Prandtl Number Pr Research Articles

Thermo-hydraulic transport characteristics of non-Newtonian nanofluid flow through wavy channel: Influence of nanoparticle volume fraction and Prandtl number

The present study numerically investigates the thermal-hydraulic transport characteristics of non-Newtonian nanofluid flowing through the trapezoidal wavy channel. Constitutive behavior of non-Newtonian fluid was used to elucidate the power law model. The average Nusselt number, pressure drop, and performance factor are evaluated for varying volume concentration of nanoparticles (0 ≤ ϕ ≤ 0.04) and Prandtl number (Pr = 0.76, 1, 6.39, 20, 50, and 100) at different values of Reynold number (Re = 50 and 500), power index values (n = 0.5, 1, 1.5) and wave phase shift (θ = 0°, 90°and 180°). An increase in average Nusselt number and pressure drop was observed for increasing volume concentration of nanoparticles, Prandtl number, and Reynold number. At the same time, the performance factor decreases with an increase in ϕ, Pr, and Re. The heat transfer rate was observed to be more for shear thinning fluids than shear thickening fluids.

The Impact of Roughness and Partitions in Thermal Convection to Enhance the Heat Transport

Abstract In this investigation, we explore the profound impact of adiabatic partitions on heat transport within a square Rayleigh-Bénard (RB) convection enclosure characterized by surface roughness on the lower hot and upper cold plates. The surface irregularities take the form of a rectangular base and a triangular apex. Our study employs two-dimensional direct numerical simulations spanning the Rayleigh number (Ra) range of 106–108 and a Prandtl number (Pr) of 1. Adiabatic partitions, strategically positioned between successive roughness, serve as the focal point of our exploration. Remarkably, our findings reveal a substantial enhancement in heat transport with the introduction of a partition board between consecutive roughness elements. As we escalate the number of partitions from one to four, the heat flux experiences a notable augmentation, reaching 2.3 times that of the classical square RB configuration. This enhancement is attributed to the breakdown of large-scale rolls into multiple rolls, a phenomenon intensified by the increased partition height. Further intriguing observations unfold as we investigate the interplay of surface roughness and partitions. Configurations featuring roughness with partitions exhibit an impressive 2.7 times heat flux enhancement compared to the classical square RB setup. The complex interplay of heat transport improvement is closely connected to optimizing the distance between the conduction plate and the partition. Through meticulous analysis, we identify that the optimal gap facilitates heightened local velocity, effectively thinning the thermal boundary layer and consequently augmenting the overall heat flux. In essence, our study sheds light on the synergistic effects of adiabatic partitions and surface roughness in the context of RB convection. The observed enhancements in heat transport underscore the potential for tailored design strategies involving partitions and surface modifications to optimize thermal performance in diverse applications.

Experimental Investigations of Heat Transfer in Simultaneously Developing Transitional Regime of Mixed Convection Flows in a Vertical Tube

Abstract The study of flow behavior in the simultaneously developing transitional regime of mixed convection flows is rare. It has been believed that the transitional regime will give a good compromise between pressure drop and heat transfer compared to laminar and turbulent flow regime. In this experimental study, the friction factor (f) and Nusselt number (Nu) characteristics for buoyancy-assisted and opposed flows of water in concurrently developing transitional regime of mixed convection through a vertical tube are studied. Experiments were done for Reynolds numbers (Re) varying from 500 to 15,000, Grashof numbers (Gr) from 1.25 × 104 to 5 × 106, Prandtl numbers (Pr) from 3 to 7, and Richardson numbers (Ri) from 0 to 0.1 subjected to uniform heat flux boundary conditions. A flow visualization provision after the test section which confirms an early transition in buoyancy-opposing flow (Rec = 2264) compared to buoyancy-aiding flow (Rec = 2468) at a fixed Ri of 0.1. Further, with the increase in Ri from 0 to 0.1, the average f decreases, and the average Nu increases in both aiding and opposing flows. It confirms that the onset of transition gets delayed with the increase of heat flux supplied in both the flows. Based on the present outcomes, an efficient heat exchanging device can be operated either to delay or advance the transition in a vertical pipe flow for optimum heat transfer.

