Amplitude Convection Research Articles

Weak nonlinear thermo bioconvection: Heat transfer via artificial neural network

The present study undertakes an analytical exploration of the onset of regular and chaotic thermo-bioconvection in a suspension of gravitactic microorganisms. Additionally, it employs a machine learning approach for numerical computation and prediction of heat transfer rates. The two-dimensional flow governing dynamics are modeled using the Hamilton-Crosser model for microorganisms. The amplitude of convection is determined by solving the cubic Ginzburg-Landau equation derived by applying the Lorenz technique. Stationary curves are plotted with thermal Rayleigh number and wave number, while Nusselt numbers are depicted over a range of time. The onset of chaotic motion is briefly discussed through Lyapunov plots and a bifurcation diagram. Further, to predict the heat transfer rate with multiple interconnected parameters, an artificial neural network is trained with the Levenberg-Marquardt algorithm to understand the underlying patterns of simulated data. The trained neural network is then employed to estimate the Nusselt number for various values of bioconvection Rayleigh number, bioconvection Lewis number, and bioconvection Péclet number. The values obtained from the artificial neural network models are compared with numerical data for validation and are found to be in good agreement. The findings of weak non-linear stability indicate that chaotic motion emerges in the system at the Hopf-Rayleigh number of 24.635, and fast-swimming microorganisms significantly increase the heat transfer rate. The coefficient of correlation is higher than 0.99, supporting the accuracy of developed ANN models to predict the Nusselt number with high accuracy. This observation supports the potential utilization of microbes in heat transfer applications.

Flame transfer functions of asymmetric conical and V-shaped flames

Transfer functions of asymmetric flames subjected to incident flow perturbations are explored using the classical kinematic model, the G-equation, parameterized by flame tip angle α, flame-base incline angle β, and eccentricity e. With perturbations of various frequencies, we analyze perturbed asymmetric flames and derive analytical formulations of Flame Transfer Functions (FTF) for various flame conditions. It is observed that the gain of the asymmetric conical flame is increased compared to the symmetric case. Meanwhile, the amplification effect of the V-shaped flame is considerably suppressed as the flame becomes asymmetric. That means with a proper asymmetric geometry setting, the V-shaped flame no longer tends to amplify the perturbation and in other words becomes less susceptible to combustion instability. These findings have significant value for the future design and optimization of propulsion systems, where improving flame stability and reducing thermoacoustic instabilities are critical. Subsequently, a numerical study is conducted to verify the FTF results and examine the response of asymmetric flames under various perturbation levels. It has been demonstrated that the asymmetric conical flame is minimally affected by the amplitude of these perturbations, and the asymmetric V-shaped flame is highly sensitive to the convective amplitudes.

Existence of small-scale Rossby waves points to low convective velocity amplitudes in the Sun

Inertial waves occur naturally in rotating fluids such as the Sun and the Earth's atmosphere. Rossby waves in the Sun have the potential to shed fresh light on interior turbulence and convection that prior seismic methods, reliant on sound waves, have been unable to accomplish. Here, we utilize ∼13 years of observational products taken by the space-based helioseismic and magnetic imager, onboard the solar dynamics observatory, to characterize solar equatorial Rossby waves. By examining maps of motions at the surface using two different methods, we are able to identify Rossby modes up to azimuthal order m = 30, approximately up to twice the spatial wavenumber limit of previous studies. The dispersion relation of these modes departs significantly from the classical two-dimensional Rossby-Haurwitz description. A parameter study of the effect of superadiabaticity and viscous diffusion on these inertial modes indicates that each parameter plays a role in influencing both the frequencies and linewidths of high m modes. Using the Rhines-scale relation, we constrain the root mean square amplitude of turbulent convection more tightly to ∼2 m/s, adding more evidence to the paradigm of weakly convective amplitudes at large scales.

