [36], > 20 [69], and > 10 [38].…”

A critical review of buoyancy-induced flow transitions in horizontal annuli

“…A complete solution of the steady laminar boundary layer regime in a horizontal annulus is due to Jischke and Farshchi [13]. Recently, an expression for the flow and temperature fields was derived by Desrayaud et al [6], for the pseudo-diffusive regime in the limit R/1, for pure fluids and binary mixtures.…”

“…As depicted in Fig. 3, from [13], the boundary layer regime can be subdivided into five different flow regions, with a thin boundary layer developing around the inner cylinder, and giving rise to a buoyant plume in the top region of the annulus; for large values of R, the dynamics of the plume is the leading phenomenon for transition to turbulent flow. Along the cooler, outer cylinder walls, the fluid redescends, forming a second, downward boundary layer.…”

“…Flow regions in the boundary layer limit for the horizontal annulus, after Jischke and Farshchi[13].…”

The numerical and analytical study of bifurcation and multicellular flow instability due to natural convection between narrow horizontal isothermal cylindrical annuli at high Rayleigh numbers

“…Hence, for Pr ~ 1, a thermal-type instability should arise near the top of the annul us. Jischke and Farshchi (1980) studied the boundary-layer regime for laminar free convection between 2-D horizontal annuli at the large Rayleigh number limit. They divided the flow field into five physically distinct regions, valid for the high Rayleigh number limiting condition.…”