Stability of mixed-convection flow in a tall vertical channel under non-boussinesq conditions

1995 ◽  
Vol 302 ◽  
pp. 91-115 ◽  
Author(s):  
Sergey A. Suslov ◽  
Samuel Paolucci
Keyword(s):  
Mixed Convection ◽  
Three Dimensional ◽  
Vertical Channel ◽  
Reynolds Numbers ◽  
Convection Flow ◽  
Two Dimensional ◽  
Mixed Convection Flow ◽  
The Stability ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

We have examined the linear stability of the fully developed mixed-convection flow in a differentially heated tall vertical channel under non-Boussinesq conditions. The Three-dimensional analysis of the stability problem was reduced to an equivalent two-dimensional one by the use of Squire's transformation. The resulting eigenvalue problem was solved using an integral Chebyshev pseudo-spectral method. Although Squire's theorem cannot be proved analytically, two-dimensional disturbances are found to be the most unstable in all cases. The influence of the non-Boussinesq effects on the stability was studied. We have investigated the dependence of the critical Grashof and Reynolds numbers on the temperature difference. The results show that four different modes of instability are possible, two of which are new and due entirely to non-Boussinesq effects.

Nonlinear stability of mixed convection flow under non-Boussinesq conditions. Part 2. Mean flow characteristics

1999 ◽  
Vol 398 ◽  
pp. 87-108 ◽  
Author(s):  
S. A. SUSLOV ◽  
S. PAOLUCCI
Keyword(s):  
Mixed Convection ◽  
Mass Flux ◽  
Flow Characteristics ◽  
Vertical Channel ◽  
Physical Nature ◽  
Reynolds Numbers ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Mean Flow ◽  
Wide Range

Based on amplitude expansions developed in Part 1 (Suslov & Paolucci 1999), we examine the mean flow characteristics of non-Boussinesq mixed convection flow of air in a vertical channel in the vicinity of bifurcation points for a wide range of temperature differences between the walls, and Grashof and Reynolds numbers. The constant mass flux and constant pressure gradient formulations are shown to lead to qualitatively similar, but quantitatively different, results. The physical nature of the distinct shear and buoyancy disturbances is investigated, and detailed mean flow and energy analyses are presented. The variation of the total mass of fluid in a flow domain as disturbances develop is discussed. The average Nusselt number and mass flux are estimated for supercritical regimes for a wide range of governing parameters.

Instability and Heat Transfer in Mixed Convection Flow in a Horizontal Duct With Discrete Heat Sources

2001 ◽  
Author(s):  
Qinghua Wang ◽  
Yogesh Jaluria
Keyword(s):  
Mixed Convection ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Forced Flow ◽  
Bottom Surface ◽  
Convection Flow ◽  
Heat Sources ◽  
Mixed Convection Flow ◽  
Mean Velocity ◽  
Low Reynolds Numbers

Abstract Three dimensional mixed convection flow in a horizontal rectangular duct at low Reynolds numbers 5 ≤ Re ≤ 100 has been investigated numerically. Multiple strip heat sources are flushed-mounted on the bottom surface, modeling IC chips on PCBs. Two different flow patterns were observed. For Re ≥ 20, and Gr ≤ 1.5 × 104, only steady longitudinal rolls appear in the channel. The discontinuous deployment of heat sources on the bottom makes the longitudinal rolls expand and shrink periodically. The unsteady flow consists of steady longitudinal rolls near the side walls and traveling transverse rolls at the core region of the channel. The traveling velocity of the transverse rolls was found to be equal to the mean velocity of the forced flow. The implications of these observations to the cooling of electronic equipment are discussed.

scholarly journals Benchmark Solution for a Three-Dimensional Mixed-Convection Flow, Part 1: Reference Solutions

2011 ◽  
Vol 60 (5) ◽  
pp. 325-345 ◽  
Author(s):  
Xavier Nicolas ◽  
Marc Medale ◽  
Stéphane Glockner ◽  
Stéphane Gounand
Keyword(s):  
Mixed Convection ◽  
Three Dimensional ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Flow Part ◽  
Benchmark Solution

Unsteady mixed convection flow at a three-dimensional stagnation point

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Amin Noor ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Unsteady Mixed Convection

Purpose This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function. Findings The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions. Practical implications This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans. Originality/value The case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel.

Linear stability analysis of mixed-convection flow in a vertical pipe

2000 ◽  
Vol 422 ◽  
pp. 141-166 ◽  
Author(s):  
YI-CHUNG SU ◽  
JACOB N. CHUNG
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Shear Instability ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Vertical Pipe ◽  
Prandtl Numbers ◽  
The Stability ◽  
Rayleigh Numbers

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.

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