Axisymmetric Modes Research Articles

The global flow state in a precessing cylinder

We examine the fluid flow forced by precession of a rotating cylindrical container using numerical simulations and experimental flow measurements with ultrasonic Doppler velocimetry. The analysis is based on the decomposition of the flow field into contributions with distinct azimuthal symmetry or analytically known inertial modes and the corresponding calculation of their amplitudes. We show that the predominant fraction of the kinetic energy of the precession-driven fluid flow is contained only within a few large-scale modes. The most striking observation shown by simulations and experiments is the transition from a flow dominated by large-scale structures to a more turbulent behaviour with the small-scale fluctuations becoming increasingly important. At a fixed rotation frequency (parametrized by the Reynolds number, $Re$ ) this transition occurs when a critical precession ratio is exceeded and consists of a two-stage collapse of the directly driven flow going along with a massive modification of the azimuthal circulation (the zonal flow) and the appearance of an axisymmetric double-roll mode limited to a narrow range of precession ratios. A similar behaviour is found in experiments which make it possible to follow the transition up to Reynolds numbers of $Re\approx 2\times 10^6$ . We find that the critical precession ratio decreases with rotation, initially showing a particular scaling ${\propto }Re^{-({1}/{5})}$ but developing an asymptotic behaviour for $Re\gtrsim 10^5$ which might be explained by the onset of turbulence in boundary layers.

Mass and spin measurements of black hole and neutron stars X-ray binaries through axisymmetric oscillation modes of thick torus

Abstract This paper examines the oscillatory behaviour of relativistic, non-self-gravitating, charged-fluid toroidal structures within the context of the Kerr metric. The primary objective is to explore how thick accretion discs influence the mass and spin measurements of black holes and neutron stars in Low-Mass X-ray Binaries (LMXBs) through Quasi-Periodic Oscillations (QPOs) models. To achieve this, we conduct a local analysis within a general relativistic framework, determining the radial epicyclic and orbital frequencies in a perfect fluid disk. The tori are modelled using a non-Keplerian distribution of specific angular momentum, and we analyse how the oscillation properties depend on the model’s angular momentum distribution parameters. Subsequently, we connect these oscillatory frequencies to high-frequency QPOs observed in low-mass X-ray binaries, enabling us to calculate the optimal mass and spin values for each studied source.

T-matrix of piezoelectric shunt inclusions on a thin plate

Developing piezoelectric-based plate-like metamaterials necessitates an effective modeling method to elucidate the omnidirectional wave properties of piezoelectric coupled inclusions on a thin plate. The commonly used methods, such as the transfer-matrix method and finite element method, are inadequate for analyzing the transmission and reflection of omnidirectional waves in a two-dimensional elastic medium. Unlike the existing methods, the multiple scattering method employs Bessel functions as the displacement-basis methods which can accurately describe the propagation and scattering characteristics of omnidirectional waves. This paper develops a novel T-matrix formulation to support the multiple scattering method, representing the input-output relationship between incident and reflected waves from a piezoelectric shunt inclusion on a host thin plate. The piezoelectric shunt inclusion comprises a varying-thickness substrate bonded with piezoelectric shunting patches. The T-matrix of the piezoelectric shunt inclusion is formulated by integrating the wave-based method with Rayleigh-Ritz method. The derived T-matrix is then used to semi-analytically analyze the far-field scattering and reflection properties of a single inclusion. Numerical results capture the scattering properties resulting from trapped mode resonances of the piezoelectric shunt inclusion. Additionally, the capability of the piezoelectric shunt damping to design and tune multiple critical coupling conditions for axisymmetric modes of thin plates is parametrically investigated by varying the values of inductors and resistors.

Vertical Shear Instability with Partially Reflecting Boundary Conditions

Abstract The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary disks. Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disk surfaces. VSI depends critically on the boundary behaviors of waves at the disk surfaces. We extend earlier studies by performing a comprehensive numerical analysis of VSI with partially reflecting BCs for both the axisymmetric and non-axisymmetric unstable VSI modes. We find that the growth rates of the unstable modes diminish when the outgoing component of the flow is greater than the incoming one for high-order body modes. When the outgoing wave component dominates, the growth of VSI is notably suppressed. We find that the non-axisymmetric modes are unstable and they grow at a rate that decreases with the azimuthal wavenumber. The different BCs at the lower and upper disk surfaces naturally lead to non-symmetric modes relative to the disk midplane. The potential implications of our studies for further understanding planetary formation and evolution in protoplanetary disks (PPDs) are also briefly discussed.

