scholarly journals Prandtl number dependence of stellar convection: Flow statistics and convective energy transport

2021 ◽  
Author(s):  
P. J. Käpylä
Keyword(s):  
Prandtl Number ◽  
Energy Transport ◽  
Convection Flow ◽  
Stellar Convection

Numerical simulations of MHD forced convection flow of micropolar fluid inside a right-angled triangular cavity saturated with porous medium: Effects of vertical moving wall

2019 ◽  
Vol 97 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Mubbashar Nazeer ◽  
N. Ali ◽  
Tariq Javed
Keyword(s):  
Porous Medium ◽  
Prandtl Number ◽  
Forced Convection ◽  
Micropolar Fluid ◽  
Richardson Number ◽  
Hartmann Number ◽  
Darcy Number ◽  
Convection Flow ◽  
Penalty Parameter ◽  
Forced Convection Flow

The present article explores the effects of moving lid on the forced convection flow of micropolar fluid inside a right-angle triangular cavity saturated with porous medium. The base and hypotenuse or inclined sides of the cavity are maintained at constant temperatures, while the vertical side of the enclosure is adiabatic and moving with constant velocity in upward or downward direction. The flow equations are simulated by using the robust finite element numerical technique. The pressure term from the momentum equations is eliminated by using the penalty parameter. For a consistent solution, the value of the penalty parameter is selected as 107. The simulations are performed for the cases based on the direction of moving lid. The numerical outcomes are shown in terms of streamlines, temperature contours, and local and average Nusselt numbers for sundry parameters, such as micropolar parameter, Reynolds number, Richardson number, Darcy number, Hartmann number, and Prandtl number. It is observed that the shape of the inner circulating cell is elliptic when the lid is moving in the upward direction and fluid is clear (Newtonian fluid). It is also found that average Nusselt number in both cases increases with increasing Prandtl number, Richardson number, micropolar parameter, and Darcy number, whereas it decreases with increasing Hartmann number. Further, it achieves a maximum when the lid is moving in the downward direction, regardless of the choice of involved parameters. The numerical code is also validated with previous published results. The investigation of the current study is beneficial in porous heat exchangers, construction of triangular-shaped solar collectors, rigid crystal, polymeric fluid transport, etc.

scholarly journals Stellar Convection as a Low Prandtl Number Flow

1991 ◽  
Vol 130 ◽  
pp. 57-61
Author(s):  
Josep M. Massaguer
Keyword(s):  
Nusselt Number ◽  
Prandtl Number ◽  
Heat Transport ◽  
Large Scale ◽  
Shear Layers ◽  
Turbulent Convection ◽  
The Sun ◽  
Stellar Convection ◽  
Cool Stars ◽  
Number Flow

AbstractThermal convection in the Sun and cool stars is often modeled with the assumption of an effective Prandtl number σ ≃ 1. Such a parameterization results in masking of the presence of internal shear layers which, for small σ, might control the large scale dynamics. In this paper we discuss the relevance of such layers in turbulent convection. Implications for heat transport – i.e. for the Nusselt number power law – are also discussed.

scholarly journals 3-D Convection Models: Are They Compatible with 1-D Models?

2000 ◽  
Vol 176 ◽  
pp. 362-372
Author(s):  
Å. Nordlund ◽  
R. F. Stein
Keyword(s):  
Numerical Modeling ◽  
Energy Transport ◽  
Three Dimensional ◽  
Stellar Structure ◽  
Surface Layers ◽  
Stellar Convection ◽  
Fair Representation ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
Hr Diagram

AbstractWe review properties of stellar convection, as derived from detailed 3-D numerical modeling, and assess to what extent 1-D models are able to provide a fair representation of stellar structure in various regions of the HR diagram. We point out a number of problems and discrepancies that are inevitable when using conventional 1-D models. The problems originate mainly in the surface layers, where horizontal fluctuations become particularly large, and where convective energy transport gives way to radiation. We conclude that it is necessary (and possible) to use three-dimensional models of these layers, in order to avoid the uncertainties and inaccuracies associated with 1-D representations.

Parametric Study of Turbulent Separated Convection Flow Over a Backward-Facing Step in a Duct

2007 ◽  
Author(s):  
Jianhu Nie ◽  
Yitung Chen ◽  
Robert F. Boehm ◽  
Hsuan-Tsung Hsieh
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Prandtl Number ◽  
Inclination Angle ◽  
Stanton Number ◽  
Step Height ◽  
Recirculation Region ◽  
Convection Flow ◽  
Backward Facing Step ◽  
Simulation Code