Effects of inclination angle and fluid parameters on binary fluid convection in a tilted rectangular cavity

Thermal convection of binary fluid mixtures with negative separation ratios in a tilted rectangular cavity heated from below is numerically investigated using a high-accuracy finite-difference method. The fluids under consideration are Newtonian fluids with the Prandtl number (Pr) and Lewis number (Le) in the ranges of 0.01≤Pr≤10 and 0.001≤Le≤1, respectively. Extensive direct numerical simulations are conducted to explore the dynamics of the system by varying the control parameters, namely, the relative Rayleigh number (r) and the inclination angle of the cavity (β) together with the separation ratio (ψ) in the ranges of 1.0≤r≤2.0, 0°≤β≤90°, and −0.6≤ψ≤0. It is found that the inclination angle leads to a distinct trend for heat and mass transfer: the Nusselt number first decreases for small β, then gradually increases for moderate β, and finally decreases again for large β when r varies from 1.4 to 2.0. The optimal inclination angle lies in the range of 54°≤β∗≤64°, where the heat transport peaks. The Sherwood number initially decreases for small β, then increases with increasing β, and finally remains constant for large β. We present the bifurcation diagram of the solutions for different separation ratios, focusing on the distinct variation trends of the inclination angle. The corresponding heat- and mass-transfer properties of the flow on different branches of the bifurcation diagram are investigated. Furthermore, we explore the effect of the relative Rayleigh number, Prandtl number and Lewis number as well as the separation ratio on heat and mass transfer for various inclination angles, and obtain the Nusselt number as a function of the separation ratio and inclination angle.

Computational study of micropolar Eyrling-Powell ferrofluid flow

This study investigates the behavior of micropolar Eyring-Powell ferrofluids over a stretchable surface, considering heterogeneous-homogeneous chemical reactions, thermal radiation, and magnetic dipole effects. The governing partial differential equations are transformed into ordinary differential equations (ODEs) using similarity transformations, which are then solved using the shooting method with Runge-Kutta updates. The effects of various parameters on the flow and temperature fields are computed and visualized using MATLAB 2023. The results show that the velocity field decreases with increasing ferro-magnetic parameter β and fluid material parameter ß, while the temperature field increases with thermal radiation R, but decreases with higher dissipation parameter λ 1 and Prandtl number Pr. The results are in excellent agreement with previously published data, validating the accuracy of our approach.

Impact of solar radiation in the presence of temperature-dependent thermal conductivity of non-Newtonian Casson flow on natural convection heat transfer in plume generated due to the combined effects of heat source and aligned magnetic field

Understanding the non-Newtonian Casson fluid is crucial for addressing various challenges in industrial, biological, and environmental applications. In this novel research, Casson fluid with temperature-dependent variable thermal conductivity is analyzed by a natural convective plume generated by horizontal line heat source. The plume system is under the influence of solar radiation and an aligned magnetic field. The momentum equation is transmuted for Casson fluid, while energy equation transmuted for solar radiation and variable thermal conductivity. The coupled partial differential equations changed into ordinary differential equation by employing stream function formulation. For computational evaluation, bvp4c built-in tool of MATLAB is employed in combination with Shooting technique in order to analyze both missing and specified boundary conditions. The upshots of Casson parameter β 1 , thermal conductivity variable γ 1 , radiation parameter Rd , magnetic force parameter S , Prandtl number Pr and magnetic Prandtl number γ on specified and missing conditions are highlighted in the graphical illustrations. The computed outcomes for missing conditions depicts that for Casson parameter β 1 velocity f ′ and temperature θ drops while current density increased with increment in β 1 . Whereas, for specified boundary conditions, the skin friction f ″ and magnetic flux ϕ ′ decreases while heat transfer rate θ ′ enhances for increasing β 1 . For missing conditions, the increasing thermal conductivity variable γ 1 causes velocity f ′ , current density ϕ ″ , and temperature θ to drop. While for specified conditions, the skin friction f ″ , magnetic flux ϕ ′ increases but heat transfer rate θ ′ exhibits reverse trend with enhancing γ 1 . Additionally, a validation analysis has been performed by comparing the values of f ′ ( 0 ) for various values of Pr with prior work, while excluding the other parameters to check its limitations at the boundary layer.