Enhanced control and efficiency in millimeter-scale composite droplets preparation

A microfluidic device utilising the flow focusing method was designed and fabricated for the high-throughput and controllable preparation of millimeter-scale water-in-oil (W1/O/W2) droplets. Two distinct flow focusing modes were employed in order to prepare the composite droplets. In the flow-focused axisymmetric jetting mode, the continuous phase propels the dispersed phase, forming a cone, which subsequently leads to a jet formation downstream of the small hole. When the outer phase is activated, perturbation growth interferes with downstream fragmentation, resulting in composite droplets with excellent monodispersity. In the dripping mode, the dispersed phase fails to form a jet downstream, and the interface disintegrates, resulting in droplet formation at the exit of the small orifice. In the jetting mode, the size and shell-to-core ratio of the generated droplets can be controlled by adjusting the volume of flow of the outer and inner phases, as well as the applied frequency. Furthermore, the applied perturbation allows for precise control of droplet size, which significantly reduces satellite droplet formation and enhances droplet monodispersity. In the dripping mode, the shell-to-core ratio is adjusted by manipulating the ratio of inner to outer flow rates, which is tailored to the specific requirements of the flow-focused dripping mode. The prepared compound droplets exhibit good monodispersity. Finally, the rotational solidification method can be employed to obtain spherical shells with a shell thickness of less than 20 μm. In conclusion, the flow focusing method is an effective, controllable, and stable method for synthesising millimetre-sized composite droplets.

On the Possibility of Multiplying the Frequency of a Gigawatt Ultrashort Microwave Pulse

It has been shown that the frequency of an ultrashort microwave pulse of a lowest axisymmetric electric mode at the interaction with a counterpropagating relativistic tubular electron beam under the cyclotron resonance conditions can be doubled due to re-emission into a mode having resonance at the second harmonic of the gyrofrequency. The conversion of the 3-cm 1-ns gigawatt microwave pulse in a circular waveguide from the TM01 mode to the TM02 mode with the doubling of the frequency, reduction of the duration to 0.22 ns, and the achievement of the peak power above the initial value has been demonstrated in a numerical experiment. The possibility of forming an intense ultrashort frontal splash of oscillations with the doubled frequency has been shown for longer initial pulses with a subnanosecond front.

Properties of observable mixed inertial and gravito-inertial modes in gamma Doradus stars

The space missions Kepler and TESS provided a large number of highly detailed time series for main-sequence stars, including gamma Doradus stars. Additionally, numerous gamma Doradus stars are to be observed in the near future thanks to the upcoming PLATO mission. In gamma Doradus stars, gravito-inertial modes in the radiative zone and inertial modes in the convective core can interact resonantly, which translates into the appearance of dip structures in the period spacing of modes. Those dips are information-rich, as they are related to the star core characteristics. Our aim is to characterise these dips according to stellar properties and thus to develop new seismic diagnostic tools to constrain the internal structure of gamma Doradus stars, especially their cores. We used the two-dimensional oscillation code TOP to compute sectoral prograde and axisymmetric dipolar modes in gamma Doradus stars at different rotation rates and evolutionary stages. We then characterised the dips we obtained by their width and location on the period spacing diagram. We found that the width and the location of the dips depend quasi-linearly on the ratio of the rotation rate and the Brunt-Väisälä frequency at the core interface. This allowed us to determine empirical relations between the width and location of dips as well as the resonant inertial mode frequency in the core and the Brunt-Väisälä frequency at the interface between the convective core and the radiative zone. We propose an approximate theoretical model to support and discuss these empirical relations. The empirical relations we established could be applied to dips observed in data, which would allow for the estimation of frequencies of resonant inertial modes in the core and of the Brunt-Väisälä jump at the interface between the core and the radiative zone. As those two parameters are both related to the evolutionary stage of the star, their determination could lead to more accurate estimations of stellar ages.

