Laminar Rayleigh–Bénard Convection of Power-Law Fluids in Trapezoidal Enclosures

2021 ◽  
pp. 1-6
Author(s):  
Mir Elyad Vakhshouri ◽  
Burhan Çuhadaroğlu
Keyword(s):  
Power Law ◽  
Bénard Convection ◽  
Benard Convection ◽  
Power Law Fluids ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

scholarly journals Rayleigh-Bénard Convection of Non-Newtonian Power-Law Fluids with Temperature-Dependent Viscosity

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kaddiri ◽  
Mohamed Naïmi ◽  
Abdelghani Raji ◽  
Mohammed Hasnaoui
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Bénard Convection ◽  
Benard Convection ◽  
Power Law Fluids ◽  
Dependent Viscosity ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Two-dimensional steady-state Rayleigh-Bénard convection of thermodependent power-law fluids confined in a square cavity, heated from the bottom and cooled on the top with uniform heat fluxes, has been conducted numerically using a finite difference technique. The effects of the governing parameters, which are the Pearson number (0≤m≤10), the flow behaviour index (0.6≤n≤1.4), and the Rayleigh number (0<Ra≤105), on the flow onset, flow structure, and heat transfer have been examined. The heatlines concept has been used to explain the heat transfer deterioration due to temperature-dependent viscosity effect that m expresses.

scholarly journals Bulk scaling in wall-bounded and homogeneous vertical natural convection

2018 ◽  
Vol 841 ◽  
pp. 825-850 ◽  
Author(s):  
Chong Shen Ng ◽  
Andrew Ooi ◽  
Detlef Lohse ◽  
Daniel Chung
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Power Law ◽  
Exact Relation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Previous numerical studies on homogeneous Rayleigh–Bénard convection, which is Rayleigh–Bénard convection (RBC) without walls, and therefore without boundary layers, have revealed a scaling regime that is consistent with theoretical predictions of bulk-dominated thermal convection. In this so-called asymptotic regime, previous studies have predicted that the Nusselt number ($\mathit{Nu}$) and the Reynolds number ($\mathit{Re}$) vary with the Rayleigh number ($\mathit{Ra}$) according to $\mathit{Nu}\sim \mathit{Ra}^{1/2}$ and $\mathit{Re}\sim \mathit{Ra}^{1/2}$ at small Prandtl numbers ($\mathit{Pr}$). In this study, we consider a flow that is similar to RBC but with the direction of temperature gradient perpendicular to gravity instead of parallel to it; we refer to this configuration as vertical natural convection (VC). Since the direction of the temperature gradient is different in VC, there is no exact relation for the average kinetic dissipation rate, which makes it necessary to explore alternative definitions for $\mathit{Nu}$, $\mathit{Re}$ and $\mathit{Ra}$ and to find physical arguments for closure, rather than making use of the exact relation between $\mathit{Nu}$ and the dissipation rates as in RBC. Once we remove the walls from VC to obtain the homogeneous set-up, we find that the aforementioned $1/2$-power-law scaling is present, similar to the case of homogeneous RBC. When focusing on the bulk, we find that the Nusselt and Reynolds numbers in the bulk of VC too exhibit the $1/2$-power-law scaling. These results suggest that the $1/2$-power-law scaling may even be found at lower Rayleigh numbers if the appropriate quantities in the turbulent bulk flow are employed for the definitions of $\mathit{Ra}$, $\mathit{Re}$ and $\mathit{Nu}$. From a stability perspective, at low- to moderate-$\mathit{Ra}$, we find that the time evolution of the Nusselt number for homogenous vertical natural convection is unsteady, which is consistent with the nature of the elevator modes reported in previous studies on homogeneous RBC.

Boundary layer fluctuations in turbulent Rayleigh–Bénard convection

2018 ◽  
Vol 840 ◽  
pp. 408-431 ◽  
Author(s):  
Yin Wang ◽  
Wei Xu ◽  
Xiaozhou He ◽  
Hiufai Yik ◽  
Xiaoping Wang ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Numerical Study ◽  
Mixing Zone ◽  
Scaling Properties ◽  
Cell Height ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We report a combined experimental and numerical study of the effect of boundary layer (BL) fluctuations on the scaling properties of the mean temperature profile$\unicode[STIX]{x1D703}(z)$and temperature variance profile$\unicode[STIX]{x1D702}(z)$in turbulent Rayleigh–Bénard convection in a thin disk cell and an upright cylinder of aspect ratio unity. Two scaling regions are found with increasing distance$z$away from the bottom conducting plate. In the BL region, the measured$\unicode[STIX]{x1D703}(z)$and$\unicode[STIX]{x1D702}(z)$are found to have the scaling forms$\unicode[STIX]{x1D703}(z/\unicode[STIX]{x1D6FF})$and$\unicode[STIX]{x1D702}(z/\unicode[STIX]{x1D6FF})$, respectively, with varying thermal BL thickness$\unicode[STIX]{x1D6FF}$. The functional forms of the measured$\unicode[STIX]{x1D703}(z/\unicode[STIX]{x1D6FF})$and$\unicode[STIX]{x1D702}(z/\unicode[STIX]{x1D6FF})$in the two convection cells agree well with the recently derived BL equations by Shishkinaet al.(Phys. Rev. Lett., vol. 114, 2015, 114302) and by Wanget al.(Phys. Rev. Fluids, vol. 1, 2016, 082301). In the mixing zone outside the BL region, the measured$\unicode[STIX]{x1D703}(z)$remains approximately constant, whereas the measured$\unicode[STIX]{x1D702}(z)$is found to scale with the cell height$H$in the two convection cells and follows a power law,$\unicode[STIX]{x1D702}(z)\sim (z/H)^{\unicode[STIX]{x1D716}}$, with the obtained values of$\unicode[STIX]{x1D716}$being close to$-1$. Based on the experimental and numerical findings, we derive a new equation for$\unicode[STIX]{x1D702}(z)$in the mixing zone, which has a power-law solution in good agreement with the experimental and numerical results. Our work demonstrates that the effect of BL fluctuations can be adequately described by the velocity–temperature correlation functions and the new BL equations capture the essential physics.

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