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.

scholarly journals Vadasz Number Effects on Convection in a Horizontal Porous Layer Subjected to Internal Heat Generation and G-Jitter

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 124
Author(s):  
Saneshan Govender
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Heat Generation ◽  
Critical Rayleigh Number ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Onset Of Convection ◽  
Vadasz Number ◽  
The Impact

Flow and heat transfer in a horizontal porous layer subjected to internal heat generation and g-jitter is considered for the Dirichlet thermal boundary condition. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number. For the low amplitude, high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection when the porous layer is heated from below. When the porous layer is cooled from below and heated from above, the vibration has a destabilizing effect in the presence of internal heat generation. It is also demonstrated that when the top and bottoms walls are cooled and rigid/impermeable, the critical Rayleigh number is infinitely large and conduction is the only possible mode of heat transfer. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions.

scholarly journals Chaotic Convection in a Ferrofluid with Internal Heat Generation

CFD letters ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 62-74
Author(s):  
Nor Halawati Senin ◽  
Nor Fadzillah Mohd Mokhtar ◽  
Mohamad Hasan Abdul Sathar
Keyword(s):  
Heat Generation ◽  
Mathematical Formulation ◽  
Internal Heat ◽  
Boussinesq Approximation ◽  
Internal Heat Generation ◽  
Lorenz Attractor ◽  
Nonlinear Stability Analysis ◽  
Layer System ◽  
Chaotic Convection ◽  
The Impact

The nonlinear stability analysis of a ferrofluid layer system is formulated mathematically. This system considered the upper and lower free isothermal boundary with the system heated from below. A mathematical formulation is produced to study the behaviour of the chaotic convection in a ferrofluid layer system using Galerkin truncated expansion. The Boussinesq approximation is opted with the existence of internal heating and the magnetic number. It is found that the transition to chaos in this present study is identical to the Lorenz attractor and thus validate the method and analysis of this study. The impact of elevating the internal heat generation is found to hasten the instability of the system and as for the magnetic number, at M1 = 2.5 the homoclinic bifurcation occurs and thus accelerates the convection process.

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 Effects of Gravity Modulation and Internal Heat Generation on the onset of Rayleigh-Benard convection in a Micropolar Fluid

2016 ◽  
Vol 12 (6) ◽  
pp. 6270-6285
Author(s):  
Vasudha Satri ◽  
S Pranesh ◽  
Shahnaz Bathul
Keyword(s):  
Heat Source ◽  
Heat Generation ◽  
Micropolar Fluid ◽  
Body Force ◽  
Critical Rayleigh Number ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Internal Heat Generation ◽  
Gravity Modulation ◽  
Time Periodic

The effect of gravity modulation (time periodic body force or g-jitter) on the onset of Rayleigh-Bénard convection in a micropolar fluid with internal heat generation is investigated by making a linear stability analysis. The stability of a horizontal layer of fluid heated from below is examined by assuming time periodic body force in the presence of internal heat source. A regular perturbation method is used to arrive at an expression to compute the critical Rayleigh number for small amplitude of modulation and dimensionless internal heat source. The Venezian approach is adopted to obtain the eigen value of the problem. The results obtained during the analysis have been presented graphically.

The Onset of Brinkman-Benard Ferroconvection in a Saturated Porous Layer With Internal Heat Generation

2010 ◽  
Author(s):  
C. E. Nanjundappa ◽  
H. N. Prakash
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Lower Boundary ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Darcy Number ◽  
Internal Heat Generation ◽  
Fluid Viscosity ◽  
Thermomagnetic Convection ◽  
Saturated Porous Layer

The effect of internal heat generation on the criterion for the onset of thermomagnetic convection in a horizontal ferrofluid saturated porous layer in the presence of a uniform magnetic field is studied using the Brinkman-Lapwood extended Darcy flow model with fluid viscosity different from effective viscosity. The lower boundary is taken to be rigid – insulating and the upper surface is free and subject to the general thermal condition. The resulting eigenvalue problem is solved numerically using the Galerkin method with the Rayleigh number as the eigenvalue. The effect of increase in the value of dimensionless internal heat source strength Ns, magnetic number M1 and the non-linearity of fluid magnetization parameter M3 is to hasten, while increase in the value of inverse of Darcy number Da−1, viscosity ratio Λ, Biot number Bi and magnetic susceptibility χ is to delay the onset of thermomagnetic convection in a ferrofluid saturated porous layer. Further, increase in the value of Bi, Da−1 and Ns as well as decrease in Λ M1> and M3 is to diminish the dimension of convection cells.

scholarly journals Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 75 ◽  
Author(s):  
Leiv Storesletten ◽  
D. Andrew S. Rees
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Internal Heat ◽  
Convective Motion ◽  
Linear Instability ◽  
Internal Heat Generation ◽  
Anisotropy Ratio ◽  
Heat Sources ◽  
Onset Of Convection ◽  
Set Up

The onset of convection in an inclined porous layer which is heated internally by a uniform distribution of heat sources is considered. We investigate the combined effects of inclination, anisotropy and internal heat generation on the linear instability of the basic parallel flow. When the Rayleigh number is sufficiently large, instability occurs and a convective motion is set up. It turns out that the preferred motion at convection onset depends quite strongly on the anisotropy ratio, ξ , and the inclination angle. When ξ < 1 the preferred motion is in the form of longitudinal rolls for all inclinations. When ξ > 1 transverse rolls are preferred for small inclinations but, at high inclinations, longitudinal rolls are preferred. At intermediate inclinations the preferred roll orientation varies smoothly between these two extremes.

Thermal exploration of radial porous fin fully wetted with SWCNTs and MWCNTs along with temperature-dependent internal heat generation

2020 ◽  
Vol 234 (24) ◽  
pp. 4945-4952
Author(s):  
G Sowmya ◽  
BJ Gireesha ◽  
S Sindhu
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Multiwalled Carbon ◽  
Single Walled Carbon ◽  
Swcnts And Mwcnts ◽  
The Impact

The numerical examination of radiation and natural convection in a porous radial fin along with varying internal heat generation with respect to temperature is carried out in the current study. The aim of this study is to scrutinize the heat transfer phenomenon in fin wetted with water-based carbon nanotubes like single-walled carbon nanotubes and multiwalled carbon nanotubes. In the proposed work, the Darcy’s model is employed for the analysis. The modeled equations are nondimensionalized and solved by utilizing Runge–Kutta–Fehlberg method. The impact of relevant parameters on the heat transfer rate is comprehensively explored with an aid of graphs. Here, multiwalled carbon nanotube–water shows better heat transfer from surface of fin compared to single-walled carbon nanotube–water.

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