Preparation and mechanical properties of in-situ aluminum foam-filled SS304 corrugated tubes with metallurgical bonding

In this work, AlSi10Ca3Mg0.5 alloy foam-filled SS304 corrugated tubes (FFCTs) were prepared by melt route with surface modification of the tube substrate prior to in-situ foam filling. Results showed that successful metallurgical bonding can be achieved between aluminum foam and the tube with surface modification. Under quasi-static axial loading, the foam core within FFCTs were compressed densely from top to bottom in sequence, showing an axisymmetric deformation mode. Due to the enhanced bonding between the foam and the tube, FFCTs with surface modification demonstrated approximately ∼19 % increase in specific energy absorption compared to FFCTs without surface modification.

Simulations of pulsed overpressure jets: formation of bellows and ripples in galactic environments

ABSTRACT Jets from active nuclei may supply the heating which moderates cooling and accretion from the circum-galactic medium. While steady overpressured jets can drive a circulatory flow, lateral energy transfer rarely exceeds 3 per cent of jet power, after the initial bow shock has advanced. Here, we explore if pulses in high-pressure jets are capable of sufficient lateral energy transfer into the surrounding environment. We answer this by performing a systematic survey of numerical simulations in an axisymmetric hydrodynamic mode. Velocity pulses along low Mach jets are studied at various overpressures. We consider combinations of jet velocity pulse amplitude and frequency. We find three flow types corresponding to slow, intermediate, and fast pulsations. Rapid pulsations in light jets generate a series of travelling shocks in the jet. They also create ripples which propagate into the ambient medium while a slow convection flow brings in ambient gas which is expelled along the jet direction. Long period pulses produce slowly evolving patterns which have little external effect, while screeching persists as in non-pulsed jets. In addition, rapid pulses in jets denser than the ambient medium generate a novel breathing cavity analogous to a lung. Intermediate period pulses generate a series of bows via a bellows action which transfer energy into the ambient gas, reaching power efficiencies of over 30 per cent when the jet overpressure is sufficiently large. This may adequately inhibit galaxy gas accretion. In addition, such pulses enhance the axial out-flow of jet material, potentially polluting the circum-galactic gas with metal-enriched interstellar gas.

Resonance behaviour of magnetoelectric (PSLZT multilayer - NZFO) layered composites: A comprehensive theory – Experimental perspective

In recent years, compact antenna and miniaturized power transfer devices are among the interesting applications of magnetoelectric (ME) composites in low frequency (LF) / very low frequency (VLF) range. Here we elucidate, in general, analytical calculations used to understand, the vibrational modes and resonance frequencies of the layered ME composite and; Finite Element Analyses (FEM) with isotropic and anisotropic properties to accurately predict the resonance frequencies pertaining to the axisymmetric and asymmetric mode of vibrations with respect to significant ME response. Further, ME coefficient of the composite with Longitudinal - Transverse (L-T) configuration based on the interface coupling model were utilized to completely study the ME composites. The configuration optimized through the design was in particular corroborated experimentally with a representative PSLZT multilayer on NZFO based ME layered composite system. The PSLZT multilayer on NZFO based ME composite was fabricated by tape casting the constituent thick films and co-sintering process which are further analysed for their ME responses at their resonance frequencies. ME voltage spectrum showed a maximum of 7.74 V/cm.Oe at its axisymmetric resonance mode at 30.6 kHz. Various peaks at different resonance frequencies with respect to axisymmetric and asymmetric modes of vibrations agree well and validates the above modeling studies. Overall, the complete study provides a systematic design guideline for optimizing the ME composite configuration suitable for specific application with required resonance frequency.

