Pseudo-Steady-State Natural Convection Heat Transfer Inside a Vertical Cylinder

Abstract

The SIMPLER numerical method was used to calculate the pseudo-steady-state natural convection heat transfer to a fluid inside a closed vertical cylinder for which the boundary temperature was spatially uniform and the temperatures throughout the entire system were increasing at the same rate. (Pseudo-steady state is comparable to the steady-state problem for a fluid with uniform heat generation and constant wall temperature.) Stream functions, temperature contours, axial velocities, and temperature profiles are presented. The range of calculation was 0.25 < H/D < 2, Ra < 107, and Pr = 7. This range includes conduction to weak turbulence. A characteristic length defined as 6 × (volume)/(surface area) was used since it seemed to produce good regression results. The overall heat transfer for the convection-dominated range was found to be correlated by Nu = 0.519 Ra0.255, where the temperature difference for both the Nusselt and Rayleigh numbers was the center temperature minus the wall temperature. Correlations using other temperature differences are also presented for estimating the volumetric mean and minimum temperatures.

Numerical study of laminar natural convection in a half ellipsoid of revolution subjected to heat flux of constant density

“…For the simulations, we take a time step value which is sufficient to properly observe the temporal evolutions of the streamlines corresponding to the different form factors and the different Grashof numbers [3].…”

“…Currently this study covers a wide range leading to many results including natural convection (natural convection or forced convection). In addition, researchers have focused the study of natural convection on the geometry of a system: rectangular [4], square [1], cylindrical [3], spherical [5] and elliptical [7]. These studies have made it possible to model the phenomenon of convection, to analyze the influence of various parameters for specific applications such as dryers [14], greenhouses [15] .....The study of convection on a new type of geometry allows it to highlight the conditions guaranteeing the establishment of a laminar natural convection inside a given enclosure.…”

Spherical Tanks for Use in Thermal Energy Storage Systems

“…The difference in temperature will lead to density variation in the storage fluid, which will cause the low density fluid to keep rising to the top of the tank. Lin and Akin performed an experimental study to calculate the pseudo-steady state natural convection heat transfer inside a vertical cylinder [113]. They found a characteristic length that provided the best results when compared with experimental results and other characteristic lengths relations:…”

Computation of Unstable Liquid Metal Convection in a Vertical Closed Cylinder Heated From the Side and Cooled From Above

“…Meanwhile a model experiment was conducted by Muller et al [1] to visualize the water flow in a cylinder of unit aspect ratio for various thermal conditions covering steady and unsteady convection. Steady and pseudo-steady axisymmetric numerical simulations were carried out by Huang and Hsieh [2] and Lin and Akins [3,4] to investigate natural convection in a bottom-heated vertical cylinder. Additionally, both the steady axisymmetric and asymmetric flows were predicted for liquid metal (Pr = 0.02) and water (Pr = 6.70) from the three-dimensional numerical simulation [5].…”