Study of Thermal Instability in Magneto-Convection Nanoliquid Confined within Hele-Shaw Cell Under Three Types of Thermal/Gravity Modulation

In the present paper, we investigate a thermal instability of magneto-convection in an electrically conducting nanoliquid confined within Hele-Shaw cell, subjected to an applied time-periodic boundary thermal (ATBT) or gravitational modulation (ATGM), and surrounded by a constant vertical magnetic field. A steady portion and a time-dependent oscillatory portion constitute the temperature gradient seen between liquid layer’s walls in the context of ATBT. In this scenario, both walls’ temperatures are modulated. The liquid layer oscillation can be used to realise the externally applied time periodic component of the gravity field that is present in the ATGM problem. The perturbation is described in terms of the power series of the assumed-small convective amplitude. The impact of modulations on heat/mass transfer are examined utilising Ginzburg-Landau (GBL) approach. The impact of different parameters on the transportation of mass and heat is also explored. Additionally, we observe that gravitational modulation is very much effective than thermal modulation. Lewis-number, modified-diffusivity ratio and concentration Rayleigh-number increase heat and mass transport in the system.

GRAVITY MODULATION AND ITS IMPACT ON WEAKLY NONLINEAR BIOTHERMAL CONVECTION IN A POROUS LAYER UNDER ROTATION: A GINZBURG-LANDAU MODEL APPROACH

The effect of gravity modulation on weakly nonlinear biothermal convection in a porous rotating layer has been investigated in this study. The system under consideration is a porous medium layer saturated with a Newtonian fluid containing gyrotactic microorganisms, and it is subjected to both gravity modulation and rotation. Through a weakly nonlinear analysis, the behavior of the system at finite amplitudes is studied. The Ginzburg-Landau equation, obtained from perturbation analysis, provides insights into the system's behavior in the presence of gravity modulation. The amplitude of convection in the unmodulated case is determined analytically, serving as a reference for comparison. The research explores the influence of various parameters on the system, including the Vadasz number, modified Rayleigh-Darcy number, Taylor number, cell eccentricity, and modulation parameters such as amplitude and frequency. By varying these parameters, the heat transfer, quantified by the Nusselt number, is analyzed and compared in different cases. The modulation amplitude is found to have a significant effect on enhancing heat transfer, while the modulation frequency has a diminishing effect.

Amplitude and Phase Angle of Oscillatory Heat Transfer and Current Density along a Nonconducting Cylinder with Reduced Gravity and Thermal Stratification Effects

Due to excessive heating, various physical mechanisms are less effective in engineering and modern technologies. The aligned electromagnetic field performs as insulation that absorbs the heat from the surroundings, which is an essential feature in contemporary technologies, to decrease high temperatures. The major goal of the present investigation is to use magnetism perpendicular to the surface to address this issue. Numerical simulations have been made of the MHD convective heat and amplitude problem of electrical fluid flow down a horizontally non-magnetized circular heated cylinder with reduced gravity and thermal stratification. The associated non-linear PDEs that control fluid motion can be conveniently represented using the finite-difference algorithm and primitive element substitution. The FORTRAN application was used to compute the quantitative outcomes, which are then displayed in diagrams and table formats. The physical features, including the phase angle, skin friction, transfer of heat, and electrical density for velocity description, the magnetic characteristics, and the temperature distribution, coupled by their gradients, have an impact on each of the variables in the flow simulation. In the domains of MRI resonant patterns, prosthetic heartvalves, interior heart cavities, and nanoburning devices, the existing magneto-hydrodynamics and thermodynamic scenario are significant. The main findings of the current work are that the dimensionless velocity of the fluid increases as the gravity factor Rg decreases. The prominent change in the phase angle of current density αm and heat flux αt is examined for each value of the buoyancy parameter at both α=π/6 and π angles. The transitory skin friction and heat transfer rate shows a prominent magnitude of oscillation at both α=π/6 and π/2 positions, but current density increases with a higher magnitude of oscillation.