Damping Obliquities of Hot Jupiter Hosts by Resonance Locking

When orbiting hotter stars, hot Jupiters are often highly inclined relative to their host star equator planes. By contrast, hot Jupiters orbiting cooler stars are more aligned. Prior attempts to explain this correlation between stellar obliquity and effective temperature have proven problematic. We show how resonance locking—the coupling of the planet's orbit to a stellar gravity mode (g-mode)—can solve this mystery. Cooler stars with their radiative cores are more likely to be found with g-mode frequencies increased substantially by core hydrogen burning. Strong frequency evolution in resonance lock drives strong tidal evolution; locking to an axisymmetric g-mode damps semimajor axes, eccentricities, and, as we show for the first time, obliquities. Around cooler stars, hot Jupiters evolve into spin–orbit alignment and may avoid engulfment. Hotter stars lack radiative cores and therefore preserve congenital spin–orbit misalignments. We focus on resonance locks with axisymmetric modes, supplementing our technical results with simple physical interpretations, and show that nonaxisymmetric modes also damp obliquity. Outstanding issues regarding the dissipation of tidally excited modes and the disabling of resonance locks are discussed quantitatively.

Acoustic tones generated by impinging jets: Differences between laminar and highly-disturbed nozzle-exit boundary layers

The differences between the acoustic tones generated by impinging jets with laminar and highly-disturbed nozzle-exit boundary layers are investigated. For that, jets at Mach numbers between 0.6 and 1.3 impinging on a flat plate at a distance of 8 nozzle radii from the nozzle exit are computed using large-eddy simulations. The amplitudes of the tones generated by the jets through feedback loops establishing between the nozzle and the plate are found to be significantly affected by the exit turbulent disturbances. In the present study, overall, they are lower for the initially laminar jets than for the initially disturbed ones. The level decrease varies from a few dB up to 15 dB, depending on the tones, which can change the frequencies of the dominant tones and the numbers and azimuthal structures of their associated feedback modes. For Mach numbers 0.75 and 0.8, for instance, the dominant tone frequencies are approximately two times lower for the initially laminar jets than for the other ones, yielding a better agreement with experiments of the literature in the former case. For a Mach number of 1.1, as a second example, the dominant tone is associated with the axisymmetric third feedback mode in the laminar case but with the helical fifth feedback mode in the disturbed case. The differences in the tone amplitude are finally discussed by estimating the power gains of the shear-layer instability waves between the nozzle and the plate using linear stability analysis for the axisymmetric mode. In most cases, at the frequency of a specific tone, the higher the gain, the stronger the acoustic tone.

Моделирование динамики связанных гиротронов методом крупных частиц

The problem of mutual synchronization of two coupled gyrotrons in the 170 GHz waveband was simulated using the particle-in-cells method. To reduce the calculation time, an approach based on replacing the asymmetric operating mode with an equivalent axisymmetric mode was used. As a result, the dimension of the problem is reduced, and instead of three-dimensional modeling, 2.5-dimensional modeling can be used. The limiting case is considered when the lowest axisymmetric mode of the circular waveguide TE01 is chosen as the equivalent mode. The results obtained are demonstrated to be in good agreement with the traditional approach based on modeling of averaged equations.

Experimental study on acoustic resonance of subsonic and slightly underexpanded impinging jets

The aeroacoustic feedback loops in high-speed circular jets that impinge on a large flat plate are investigated via acoustic measurements and schlieren visualizations. In the present experiments, the nozzle pressure ratio ranges from 1.39 to 2.20, the corresponding ideally expanded jet Mach number $M_j$ is from 0.70 to 1.12 and the nozzle-to-plate distance ( $H$ ) is from 4.0 $D$ to 6.0 $D$ , where $D$ is the nozzle exit diameter. The results of acoustic measurements show that the strongest tones are generated in a limited frequency band. The empirical dispersion relations obtained from the fluctuating greyscales along the jet centreline of time-resolved schlieren images have good agreement with the dispersion relations from the vortex-sheet model. The coherent flow structures at tonal frequencies are extracted by spectral proper orthogonal decomposition and are analysed in detail. For the $M_j<0.82$ jets, the upstream-propagating guided jet mode is progressively confined to the potential core of jets with increasing tonal frequency, which provides the first direct experimental support for theoretical results. The evolution in the structures of acoustic resonance loops is studied along a single frequency stage of axisymmetric impinging tones. When the acoustic resonance between the upstream- and downstream-propagating guided jet modes is formed at tonal frequencies, the impinging tones are intenser. Slightly underexpanded impinging jets can simultaneously produce impingement tones and screech tones. Shock-cell structures have modulatory effects on the downstream-propagating Kelvin–Helmholtz wavepacket and the upstream- and downstream-propagating guided jet modes. Due to the interaction between the flow structures at the frequencies of impinging and screech tones, tones of axisymmetric modes can be produced outside the frequency ranges in which the axisymmetric upstream-propagating guided jet modes are supported by jets.

