Stability of free convection in a rotating porous layer distant from the axis of rotation

1996 ◽  
Vol 23 (2) ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Free Convection ◽  
Porous Layer ◽  
Axis Of Rotation

Vadasz Number Influence on Vibration in a Rotating Porous Layer Placed Far Away From the Axis of Rotation

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
S. Govender
Keyword(s):  
Mass Transfer ◽  
Free Convection ◽  
Porous Layer ◽  
Heat Mass Transfer ◽  
Stability Criteria ◽  
Time Approximation ◽  
Axis Of Rotation ◽  
Vadasz Number ◽  
Transfer 21 ◽  
The Stability

We consider vibration effects on the classical Rayleigh–Be’nard problem and the classical Vadasz (1994, “Stability of Free Convection in a Narrow Porous Layer Subject to Rotation,” Int. Commun. Heat Mass Transfer, 21, pp. 881–890) problem, which includes rotation of a vertical porous layer about the z-axis. In particular, we focus on the influence of the Vadasz number on vibration for small to moderate and large Vadasz numbers. For small to moderate Vadasz numbers, we develop an analogy between the Vadasz problem (Vadasz, 1994, “Stability of Free Convection in a Narrow Porous Layer Subject to Rotation,” Int. Commun. Heat Mass Transfer, 21, pp. 881–890) placed far away from the axis of rotation and classical Rayleigh–Be’nard problem, both of which include the effects of vibration. It is shown here that the stability criteria are identical to the Rayleigh–Be’nard problem with vibration when g∗=ω∗2X0∗. The analysis for the large Vadasz number scaling indicates that a frozen time approximation is appropriate where the effect of vibration is modeled as small variations in the Rayleigh number definition.

scholarly journals Vadasz Number Effects on Convection in a Vertical Rotating Porous Layer, Placed Far from Axis of Rotation, and Subjected to Internal Heat Generation and Centrifugal Jitter

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 728-738
Author(s):  
Saneshan Govender
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Critical Rayleigh Number ◽  
Time Derivative ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Stability Criteria ◽  
Axis Of Rotation ◽  
Vadasz Number ◽  
The Impact

The flow and heat transfer in a rotating vertical porous layer, placed far from the axis of rotation, and subjected to internal heat generation and centrifugal jitter, is considered. The linear stability theory is used to determine the convection threshold, in terms of the critical Rayleigh number. Typical liquids used in engineering applications and heavy liquid metals are used to demonstrate conditions at which the Vadasz number is sufficiently small to warrant the retention of the time derivative in the momentum equation. When considering low amplitude and high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions. In summary, when the Vadasz number is large, centrifugal jitter has no impact on the convection stability criteria. In contrast, when the Vadasz number is small, centrifugal jitter impacts the convection stability criteria.

Pseudoplastic natural convection flow and heat transfer in a cylindrical vertical cavity partially filled with a porous layer

2019 ◽  
Vol 30 (3) ◽  
pp. 1096-1114 ◽  
Author(s):  
Kasra Ayoubi Ayoubloo ◽  
Mohammad Ghalambaz ◽  
Taher Armaghani ◽  
Aminreza Noghrehabadi ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Free Convection ◽  
Porous Layer ◽  
Power Law ◽  
Convection Flow ◽  
Governing Equations ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Vertical Cavity

Purpose This paper aims to theoritically investigate the free convection flow and heat transfer of a non-Newtonian fluid with pseudoplastic behavior in a cylindrical vertical cavity partially filled with a layer of a porous medium. Design/methodology/approach The non-Newtonian behavior of the pseudoplastic liquid is described by using a power-law non-Newtonian model. There is a temperature difference between the internal and external cylinders. The porous layer is attached to the internal cylinder and has a thickness of D. Upper and lower walls of the cavity are well insulated. The governing equations are transformed into a non-dimensional form to generalize the solution. The finite element method is used to solve the governing equations numerically. The results are compared with the literature results in several cases and found in good agreement. Findings The influence of the thickness of the porous layer, Rayleigh number and non-Newtonian index on the heat transfer behavior of a non-Newtonian pseudoplastic fluid is addressed. The increase of pseudoplastic behavior and increase of the thickness of the porous layer enhances the heat transfer. By increase of the porous layer from 0.6 to 0.8, the average Nusselt number increased from 0.15 to 0.25. The increase of non-Newtonian effects (decrease of the non-Newtonian power-law index) enhances the heat transfer rate. Originality/value The free convection behavior of a pseudoplastic-non-Newtonian fluid in a cylindrical enclosure partially filled by a layer of a porous medium is addressed for the first time.

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