Effect of rotation and internal heat generation on Darcy–Brinkman convection in Oldroyd‐B liquid

AbstractConvection in an Oldroyd‐B liquid saturated highly permeable porous medium is studied via both linear and nonlinear theories. Estimating a convection threshold is the objective of linear‐stability analysis whereas convection amplitudes and heat transfer are elucidated by performing nonlinear‐stability analysis. The eigenvalue problem is solved by the Galerkin method of weighted residuals. The oscillatory mode becomes dominant over the stationary mode. This is because of the race among diffusivity, viscoelasticity, internal‐heat generation, and rotation. The increasing permeability, internal heat generation coefficient, and stress‐relaxation parameter are liable to subcritical motions while the rotation, viscosities ratio, heat capacities ratio, and strain retardation parameter are responsible for the system attaining a supercritical state. The Runge–Kutta–Gill method presents the mechanism to evaluate the amount of heat transfer. The increasing Rayleigh number, internal Rayleigh number, Darcy number, Deborah number, Prandtl number, and the heat capacities ratio enhance the heat transfer. This offers a convenient mechanism for regulating convection. The results obtained in the present paper are expected to play a decisive role in some of the real‐life applications such as oil‐reservoir modeling, crude oil extraction, crystal growth, medicine industries, geothermal‐energy utilization, and so on.

Finite element study of nanoparticles spacing and radius on dynamics of water fluid subject to microgravity environment

This communication studies the vital role of particles spacing and radius of nanoparticles subject to microgravity environment, an inclined surface, and magnetic field. The varying particles size and spacing in the microgravity environment is taken into consideration. A mathematical formulation that is based on conservation principles is non-dimensionalized by enforcement of similarity transformation yielding a related set of ordinary differential equations (ODEs). The convective non-linearity and coupling, a finite element (FE) discretization, is implemented and run on the Matlab platform. Then computational endeavor is continued to elucidate the impacts of various inputs of radius, the amplitude of modulation, mixed convection, inclination angle, particles spacing, and magnetic parameter. The increasing inter-particles spacing and radius are directly influence to the fluid velocity and inversely influence to the fluid temperature. The growing strength of frequency of oscillation and incline angle leads to a decline in skin friction and heat transfer coefficients, but an opposite trend is reported when the thermal buoyancy parameter is enhanced. These outcomes would be very useful for researchers to control upper space transportation and devices performance.

Ginzburg Landau Model for Nanofluid Convection in the Presence of Time Periodic Plate Modulation

Here we study thermal modulation effect on nanofluid convection and discuss heat and mass transfer in the layer. The non-uniform time periodic boundary conditions of the system are considered. A weak non-linear stability analysis has been performed and obtained heat and mass transfer coefficients as a function of the system parameters. The Ginzburg Landau model was employed to derive nanofluid convective amplitude at different stages of flow disturbances and modulation. Slow variations of time scale shows that thermal modulation impact on transport phenomenon for the case of out phase modulation (OPM) and (lower boundary modulation) LBM. Also the effect of IPM (in-phase modulation) is observed low effect on Nu and which are similar to un-modulation case. It is also justified that LBM restuls are similar to gravity modulation results. It is found that thermal modulation and concentration Rayleigh numbers are either stabilize or destabilize the system. Further, GL model shows better results on regulation of transport process

Throughflow and Gravity Modulation Effects on Thermal Convection in a Couple Stress Fluids Saturating a Porous Medium with an Internal Heat Source

In this paper, the effect of throughflow and gravity modulation on thermal convection in a couple stress fluids saturating a porous medium with an internal heating source is investigated. A weakly nonlinear stability analysis is proposed to study the stationary mode of convection. The amplitude of gravity modulation is assumed to be very small and the disturbances are extended in terms of the power series of the amplitude of convection. Using a non-autonomous Ginzburg- Landau amplitude equation, heat transport is evaluated in terms of the Nusselt number. The finite-amplitude of convection has been derived in the third order. The amplitude and frequency of modulation have the effects of increasing or diminishing heat transport. The presence of a couple-stress parameter with internal heat source throughflow and modulation effects has been discussed. The effect of the internal heat source increases or decreases heat transfer in the system. For suitable ranges of Ω the throughflow and internal heating have both destabilizing and stabilizing effects. Finally flow patterns are presented in terms of streamlines and isotherms.