Frequency characteristics of an ultrasonic varifocal liquid crystal lens.

Compound lens systems with mechanical actuators are used to focus objects at near to far distances. The focal length of ultrasound varifocal liquid crystal (LC) lenses can be controlled by modulating the refractive index spatial distribution of the medium through the acoustic radiation force, resulting in thin and fast-response varifocal lenses. The frequency characteristics of such a lens are evaluated in this paper, and several axisymmetric resonant vibration modes over 20kHz are observed. The effective lens aperture decreased with the wavelength of the resonant flexural vibration generated on the lens, meaning that this parameter can be controlled with the driving frequency.

Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks

Context. The vertical shear instability (VSI) is a hydrodynamical instability predicted to produce turbulence in magnetically inactive regions of protoplanetary disks. The regions in which this instability can occur and the physical phenomena leading to its saturation are a current matter of research. Aims. We explore the secondary instabilities triggered by the nonlinear evolution of the VSI and their role in its saturation. We also expand on previous investigations on stability regions by considering temperature stratifications enforced by stellar irradiation and radiative cooling, and including the effects of dust-gas collisions and molecular line emission. Methods. We modeled the gas-dust mixture in a circumstellar disk around a T Tauri star by means of high-resolution axisymmetric radiation-hydrodynamical simulations including stellar irradiation with frequency-dependent opacities, considering different degrees of depletion of small dust grains. Results. The flow pattern produced by the interplay of the axisymmetric VSI modes and the baroclinic torque forms bands of nearly uniform specific angular momentum. In the high-shear regions in between these bands, the Kelvin–Helmholtz instability (KHI) is triggered. A third instability mechanism, consisting of an amplification of eddies by baroclinic torques, forms meridional vortices with Mach numbers up to ∼0.4. Our stability analysis suggests that protoplanetary disks can be VSI-unstable in surface layers up to tens of au for reasonably high gas emissivities. Conclusions. The significant transfer of kinetic energy to small-scale eddies produced by the KHI and possibly even the baroclinic acceleration of eddies limit the maximum energy of the VSI modes, likely leading to the saturation of the VSI. Depending on the gas molecular composition, the VSI can operate at surface layers even in regions where the midplane is stable. This picture is consistent with current observations of disks showing thin midplane millimeter-sized dust layers while appearing vertically extended in optical and near-infrared wavelengths.

Control of giant orbital angular momentum bursts of structured Laguerre-Gaussian beams in a medium with general astigmatism

We examined theoretically and experimentally the influence of astigmatic elements (for example, a cylindrical lens) on a structured Laguerre-Gaussian beam (sLG) when the lens axes are directed at an arbitrary angle to the laboratory coordinate axes (a general astigmatism). Although a structurally stable Laguerre-Gaussian (LG) beam contains a great number of axisymmetric modes (in the LG basis) with matching phases and amplitudes, their superposition already loses its original axial symmetry, but acquires new properties (for example, fast oscillations of the orbital angular momentum (OAM)), while the beam OAM cannot exceed the azimuthal number l of the original LG mode. The loss of axial symmetry occurs due to bringing phase and amplitude perturbations into each mode of the sLG beam, which destroy the ring dislocations. Since degenerate ring dislocations are formed by optical vortices with opposite topological charges, but with equal weights, their destruction is accompanied by appearing of vortex pairs in the form of topological dipoles (their number is equal to the radial number n). As a result, the mode spectrum of the sLG is extended to the value ±(2n + l). The astigmatic element (cylindrical lens) violates the equality of vortex weights in the dipoles, which leads to a sharp growing the OAM of the sLG beam. Moreover, the OAM can be controlled by changing the rotation of the cylindrical lens axes and the control parameters of the sLG beam. It is these processes that are discussed in detail in our article, both in theoretical and experimental aspects. We show that with a certain orientation of the cylindrical lens axes, the beam OAM can exceed the sum of the orbital and azimuthal numbers (OAM > n + l). Besides, we reveal that the intensity pattern of the astigmatic sLG beam can follow the rotation of the astigmatic element axes (the effect of the beam structure following the cylindrical lens axes) at certain relations between control parameters of the sLG beam and the astigmatic element.