Development and application of turbulent heat flux model for lead-bismuth eutectic based on deep learning

Existing turbulent heat flux (THF) closure models in Reynolds-averaged Navier–Stokes simulation of scalar transport are insufficient on accuracy for fluids with a low Prandtl number (Pr), such as lead–bismuth eutectic (LBE), especially under complex operating conditions like in heat exchangers of nuclear reactors. This paper aims to propose a THF model suitable for such conditions. Firstly, we established a high-fidelity database of forced convection flow past two tandem cylinders under a Reynolds number (Re) of 1 × 105 and various low Pr conditions by hybrid large eddy simulation and direct numerical simulation algorithm. Based on the database, a deep learning architecture was then built and trained to predict dimensionless THF. Finally, a posteriori test proved that the proposed THF model helps to improve the prediction performance for temperature fields and also performs well when extrapolated to cases of LBE past the tube bundles, especially under the case with large Peclet numbers.

Dominant heat transfer mechanism with conical roughness in a cubical box in turbulent Rayleigh–Bénard convection

In the present study, we numerically investigate the effect of Prandtl number on the heat transfer mechanism in turbulent Rayleigh–Bénard convection inside a cubical box endowed with conical roughness elements. The Rayleigh number is kept fixed at Ra=108, while the Prandtl number (Pr) varies from 1 to 50. In contrast to the monotonic increasing trend of the Nusselt number (Nu∼Pr0.27) in the two-dimensional (2D) roughness explored previously [Sharma et al., “Influence of Prandtl number in turbulent Rayleigh-Bénard convection over rough surfaces,” Phys. Rev. Fluids 7, 104609 (2022)], it assumes an invariant behavior (∼Pr0.012) for three dimensional (3D), though it is approximately 50% higher than its smooth counterpart. Flow intensity, measured in terms of Reynolds number (Re), drops with increasing Pr showing consistently lower magnitude for the 3D configuration. The addition of roughness elements is observed to disrupt the preferred orientation of large-scale circulation (LSC). The effect is predominant for lower Pr, where the roughness interferes most with the natural bias of LSC toward the diagonal planes of the cubical box. The analysis of plume statistics reveals that both coverage and intensity of plumes are augmented for the roughened cell. Increased homogeneity in the flow at higher Pr is reflected by the emergence of a more pronounced and distinguishable peak in probability density functions of temperature and velocity. Temporal spectra and variance data substantiate augmented intensity of fluctuations in the rough cell, while behavioral differences in the flow at different Pr are elucidated by using cross correlation of vertical velocity and temperature fluctuations.

Influence of periodicity on natural convection in a square porous cavity due to non-uniform heat under LTNE state

In this article, the influence of the local thermal non-equilibrium (LTNE) state on free convection in a square cavity filled with fluid-saturated porous medium is investigated numerically. The steady-state flow is induced due to sinusoidal heat distributed on the side walls of the cavity and insulated of the horizontal walls. The coupled flow governing equations are solved numerically by using the finite volume method (FVM) consisting of the SIMPLER (Semi-Implicit Method for Pressure Linked Equation Revised) Algorithm. The numerical simulations of temperature and stream-function contours are carried out for the non-Darcy model. The developed code is validated with existing numerical and present computed results for the case of a square enclosure associated with non-uniform heat source. Then, the present numerical results are analyzed over a range of physical parameters, like periodicity parameter ( N ≥ 1 ), interface heat transfer coefficient ( 10 − 2 ≤ H ≤ 10 2 ), porosity scaled thermal conductivity ratio ( 10 − 2 ≤ γ ≤ 10 2 ), with a fixed Rayleigh number ( Ra = 10 6 ), Darcy number ( Da = 10 − 4 ), Prandtl number (Pr = 0.71), and porosity ( ε = 0.8 ). To study the impacts of these key parameters on the fluid flow behavior and isotherm patterns of fluid as well as solid phase in the porous-square enclosure. From present numerical experiments that the structure of flow is controlled by multicellular structure with rotating clockwise and anticlockwise directions in the entire results. The flow dynamics are highly affected by the periodicity parameter (N) under LTNE circumstances. The characteristics of the local Nusselt number have the point of inflection and the maximum magnitude of it increases with N. The significant effect of H is found on the heat transfer rate of fluid phase but it is negligible on the heat transfer rate of solid phase. However, the influence of γ is found reverse in nature on the heat transfer rate of fluid as well as solid phase when as compared to the effect of H.

