A numerical investigation has been made of two-dimensional natural convection of air in an externally heated vertical or inclined square box containing uniformly distributed internal energy sources. Results have been obtained for Rayleigh numbers (both internal and external) up to 107 and inclination angles of 30, 60, and 90 deg from the horizontal. Two distinct flow pattern systems are observed: one, when the external Rayleigh number is larger than the internal Rayleigh number and the other, when the internal Rayleigh number is considerably greater than the external Rayleigh number. The average heat flux ratio (convective heat flux/corresponding conduction heat flux) along the hot surface is observed to undergo large variations in the external Rayleigh number range associated with the transition from one flow pattern to another. The average heat flux ratio along the cold plate is found to increase with increasing external Rayleigh number and decreasing internal Rayleigh number. The local heat flux ratio along a surface attains its maximum value in the vicinity of the region where the heated (or cooled) fluid from the opposite wall or from the interior encounters the surface.
A conjugate conduction-convection analysis has been made for a vertical plate fin which exchanges heat with its fluid environment by natural convection. The analysis is based on a first-principles approach whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum, and energy in the fluid boundary layer adjacent to the fin. The natural convection heat transfer coefficient is not specified in advance but is one of the results of the numerical solutions. For a wide range of operating conditions, the local heat transfer coefficients were found not to decrease monotonically in the flow direction, as is usual. Rather, the coefficient decreased at first, attained a minimum, and then increased with increasing downstream distance. This behavior was attributed to an enhanced buoyancy resulting from an increase in the wall-to-fluid temperature difference along the streamwise direction. To supplement the first-principles analysis, results were also obtained from a simple adaptation of the conventional fin model.
Numerical simulations have been conducted to study natural convection heat transfer from solid or hollow cylinders in the laminar range of Ra spanning from 104 to 108 for L/D in the range of 0.05≤(L/D)≤20. Interesting flow structures around the thin hollow cylinder have been observed for small and large L/D. It has been found that the average Nu for solid or hollow horizontal cylinders in air is marginally higher than when they are on ground for the entire range of L/D and Ra limited up to 107. Up to a Ra of 107 Nu for a solid cylinder in air is higher than that of Nu for a hollow cylinder in air but when Ra exceeds 107 Nu for a hollow cylinder is marginally higher than that of the solid cylinder until an L/D of 0.2. When, L/D rises beyond 0.2 the situation reveres causing Nu for a solid cylinder to be again higher than that of the hollow cylinder when suspended in air. A solid cylinder on ground has higher Nu compared to that of a hollow cylinder on ground up to a Ra of 106. However, for higher Ra of 108 a hollow cylinder on ground has higher Nu compared to that of a solid cylinder on ground until an L/D of 5 and after that the situation reverses again.
An analytical study is made to investigate the effect of buoyancy on laminar forced convection in a shrouded fin array. Two heating conditions are considered; in one, the fins and the base surface are hotter than the fluid, and in the other, they are colder. The results are obtained numerically for a wide range of the governing buoyancy parameter. It is found that with a hot fin and base, the secondary flow pattern is mostly made up of a single eddy. The influence of buoyancy is significant and leads to Nusselt numbers and friction factors which are much higher than for pure forced convection. With a cold fin and base, the presence of a tip clearance between the fins and the shroud generates a multiple eddy pattern. The resulting stratification is responsible for the existence of high axial velocity and temperature in the clearance region relative to that in the inter-fin space. Compared to the hot fin case, the secondary flow is weaker, and therefore a relatively smaller increase in the friction factor is obtained. The Nusselt number is found to increase only in the absence of tip clearance. The distribution of the heat transfer coefficient along the fin and the base for both heating situations is found to be highly nonuniform.
Natuml convection in an inclined enclosure with a c e n d y located, complete partition has been investigated by a finitedifference procedure. The thermal conditions along the partihon are not known beforehand; rather, they are an outcome of the coupling of the nahrrcrl convection systems on either side of the enclosure partition. To resolve this coupling, a consecutive calculation procedure is used in which the natural convection on either side of the enclosure is successively solved (until convergence) with information exchange in each cycle ofvolu!ion. Results have been obtained for enclosures wirh overall aspect ratios of 1 and 2 for Rayleigh numbers up to 10' and for incliMtion angles of 30, 45, 60, and 90 degrees. Results indicate that the strength of the convective motion and the average Nusselt number are both considembly reduced owing to the presence of the portition. The portr'tion temperature increases monotonically along its length. For a vedical enclosure, the nonuniform@ in the p d o n temperature increases with Rayleigh number, while for an inclined enclosure (8 = 4S0), the ovemll nonuniformily in the partition temperature is not signifcantly influenced by the Rayleigh number. The Nusselt number along the hot (cold) surface attains its maximum value in the neighborhood of the locakion where the cooled (heated) fluid from the portition meets the surface. Along the p d o n the maximum Nusselt number is obtained at the center of the partition when the enclosure is vem'cal. For an inclined enclosure, the maximum Nusselr number occurs at the panitian center only at low Rayleigh numbers. At high Rayhigh numbers the marimum is shifted toward the two corners of the pnrtirton.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.