Effect of Gravity and Throughflow on Double Diffusive Convection in a Couple Stress Fluid Saturated Porous Media

We have investigated effect of throughflow and gravity modulation on double diffusive convection with couple-stress fluid saturated porous media. Applying the Landau model, we have derived finite amplitude of couple-stress convection in the presence of gravity modulation. The presence of a couple-stress parameter produces both diminishing and enhancing heat mass transfer in the layer. To present the results we have used Mathematica to obtain the Nusselt number and Sherwood numbers numerically. Further, it is shown that, throughflow and modulation of gravity controls double diffusive convection through convective amplitude and alter transport phenomenon.

Transition from anti-solar to solar-like differential rotation: Dependence on Prandtl number

Context. Late-type stars such as the Sun rotate differentially due to the interaction of turbulent convection and rotation. Aims. The aim of the study is to investigate the effects of the effective thermal Prandtl number, which is the ratio of kinematic viscosity to thermal diffusivity, on the transition from anti-solar (slow equator, fast poles) to solar-like (fast equator, slow poles) differential rotation. Methods. Three-dimensional hydrodynamic and magnetohydrodynamic simulations in semi-global spherical wedge geometry were used to model the convection zones of solar-like stars. Results. The overall convective velocity amplitude increases as the Prandtl number decreases, in accordance with earlier studies. The transition from anti-solar to solar-like differential rotation is insensitive to the Prandtl number for Prandtl numbers below unity, but for Prandtl numbers greater than unity, solar-like differential rotation becomes significantly harder to excite. Magnetic fields and more turbulent regimes with higher fluid and magnetic Reynolds numbers help to achieve solar-like differential rotation in near-transition cases where anti-solar rotation is found in more laminar simulations. Solar-like differential rotation occurs only in cases with radially outward turbulent angular momentum transport due to the Reynolds stress at the equator. The dominant contribution to this outward transport near the equator is due to prograde propagating thermal Rossby waves. Conclusions. The differential rotation is sensitive to the Prandtl number only for large Prandtl numbers in the parameter regime explored in this study. Magnetic fields have a greater effect on the differential rotation, although the inferred presence of a small-scale dynamo did not lead to drastically different results. The dominance of the thermal Rossby waves in the simulations is puzzling because they are not detected in the Sun. The current simulations are shown to be incompatible with the currently prevailing mean-field theory of differential rotation.

Time-Periodic Thermal Boundary Effects on Porous Media Saturated with Nanofluids: CGLE Model for Oscillatory Mode

Abstract The stability of nonlinear nanofluid convection is examined using the complex matrix differential operator theory. With the help of finite amplitude analysis, nonlinear convection in a porous medium is investigated that has been saturated with nanofluid and subjected to thermal modulation. The complex Ginzburg-Landau equation (CGLE) is used to determine the finite amplitude convection in order to evaluate heat and mass transfer. The small amplitude of convection is considered to determine heat and mass transfer through the porous medium. Thermal modulation of the system is predicted to change sinusoidally over time, as shown at the boundary. Three distinct modulations IPM, OPM, and LBMOhave been investigated and found that OPM and LBMO cases are used to regulate heat and mass transfer. Further, it is found that modulation frequency (ω f varying from 2 to 70) reduces heat and mass transfer while modulation amplitude (δ 1 varying from 0.1 to 0.5 ) enhances both.