Natural convection and heat transmission of two-phase Bingham Fe3O4-CoFe2O4-water hybrid nanofluid flow in an enclosure with a corrugated heated cylinder

The Galerkin weighted residual finite element method (GFEM) has been used to numerically investigate the natural convection flow of two-phase Bingham hybrid nanofluid in a square cavity with a corrugated cylinder at the center. The base fluid here is water. The hybrid nanofluid is made of Fe3O4-CoFe2O4 nanoparticles. The flow inside the enclosure is considered laminar, non-Newtonian, and incompressible. The corrugated cylinder is taken heated. The top and bottom walls of the outer square are considered adiabatic, and the left and right walls are considered cold. Several non-dimensional parameters, including the Rayleigh number (Ra = 104, 105, 106), the Bingham number (Bn = 0, 0.5, 1), the volume fraction (ϕ = 0.00, 0.04), the Brownian parameter (Nb = 0.1, 0.2, 0.3), thermophoresis parameter (Nt = 0.1, 0.2, 0.3), buoyancy ratio (Nr = 0.1, 0.2, 0.3), corrugation (N = 5, 6, 7), the Prandtl number (Pr = 6.2), and the Lewis number (Le = 1000) have been numerically simulated. The main focus of this work is to witness streamlines, isotherm, and nanoparticles’ volume fraction distribution and understand heat transmission with the help of average Nusselt number and local Nusselt number for several parameters for a two-phase Bingham hybrid nanofluid. The results show that an upsurge in Ra increases the extent of the upper two vortices and decreases the extent of the lower two vortices. All four vortices are seen to increase in dimension for an increase in Bn. The same observation is found for an increase in ϕ. The lower vortices are growing, and the top ones are nearly eliminated for base fluid, while those are visible for nanofluid when corrugation is increased. A further expansion completely destroyed the higher ones and increased the size of the bottom ones. The average Nusselt number ( Nu¯ ) increases when Ra is incremented. Nu¯ rises with a rise in ϕ. An increment in ϕ to 0.04 results in a 4.43% gain in Nu¯ . An increase in Bn is causing Nu¯ to drop by 18.02%. For Ra = 105 and Bn = 2, ϕ = 0.02 has the maximum heat transfer enhancement between 0.00 ≤ ϕ ≤ 0.04. In the future, we plan to use mixed convection in a three-dimensional domain along with the impact of magnetohydrodynamics (MHD).

Finite difference simulation of natural convection of two-phase hybrid nanofluid along a vertical heated wavy surface

This study employs finite difference modelling to investigate the natural convection of a two-phase hybrid nanofluid consisting of Al 2 O 3 and Cu nanoparticles dispersed in water along a vertically heated wavy surface. The hybrid nanofluid has unique features that influence convective heat transfer. Numerical solutions analyze fluid flow patterns and temperature distributions, providing insights into heat exchange and thermal management. The research highlights the importance of hybrid nanofluids, notably those containing Al 2 O 3 and Cu in a water base, in improving overall heat transfer efficiency. The mathematical model accounts for laminar and incompressible fluid flow with a Prandtl number of Pr = 6.2, Lewis number Le = 10, and maximum 10 % concentration of hybrid nanoparticles. After transforming the governing equations into a non-dimensional form, the implicit finite difference method is used to solve them. The solution employs the in-house FORTRAN 90 code and compares its outcomes with the benchmark results. Various parameters, such as the Schmidt number (Sc = 1 to 10), volume fraction of nanoparticles ( ϕ = 0.0 to 0.1), wavy amplitude (A = 0.0 to 0.3), and N BT = (0.05 to 0.2), are investigated regarding temperature, velocity, local skin friction coefficient ( C f ) , local Nusselt number (Nu), streamlines, and isotherms. Elevated volume fraction generally decreases skin friction, increases temperature, and may reduce velocity. Meanwhile, higher skin friction, temperature, velocity, and local Nusselt numbers often correlate with elevated Schmidt numbers. Changes in amplitude and N BT affect skin friction, temperature, velocity, and local Nusselt numbers, providing information on the dynamics of fluid systems. For example, when the volume fraction (ϕ) increases from 0 to 0.1 at Y = 2, the temperature rises by 75 % , while the velocity gradually decreases by 11.11 % . This is in contrast to findings according to when the N BT rises from 0.05 to 0.2 at Y = 1. In this case, the temperature drops by 18.75 % , followed by a 9.68 % fall in fluid velocity. Understanding these interactions enhances comprehension of heat transfer and fluid dynamics. By investigating these interactions, we not only improve our understanding of heat transfer and fluid dynamics, but also open the door to new strategies for improving thermal systems and manufacturing procedures.

