Patterned ground formation and solar radiation ground heating

1992 ◽  
Vol 438 (1903) ◽  
pp. 249-263 ◽  
Keyword(s):  
Boundary Condition ◽  
Modulation Amplitude ◽  
Patterned Ground ◽  
Onset Of Convection ◽  
Variable Permeability ◽  
Periodic Temperature ◽  
The Galerkin Method ◽  
Time Periodic ◽  
Geological Phenomenon ◽  
Critical Wavenumber

A mathematical analysis is presented for the onset of cellular convection in a saturated horizontal porous layer which is subject to a time-periodic boundary condition. Darcy’s law is used but variable permeability is allowed for and a parabolic equation of state is assumed. The modulated boundary condition produces a time-periodic temperature gradient in the layer. To obtain predictions for the onset of convection and the critical wavenumber from the linear system, we use the Galerkin method and Floquet theory. Similar predictions are obtained from the nonlinear system via the energy method. We study the effect varying frequency and modulation amplitude have on these predictions. To illustrate this we apply our analysis to the formation of polygonal ground, a geological phenomenon consisting of stone borders forming regular hexagons and soil centres. The theoretical model for patterned ground is based on the onset of convection in a saturated soil below which is a cold permafrost layer.

Effects of a centered conducting body on natural convection of non-Newtonian fluid in a square enclosure with time-periodic temperature distribution

2020 ◽  
Author(s):  
Peixin Ye ◽  
Dinggen Li ◽  
Zihao Yu ◽  
Haifeng Zhang
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Capacity ◽  
Transient Heat Transfer ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Transfer Ratio ◽  
Periodic Temperature ◽  
Power Law Index ◽  
Time Periodic

In this paper, a modified lattice Boltzmann model that incorporates the effect of heat capacity is adopted to study the effects of a centered conducting body on natural convection of non-Newtonian fluid in a square cavity with time-periodic temperature distribution. The effects of power-law index, Rayleigh number, heat capacity ratio, thermal conductivity ratio, body size, temperature pulsating period and the temperature pulsating amplitude on fluid flow and heat transfer are analyzed in detail. The results showed that the increase of Rayleigh number and thermal conductivity ratio as well as the decrease of power-law index can strengthen both transient and global heat transfer, while the increase of heat capacitance of fluid to the solid wall can only enhance the transient heat transfer, and has little effect on the overall heat transfer. Further, the increase of body size will reduce both the transient heat transfer ratio and the overall heat transfer ratio. In addition, the decrease of temperature pulsating period can enhance the transient heat transfer, but it will slightly weaken the overall heat transfer. Finally, the results show that both the transient and the overall heat transfer ratio are increased with the increase of temperature pulsating amplitude.

Stability of a Horizontal Porous Layer with Timewise Periodic Boundary Conditions

1979 ◽  
Vol 101 (2) ◽  
pp. 244-248 ◽  
Author(s):  
B. Chhuon ◽  
J. P. Caltagirone
Keyword(s):  
Porous Layer ◽  
Periodic Boundary ◽  
Lower Boundary ◽  
Periodic Boundary Conditions ◽  
Temperature Oscillation ◽  
Linear Stability Theory ◽  
Onset Of Convection ◽  
Thermal Signal ◽  
Periodic Temperature ◽  
The Stability

The stability of a horizontal porous layer bounded by two impermeable planes is investigated. A time dependent periodic temperature profile is imposed on the lower boundary while the upper plane is kept at constant temperature. Starting from the preconvective temperature distribution, and using the linear stability theory, a criterion for the onset of convection is defined as a function of the perturbation wavenumber and of the amplitude and frequency of the temperature oscillation. Experimental work with a setup allowing both the amplitude and the frequency of the thermal signal to vary is done. Finally, the equations are also solved numerically and the results are compared to the previous ones. A synthesis of all results is included.

Unsteady Heating of Rayleigh-Benard Convection

2004 ◽  
Vol 59 (4-5) ◽  
pp. 266-274
Author(s):  
B. S. Bhadauria
Keyword(s):  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Dependent Part ◽  
Prandtl Numbers ◽  
Periodic Temperature ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Unsteady Heating ◽  
Horizontal Fluid Layer ◽  
Time Periodic

The linear thermal instability of a horizontal fluid layer with time-periodic temperature distribution is studied with the help of the Floquet theory. The time-dependent part of the temperature has been expressed in Fourier series. Disturbances are assumed to be infinitesimal. Only even solutions are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers and for various values of the frequency. It is found that the disturbances are either synchronous with the primary temperature field or have half its frequency. - 2000 Mathematics Subject Classification: 76E06, 76R10.

Pole Placement for Delay Differential Equations with Time-Periodic Delays Using Galerkin Approximations (CND-20-1378)

2021 ◽  
Author(s):  
Shanti Swaroop Kandala ◽  
Thomas K. Uchida ◽  
C. P. Vyasarayani
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Delay Differential Equations ◽  
Second Order ◽  
Delay Systems ◽  
First Order ◽  
The Galerkin Method ◽  
Delay Differential ◽  
Time Periodic ◽  
Periodic Delays

Abstract Many practical systems have inherent time delays that cannot be ignored; thus, their dynamics are described using delay differential equations (DDEs). The Galerkin approximation method is one strategy for studying the stability of time-delay systems. In this work, we consider delays that are time-varying and, specifically, time-periodic. The Galerkin method can be used to obtain a system of ordinary differential equations (ODEs) from a second-order time-periodic DDE in two ways: either by converting the DDE into a second-order time-periodic partial differential equation (PDE) and then into a system of second-order ODEs, or by first expressing the original DDE as two first-order time-periodic DDEs, then converting into a system of first-order time-periodic PDEs, and finally converting into a first-order time-periodic ODE system. The difference between these two formulations in the context of control is presented in this paper. Specifically, we show that the former produces spurious Floquet multipliers at a spectral radius of 1. We also propose an optimization-based framework to obtain feedback gains that stabilize closed-loop control systems with time-periodic delays. The proposed optimization-based framework employs the Galerkin method and Floquet theory, and is shown to be capable of stabilizing systems considered in the literature. Finally, we present experimental validation of our theoretical results using a rotary inverted pendulum apparatus with inherent sensing delays as well as additional time-periodic state-feedback delays that are introduced deliberately.

Instability of unsteady flows or configurations. Part 2. Convective instability

1972 ◽  
Vol 54 (1) ◽  
pp. 143-152 ◽  
Author(s):  
Chia-Shun Yih ◽  
Chin-Hsiu Li
Keyword(s):  
Prandtl Number ◽  
Convective Instability ◽  
Floquet Theory ◽  
Critical Rayleigh Number ◽  
Unsteady Flows ◽  
Temperature Oscillation ◽  
Numerical Results ◽  
Periodic Temperature ◽  
Convective Cells ◽  
Time Periodic

The formation of convective cells in a fluid between two horizontal rigid boundaries with time-periodic temperature distribution is studied by the use of the Floquet theory. Numerical results for the critical Rayleigh number are given for a Prandtl number of 0·73 (air) and for various values of the frequency and magnitude of the primary temperature oscillation. Some numerical results for a Prandtl number of 7·0 (water) are also given. The most striking feature of the results is that the disturbances (or convection cells) oscillate either synchronously or with half frequency.

Sign in / Sign up

Export Citation Format

Share Document