Effects of Throughflow and Gravity Modulation on Thermal Convection in a Couple Stress Fluid Saturated Porous Layer

In this paper, we have investigated the effects of throughflow and gravity modulation on a couple stress fluid saturated porous layer using non-autonomous Ginzburg-Landau model. A small variation of disturbances has been considered to examine the nonlinear thermal instability in a couple stress fluid saturated porous media. At third order, the finite amplitude of convection has been calculated which determines heat transfer. The effect of throughflow i.e., inflow and outflow have dual nature of heat transfer. The couple-stress parameter has stabilizing nature on thermal instability. The couple-stress parameter has stabilizing nature on thermal instability. Further it is found that upward directed flow enhances and downward directed flow diminishes heat transfer.

Stationary wave biases and their effect on upward troposphere– stratosphere coupling in sub-seasonal prediction models

Abstract. The simulated Northern Hemisphere winter stationary wave (SW) field is investigated in 11 Subseasonal-to-Seasonal (S2S) prediction project models. It is shown that while most models considered can well simulate the stationary wavenumbers 1 and 2 during the first 2 weeks of integration, they diverge from observations following week 3. Those models with a poor resolution in the stratosphere struggle to simulate the waves, in both the troposphere and the stratosphere, even during the first 2 weeks. Focusing on the tropospheric regions where SWs peak in amplitude reveals that the models generally do a better job in simulating the northwestern Pacific stationary trough, while certain models struggle to simulate the stationary ridges in both western North America and the North Atlantic. In addition, a strong relationship is found between regional biases in the stationary height field and model errors in simulated upward propagation of planetary waves into the stratosphere. In the stratosphere, biases are mostly in wave 2 in those models with high stratospheric resolution, whereas in those models with low resolution in the stratosphere, a wave 1 bias is evident, which leads to a strong bias in the stratospheric mean zonal circulation due to the predominance of wave 1 there. Finally, biases in both amplitude and location of mean tropical convection and the subsequent subtropical downwelling are identified as possible contributors to biases in the regional SW field in the troposphere.

Gravitational Modulation Effect on Double-Diffusive Oscillatory Convection in a Viscoelastic Fluid Layer

The complex Ginzburg-Landau model has been employed to derive the temporal amplitude of convection in a viscoelastic fluid layer under gravity modulation. The finite amplitude is based on a weakly nonlinear thermal convection. The perturbation technique is applied to simplify the nonlinear system of partial differential equations into a non-autonomous amplitude equation. Heat and mass transfer obtained in terms of the Nusselt and Sherwood numbers, and the corresponding results are presented for the small amplitude of modulation. The moderate values of amplitude and frequencies of gravity modulation are considered, their effect is to enhance the heat and mass transfer in the layer. Thus, the modulation plays dual role in heat and mass transfer. The variations of Nusselt and Sherwood numbers with slow time becomes rapid on either increasing the parameters Rs, Pr, λ, δ or decreasing the parameters Γ, ε, Ω. Each parameter effect has been presented graphically with their effect on Nu and Sh. Further, it is found that an oscillatory mode of convection enhances the heat and mass transfer than a stationary mode.

On trigonometric cosine, square, sawtooth, and triangular wave‐type rotational modulations on triple‐diffusive convection in salted water

AbstractThe effect of sinusoidal (trigonometric cosine) and nonsinusoidal (square, sawtooth, and triangular) rotational modulations on triple‐diffusive convection in a Newtonian fluid is studied in this paper. The derived Ginzburg–Landau equation for the stationary mode of convection is used to quantify heat and mass transport. The enhancement of heat and mass transport in water due to the addition of different salts is explained in terms of the thermophysical properties of the fluid and the aqueous solutes. The flow equations are reduced to a Lorenz‐type scheme of nonlinear evolution equations using a truncated Fourier series. The equations describing the growth of convection amplitudes are solved using the multidomain spectral collocation method. With the aid of thermophysical properties of the fluid, numerical computations are performed for different values of the revised Rayleigh number (), Taylor number (), the amplitude of modulation , and modulation frequency . A comparison of heat and mass transport in different combinations of aqueous solutions is made. The study reveals that all modes of rotational modulation can control the rate of heat and mass transport. It is noted that amongst all other modulations, the square wave modulation is the most destabilizing one.