A comparative analysis on charging performance of triplex-tube heat exchanger under various configurations of composite phase change material

In present work, the melting performance of triplex-tube latent heat thermal energy storage (LHTES) unit was numerically studied using equal volumes of PCM and metal foam composite PCM (CPCM) in various arrangements. For the n-eicosane (as PCM), the study was conducted at the fixed Rayleigh number (Ra) = 4.08x107, Prandtl number (Pr) = 62.9, and Stefan number (Ste) = 0.14. The results showed that positioning the metal foam on the bottom side and distributing segmented CPCM with alternating PCM zones effectively improved the system performance. Moreover, this also prevents the overheating of thermal layers in the LHTES unit. While the model labelled M2 exhibited the highest economic efficiency among all isotropic models, its low dimensionless thermal energy storage (TES) density (i.e., q’ ∼ 0.6) led this study to focus on models falling under the category having a TES density of ∼ 0.8. Compared to a pure PCM model, the configurations under equal volume ratio category demonstrated up to ∼ four times higher TES rate (p’) and the significant reduction of ∼ 75 % in melting time. The optimized isotropic model achieved the highest TES rate per unit cost with peak value of ∼ 3 at a price ratio (N) of 1. Lastly, the testing of metal foam anisotropy on the chosen design showed a substantial increase in melting/heat storage rates. The largest drop of ∼ 33 % in the total melting time was noticed for model M2 as compared to isotropic case.

Wall modes and the transition to bulk convection in rotating Rayleigh-Bénard convection

We investigate states of rapidly rotating Rayleigh-Bénard convection in a cylindrical cell over a range of Rayleigh numbers 3×105≤Ra≤5×109 and Ekman numbers 10−6≤Ek≤10−4 for Prandtl number Pr=0.8 and aspect ratios 1/5≤Γ≤5 using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states, including a secondary transition to time dependence. We show how the radial structure of the vertical velocity uz and the temperature T is captured well by the linear eigenfunctions of the wall mode instability where the radial width of uz is δuz∼Ek1/3r/H whereas δT∼e−kr (k is the wave number of a laterally infinite wall mode state). The disparity in spatial scales for Ek=10−6 means that the heat transport is dominated by the radial structure of uz since T varies slowly over the radial scale δuz. We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number Nu as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow being the robust remnant of nonlinear wall mode states. We also show how the heat transport (Nu) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions. Published by the American Physical Society 2024

Experimental investigation of the heat transfer characteristics of a synthetic annular jet impingement on a flat surface

ABSTRACT Annular impinging jets create a more uniform flow on the impact surface compared to circular impinging jets, allowing the surface to cool better. Additionally, periodic flow oscillations significantly increase heat transfer by reducing the thermal resistance on the surface. Therefore, this study experimentally investigated the heat transfer characteristics of a synthetic annular jet impinging on a flat surface with constant heat flux. In the experiments, the jet-target surface distance (H/D), jet Reynolds number (Re j), oscillation amplitude (A o), and Womersley number (Wo) were changed. In contrast, the Prandtl number (Pr) and other geometric parameters were kept constant. The effects of these parameters on heat transfer were analyzed and the results were compared with continuous circular and annular impinging jets. Local temperature values on the target surface were obtained for different parameters and heat transfer from the surface was calculated. Experimental results showed that heat transfer increased with decreasing H/D ratio for all jet types. The highest heat transfer on the surface was achieved in synthetic jet flow. Heat transfer increased as the oscillation amplitude decreased. It was observed that there is a specific value for the Womersley number (Wo = 94) and that the heat transfer decreases after this value. For Re = 50000 and H/D = 2, the annular jet provided 27% higher heat transfer than the circular jet. In synthetic jet flow, heat transfer at H/D = 2 was improved by 21% compared to H/D = 8 for Re = 6000, A o = 1.87 and Wo = 163.