Simulations of turbulent convection flow adjacent to a two dimensional backward-facing step are presented to explore the effects of step height, step inclination angle, a mounted rib and Prandtl number on velocity field and heat transfer. Reynolds number and duct’s height downstream from the step are kept constant at Re0 = 28000 and H = 0.19m, respectively. Uniform and constant heat flux of qw = 270W/m2 is specified at the stepped wall downstream from the step, while other walls are treated as adiabatic. The selection of the values for these parameters is motivated by the fact that measurements are available for this geometry and they can be used to validate the flow and heat transfer simulation code. The simulated results compare very well the measurements. The primary and secondary recirculation regions increase in size as the step height increases. The friction coefficient becomes smaller in magnitude with the increase of the step height. The peak Stanton number becomes smaller as the step height increases. The reattachment location becomes longer as the step inclination angle increases. With increase of the step inclination angle, the secondary recirculation region disappears. The peak friction coefficient inside the primary recirculation region becomes smaller as the step inclination angle decreases. Installation of a baffle on the upper wall causes the primary recirculation region to become smaller. The Stanton number decreases as the Prandtl number increases.

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.

scholarly journals Kinetic energy transport in Rayleigh–Bénard convection

2015 ◽  
Vol 773 ◽  
pp. 395-417 ◽  
Author(s):  
K. Petschel ◽  
S. Stellmach ◽  
M. Wilczek ◽  
J. Lülff ◽  
U. Hansen
Keyword(s):  
Energy Balance ◽  
Kinetic Energy ◽  
Prandtl Number ◽  
Viscous Dissipation ◽  
Energy Transport ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Viscous Stresses

The kinetic energy balance in Rayleigh–Bénard convection is investigated by means of direct numerical simulations for the Prandtl number range $0.01\leqslant \mathit{Pr}\leqslant 150$ and for fixed Rayleigh number $\mathit{Ra}=5\times 10^{6}$. The kinetic energy balance is divided into a dissipation, a production and a flux term. We discuss the profiles of all the terms and find that the different contributions to the energy balance can be spatially separated into regions where kinetic energy is produced and where kinetic energy is dissipated. By analysing the Prandtl number dependence of the kinetic energy balance, we show that the height dependence of the mean viscous dissipation is closely related to the flux of kinetic energy. We show that the flux of kinetic energy can be divided into four additive contributions, each representing a different elementary physical process (advection, buoyancy, normal viscous stresses and viscous shear stresses). The behaviour of these individual flux contributions is found to be surprisingly rich and exhibits a pronounced Prandtl number dependence. Different flux contributions dominate the kinetic energy transport at different depths, such that a comprehensive discussion requires a decomposition of the domain into a considerable number of sublayers. On a less detailed level, our results reveal that advective kinetic energy fluxes play a key role in balancing the near-wall dissipation at low Prandtl number, whereas normal viscous stresses are particularly important at high Prandtl number. Finally, our work reveals that classical velocity boundary layers are deeply connected to the kinetic energy transport, but fail to correctly represent regions of enhanced viscous dissipation.

Effects on Prandtl Number and Transpiration Parameter on a Certain MHD Free Convection Flow With Visco-Elastic Fluid Along an Infinite Vertical Porous Plate

2002 ◽  
Author(s):  
M. N. Islam
Keyword(s):  
Free Convection ◽  
Prandtl Number ◽  
Variable Viscosity ◽  
Porous Plate ◽  
Order Perturbation ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Elastic Fluid ◽  
Vertical Porous Plate ◽  
Perturbation Velocity

The effect of prandtl number and transpiration parameter variable viscosity on a MHD free convection flow with visco-elastic fluid along an infinite vertical porous plate. The governing partial differential equations have been solved numerically using Local non-similarity method. An analysis is presented to study the effect of prandtl number and transpiration parameter result for the zero order perturbation velocity profile, the first order perturbation velocity and temperature profiles.

Mixed convection flow due to a moving vertical plate parallel to free stream under the influence of Newtonian heating and thermal radiation

2014 ◽  
Vol 5 (3) ◽  
pp. 859-870
Author(s):  
Prabhugouda Patil ◽  
S. Roy
Keyword(s):  
Prandtl Number ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Vertical Plate ◽  
Free Stream ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Newtonian Heating ◽  
Mixed Convection Parameter ◽  
Convection Parameter

The steady mixed convection flow from a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of thermal radiation as well as Newtonian heating effects. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in conjunction with the quasi-linearization technique. Computations are performed and representative set is displayed graphically to illustrate the influence of the mixed convection parameter ( ), Prandtl number (Pr), the ratio of free stream velocity to the composite reference velocity ( ) and the radiation parameter (R) on the velocity and temperature profiles. The numerical results for the local skinfriction coefficient ( ) and surface temperature ( ) are also presented. The results show that the streamwise co-ordinate  significantly influences the flow and thermal fields which indicate the importance of non-similar solutions. Also, it is observed that the increase of mixed convection parameter causes the increase in the magnitude of velocity profile about 65% for lower Prandtl number fluids (Pr=0.7), while it decreases in the temperature profile about 30%. Present results are compared with previously published work and are found to be in excellent agreement.

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