Helioseismological determination of the subsurface spatial spectrum of solar convection: Demonstration using numerical simulations

Context. Understanding convection is important in stellar physics, for example, when it is an input in stellar evolution models. Helioseismic estimates of convective flow amplitudes in deeper regions of the solar interior disagree by orders of magnitude among themselves and with simulations. Aims. We aim to assess the validity of an existing upper limit of solar convective flow amplitudes at a depth of 0.96 solar radii obtained using time-distance helioseismology and several simplifying assumptions. Methods. We generated synthetic observations for convective flow fields from a magnetohydrodynamic simulation (MURaM) using travel-time sensitivity functions and a noise model. We compared the estimates of the flow amplitude with the actual value of the flow. Results. For the scales of interest (ℓ < 100), we find that the current procedure for obtaining an upper limit gives the correct order of magnitude of the flow for the given flow fields. We also show that this estimate is not an upper limit in a strict sense because it underestimates the flow amplitude at the largest scales by a factor of about two because the scale dependence of the signal-to-noise ratio has to be taken into account. After correcting for this and after taking the dependence of the measurements on direction in Fourier space into account, we show that the obtained estimate is indeed an upper limit. Conclusions. We conclude that time-distance helioseismology is able to correctly estimate the order of magnitude (or an upper limit) of solar convective flows in the deeper interior when the vertical correlation function of the different flow components is known and the scale dependence of the signal-to-noise ratio is taken into account. We suggest that future work should include information from different target depths to better separate the effect of near-surface flows from those at greater depths. In addition, the measurements are sensitive to all three flow directions, which should be taken into account.

A Refined Model of Convectively Driven Flicker in Kepler Light Curves

Abstract Light curves produced by the Kepler mission demonstrate stochastic brightness fluctuations (or flicker) of stellar origin which contribute to the noise floor, limiting the sensitivity of exoplanet detection and characterization methods. In stars with surface convection, the primary driver of these variations on short (sub-eight-hour) timescales is believed to be convective granulation. In this work, we improve existing models of this granular flicker amplitude, or F 8, by including the effect of the Kepler bandpass on measured flicker, by incorporating metallicity in determining convective Mach numbers, and by using scaling relations from a wider set of numerical simulations. To motivate and validate these changes, we use a recent database of convective flicker measurements in Kepler stars, which allows us to more fully detail the remaining model-prediction error. Our model improvements reduce the typical misprediction of flicker amplitude from a factor of 2.5–2. We rule out rotation period and strong magnetic activity as possible explanations for the remaining model error, and we show that binary companions may affect convective flicker. We also introduce an envelope model that predicts a range of flicker amplitudes for any one star to account for some of the spread in numerical simulations, and we find that this range covers 78% of observed stars. We note that the solar granular flicker amplitude is lower than most Sun-like stars. This improved model of convective flicker amplitude can better characterize this source of noise in exoplanet studies as well as better inform models and simulations of stellar granulation.

Effect of rotational speed modulation on weakly nonlinear magneto convective heat transfer with temperature-dependent viscosity

We have examined the effect of rotational speed modulation on the onset of magneto-thermal convection through analytical method. The fluid is confined between two parallel plates, cooled from above and heated from below. The flow formulation is influenced by the induced magnetic field with temperature-dependent viscous fluid layers. The convective system is influenced by the Coriolis term and rotating about z− axis in an anti-clockwise direction with time-dependent rotational speed. The analytical solution has expressed in term of the real cubical Landau equation. The time-dependent rate of heat transfer is shown in terms of the amplitude of convection. The results show that within a range of moderate values, Taylor number has a stabilization effect on the magneto-thermal convection. The significant result is that the thermo-rheological parameter enhances the heat transport while Taylor number reduces it.