Laminar Mixed Convection in a Shrouded Fin Array

Abstract

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.

A numerical study of entry region laminar mixed convection over shrouded vertical fin arrays

“…It may be said that present investigation considers the case of a highly conducting fin, in which case fin becomes isothermal. This simplifying assumption of isothermal fin is made by several investigators, examples being the papers by Karki and Patankar [8], Acharya and Patankar [19], Zhang and Patankar [22], Al-Sarkhi et al [23]. Under such a situation, there is an induced upward flow due to natural convection along the fin length.…”

“…Acharya and Patankar [19] computationally studied combined free and forced convection from shrouded vertical fin attached to a horizontal base. Recent experimental study on mixed convection from longitudinal fin in a horizontal channel for both high and low Richardson number by Dogan and Sivrioglu [20,21] reveals optimum fin spacing for which heat transfer is maximum.…”

Combined free and forced laminar convection in horizontal rectangular channels for high rera

“…However, there are also two pairs of eddies which appeared in the thermal entrance region of horizontal rectangular channels (Ou et a]., 1974). The high buoyancy parameter also generates a second pair of counter-rotating eddies in mixed laminar convection in a shrouded fin array for zero tip clearance (Acharya and Patankar, 1981). In circumferentiallynonuniform heating tubes, a second pair of counter-rotating eddies appeared when the modified Grashof number was up to 5 X lo6 for bottom heating of the tube (Patankar et a]., 1978).…”

“…In circumferentiallynonuniform heating tubes, a second pair of counter-rotating eddies appeared when the modified Grashof number was up to 5 X lo6 for bottom heating of the tube (Patankar et a]., 1978). The high buoyancy parameter also generates a second pair of counter-rotating eddies in mixed laminar convection in a shrouded fin array for zero tip clearance (Acharya and Patankar, 1981).…”

Laminar mixed convection in the entrance region of shrouded arrays of heated rectangular blocks

“…Mixed laminar convection in the thermal entrance region of horizontal tubes and rectangular channels has been investigated for large Prandtl number fluids by Cheng et al (1972), Cheng and Ou (1974), Hong et al (1974), and Ou and Cheng (1977). Laminar mixed convection in a shrouded array of thin fins subjected to two heating conditions was studied by Acharya and Patankar (1981), and mixed convection between parallel planes with local heat sources has been studied both numerically and experimentally by kennedy and Zebib (1983). The above studies have shown that buoyancy effects can lead to a significant improvement in heat transfer over that obtained by pure forced convection.…”