Voltage-controlled non-axisymmetric vibrations of soft electro-active tubes with strain-stiffening effect

Material properties of soft electro-active (SEA) structures are significantly sensitive to external electro-mechanical biasing fields (such as pre-stretch and electric stimuli), which generate remarkable knock-on effects on their dynamic characteristics. In this work, we analyze the electrostatically tunable non-axisymmetric vibrations of an incompressible SEA cylindrical tube under the combination of a radially applied electric voltage and an axial pre-stretch. Following the theory of nonlinear electro-elasticity and the associated linearized theory for superimposed perturbations, we derive the nonlinear static response of the SEA tube to the inhomogeneous biasing fields for the Gent ideal dielectric model. Using the State Space Method, we efficiently obtain the frequency equations for voltage-controlled small-amplitude three-dimensional non-axisymmetric vibrations, covering a wide range of behaviors, from the purely radial breathing mode to torsional modes, axisymmetric longitudinal modes, and prismatic diffuse modes. We also perform an exhaustive numerical analysis to validate the proposed approach compared with the conventional displacement method, as well as to elucidate the influences of the applied voltage, axial pre-stretch, and strain-stiffening effect on the nonlinear static response and vibration behaviors of the SEA tube. The present study clearly indicates that manipulating electro-mechanical biasing fields is a feasible way to tune the small-amplitude vibration characteristics of an SEA tube. The results should benefit experimental work on, and design of, voltage-controlled resonant devices made of SEA tubes.

The gap-size influence on the excitation of magnetorotational instability in cylindricTaylor–Couette flows

The excitation conditions of the magnetorotational instability (MRI) are studied for axially unbounded Taylor–Couette (TC) flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wavenumber and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes, we find the critical Lundquist number of the applied axial magnetic field: the lower, the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap, the more spherical the cells are. The marginal rotation rate of the inner cylinder – for a fixed size of the outer cylinder – always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at $r_{{\rm in}}\simeq 0.4$ , where $r_{{\rm in}}$ is the ratio of the radii of the two rotating cylinders. The lowest magnetic field amplitudes to excite the instability are required for TC flows between perfect-conducting cylinders with gaps corresponding to $r_{{\rm in}}\simeq ~0.2$ . For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the non-axisymmetric modes with $|m|=1$ have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison with those for the axisymmetric modes. If TC experiments with too slow rotation for the applied magnetic fields yield unstable modes of any azimuthal symmetry, such as the currently reported Princeton experiment (Wang et al., Phys. Rev. Lett., vol. 129, 115001), then also other players, including axial boundary effects, than the MRI-typical linear combination of current-free fields and differential rotation should be in the game.

Unsteady double-diffusive Brinkman–Bénard convection in cylindrical enclosure saturated with hybrid bi-viscous Bingham nanoliquid

This paper aims to present an analytical as well as a comparative study to investigate the effect of the Brinkman porous medium on the onset of regular and chaotic motion in cylindrical enclosures of different heights. The hybrid bi-viscous Bingham nanoliquid is considered as the working fluid. Modified Brinkman–Buongiorno and bi-viscous Bingham fluid models are incorporated to obtain the flow governing dynamics. The thermophysical properties of the hybrid nanoliquid are calculated using phenomenological laws and the mixture theory. The study is carried out for the axisymmetric mode, and the Bessel functions are taken as the eigenfunctions of the problem. Double Fourier–Bessel series expansions are used for weakly non-linear stability analysis. The limiting cases of the study are obtained, and the results on the onset of convection, heat, and mass transport are discussed graphically. The behavior of the dynamical system is analyzed using the maximum Lyapunov exponent plot, the bifurcation diagram, and phase plots. Outcomes suggest that convection sets in earlier in the water-based hybrid nanoliquid than in the bi-viscous Bingham hybrid nanoliquid. The use of Single-walled carbon nanotubes enhances the heat transfer rate by approximately 17%. Further, it is concluded that a tall cylindrical enclosure is the most favorable geometry for achieving a higher heat transfer rate among the others.