Combined Free and Forced Convection Laminar Heat Transfer in a Vertical Annulus
01 Feb 1975-Journal of Heat Transfer-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 97, Iss: 1, pp 135-137
About: This article is published in Journal of Heat Transfer-transactions of The Asme.The article was published on 1975-02-01. It has received 52 citations till now. The article focuses on the topics: Combined forced and natural convection & Forced convection.
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TL;DR: In this paper, three fundamental combinations of thermal boundary conditions on the respective wall surface (i.e., isoflux-isoflux, isoftluxisothermal, and isothermal-isothermal) are considered separately so as to investigate extensively their distinct influence on the flow pattern.
Abstract: The present analysis is concerned with flow reversal phenomena and heat transfer characteristics of the fully developed laminar combined free and forced convection in the heated vertical channels. Three fundamental combinations of thermal boundary conditions on the respective wall surface (namely isoflux-isoflux, isofluxisothermal, and isothermal-isothermal) are considered separately so as to investigate extensively their distinct influence on the flow pattern. Results of the velocity distribution and temperature distribution as well as the Nusselt number in terms of bulk mean temperature are carried out. Based on the analytical solutions obtained, flow reversal adjacent to the relatively colder wall is found to exist within the channel as Re/Gr is below than a threshold value, which is related to the thermal boundary conditions. Parameter zones for the occurrence of reversed flow are presented. Comparisons and verification are made using the existing numerical solutions at locations far downstream of developing flow.
124 citations
TL;DR: In this article, the effect of eccentricity in horizontal, inclined and vertical directions on heat transfer rate in most numerical and experimental investigations for horizontal and vertical annular tubes is studied.
109 citations
TL;DR: In this paper, the stability of mixed-convection flow in a vertical channel is investigated for both buoyancy-assisted and -opposed conditions, and the Galerkin method is used to solve the disturbance momentum and energy equations.
Abstract: In this study, the linear stability of mixed-convection flow in a vertical channel is investigated for both buoyancy-assisted and -opposed conditions. The disturbance momentum and energy equations were solved by the Galerkin method. In addition to the case with a zero heat flux perturbation boundary condition, we also examined the zero temperature perturbation boundary condition. In general, the mixed-convection flow is strongly destabilized by the heat transfer and therefore the fully developed heated flow is very unstable and very difficult to maintain in nature. For buoyancy-assisted flow, the two-dimensional disturbances dominate, while for buoyancy-opposed flow, the Rayleigh–Taylor instability prevails for zero heat flux perturbation boundary condition, and for the zero temperature perturbation on the boundaries the two-dimensional disturbances dominate except at lower Reynolds numbers where the Rayleigh–Taylor instability dominates again. The instability characteristics of buoyancy-assisted flow are found to be strongly dependent on the Prandtl number whereas the Prandtl number is a weak parameter for buoyancy-opposed flow. Also the least-stable disturbances are nearly one-dimensional for liquids and heavy oils at high Reynolds numbers in buoyancy-assisted flows.From an energy budget analysis, we found that the thermal–buoyant instability is the dominant type for buoyancy-assisted flow. In buoyancy-opposed flow, under the zero temperature perturbation boundary condition the Rayleigh–Taylor instability dominates for low-Reynolds-number flow and then the thermal–shear instability takes over for the higher Reynolds numbers whereas the Rayleigh–Taylor instability dominates solely for the zero heat flux perturbation boundary condition. It is found that the instability characteristics for some cases of channel flow in this study are significantly different from previous results for heated annulus and pipe flows. Based on the distinctly different wave speed characteristics and disturbance amplification rates, we offer some suggestions regarding the totally different laminar–turbulent transition patterns for buoyancy-assisted and -opposed flows.
81 citations
TL;DR: In this article, a comprehensive numerical study on the linear stability of mixed-convection flow in a vertical pipe with constant heat flux is presented with particular emphasis on the instability mechanism and the Prandtl number effect.
Abstract: A comprehensive numerical study on the linear stability of mixed-convection flow in a vertical pipe with constant heat flux is presented with particular emphasis on the instability mechanism and the Prandtl number effect. Three Prandtl numbers representative of different regimes in the Prandtl number spectrum are employed to simulate the stability characteristics of liquid mercury, water and oil. The results suggest that mixed-convection flow in a vertical pipe can become unstable at low Reynolds number and Rayleigh numbers irrespective of the Prandtl number, in contrast to the isothermal case. For water, the calculation predicts critical Rayleigh numbers of 80 and −120 for assisted and opposed flows, which agree very well with experimental values of Rac = 76 and −118 (Scheele & Hanratty 1962). It is found that the first azimuthal mode is always the most unstable, which also agrees with the experimental observation that the unstable pattern is a double spiral flow. Scheele & Hanratty's speculation that the instability in assisted and opposed flows can be attributed to the appearance of inflection points and separation is true only for fluids with O(1) Prandtl number. Our study on the effect of the Prandtl number discloses that it plays an active role in buoyancy-assisted flow and is an indication of the viability of kinematic or thermal disturbances. It profoundly affects the stability of assisted flow and changes the instability mechanism as well. For assisted flow with Prandtl numbers less than 0.3, the thermal–shear instability is dominant. With Prandtl numbers higher than 0.3, the assisted-thermal–buoyant instability becomes responsible. In buoyancy-opposed flow, the effect of the Prandtl number is less significant since the flow is unstably stratified. There are three distinct instability mechanisms at work independent of the Prandtl number. The Rayleigh–Taylor instability is operative when the Reynolds number is extremely low. The opposed-thermal–buoyant instability takes over when the Reynolds number becomes higher. A still higher Reynolds number eventually leads the thermal–shear instability to dominate. While the thermal–buoyant instability is present in both assisted and opposed flows, the mechanism by which it destabilizes the flow is completely different.
58 citations
Cites background from "Combined Free and Forced Convection..."
...A significant increase in heat transfer rates above those of laminar flow during low Reynolds number flow transition was also observed by Maitra & Raju (1975) in mixed convection of a heated vertical annulus flow....
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TL;DR: In this paper, a review of the thermal performance of heat exchanging equipment transport energy at low financial cost by various techniques is presented, which could help researchers design thermal systems supported by annular passages with the goal of retarding energy consumption by equipment and machineries in applications that could ultimately contribute to appeasing the global energy crisis.
Abstract: The enhancement of the thermal performance of heat exchanging equipment transport energy at low financial cost by various techniques is presented in this review. Various annular passage configurations have been used in the reviewed studies, namely circular, ellipse, rectangular, square, triangular, and rhombic annular channels with different fluid and boundary conditions. The effect of eccentricity in both horizontal and vertical directions on heat transfer rate in most numerical and experimental investigations for horizontal and vertical annular passages is studied. The effects of heater length, as well as the Darcy, Prandtl, Reynolds, Grashof and Rayleigh numbers on heat transfer in concentric and eccentric annular passages are also investigated. In case of rotating the inner, outer or both cylinders of the annular cylinder arrangement, the generated secondary flow influences the heat transfer to fluid flow in an annular passage. The effect of nanofluid on the increased enhancement of heat transfer in an annular channel is presented. Related studies on curved, covered annular channels showed augmented heat transfer rate in comparison with straight annular channels. In this review, a good agreement is evident between experimental and numerical data, which could help researchers design thermal systems supported by annular passages with the goal of retarding energy consumption by equipment and machineries in applications that could ultimately contribute to appeasing the global energy crisis.
56 citations
Cites background from "Combined Free and Forced Convection..."
...Thomas [212], Schwab and Witt [213], Maitra and Raju [214], AlArabi et al....
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