Correlations on heat-transfer rate and friction factor using radial and axial v-cut geometry on a twisted tape in a double-pipe heat exchanger

This study explores the transformative potential of varying radial and axial v-cut angles within twisted tape inserts in the context of heat transfer enhancement within a double-pipe heat exchanger. The research is driven by the need to enhance energy efficiency in heat exchange systems, with a focus on understanding how v-cut angles influence heat-transfer rates, friction factors, and overall performance. Using water as the working medium, a comprehensive experimental investigation is conducted across a Reynolds number range of 5500–10,000. The findings reveal compelling correlations between the Nusselt number (Nu), friction factor ( f), and performance evaluation criteria concerning different v-cut angles within the twisted tape inserts. Remarkably, the study underscores the pivotal role of radial v-cut twisted tapes in elevating heat exchanger performance, surpassing even axial v-cut configurations. The Nusselt number achieves its pinnacle (96.51) at a Reynolds number of 10,000, whereas the highest friction factor (0.0582) and performance evaluation criteria (1.65) emerge at a Reynolds number of 5500, specifically with a 45-degree radial v-cut angle. This configuration showcases remarkable enhancements in the Nusselt number (98.68%), friction factor (38.87%), and performance evaluation criterion (39.36%) compared to a plain tube, underlining the transformative potential of optimized twisted tape inserts. The presented study offers more than theoretical insights; it provides practical guidelines for designing heat exchangers with superior performance. Derived correlations for the Nusselt number and friction factor, established through regression analysis involving key parameters such as Reynolds number (Re), Prandtl number (Pr), radial v-cut angle ( ϕ), and axial v-cut angle ( θ), demonstrate robust results within a narrow range of ± 5% for the Nusselt number and ±7% for the friction factor. In summary, this investigation not only advances our understanding of heat transfer enhancement but also presents tangible pathways for implementing enhanced heat exchanger designs, contributing significantly to energy-efficient thermal systems.

Porosity and heat transfer analysis of nanofluids due to rotating-stretching disk with Joule heating

The magnetohydrodynamic (MHD), forced convective, rotating flow of nanofluid is investigated induced by eccentric rotations of a unsteady stretching porous disk and that of the fluid at infinity. The fluid is assumed to be incompressible, viscous, and electrically conductible. The disk and fluid away from the disk rotate about non-coincident axes at the same angular velocity. The forced convection is due to the temperature gradient between the uniform temperatures of the disk and that of the fluid far away from the disk. Consideration of the Joule heating as well as viscous dissipation have been taken into account. Nanofluids based on copper, alumina, and titania have also been assumed. Exact solution has been carried out for the velocity field. Numerical solution, on the other hand, is obtained using Crank–Nicolson algorithm for the temperature profiles. Several physical aspects of the investigation are discussed and explained by means of dimensionless parameters, Prandtl number Pr, Eckert number Ec, porosity parameter S, magnetic parameter [Formula: see text] and unsteady stretching parameter. With increasing nanoparticle volume fraction, the velocity profile is reduced, while the thickness of the boundary layer upsurges. As the unsteady parameter C gets higher values, the velocity profile enhanced whereas the temperature profile gets weaker. Fluid temperature decreases as suction parameter S raises.

Thermocapillary convection in a cuboid pool with a sidewall of different temperature sections

Thermocapillary convection in a liquid cuboid pool with a sidewall of different temperature sections is investigated using 3D numerical simulation. One half section of the sidewall is heated but the other cooled. Numerical simulation is performed for Marangoni number (Ma) from 100 to 4.0 × 106 with Prandtl number (Pr) of 28.6 and aspect ratios (Ah and Aw) of 0.43. A temperature field with a weak thermocapillary convection flow is dominated by conduction for small Ma. As Ma increases, the flow becomes stronger and reveals a complex transition route to a chaotic state with a series of bifurcations. It has been demonstrated that the symmetry of the temperature field breaks between Ma = 102 and 103. A Hopf bifurcation occurs between Ma = 8.0 × 105 and 9.0 × 105 in which the flow becomes periodic. As Ma increases further, a sequence of period-doubling bifurcations occurs between Ma = 2.78 × 106 and 2.95 × 106. Once Ma exceeds 3.0 × 106, the flow becomes chaotic. Typical thermocapillary convection flows in the pool are characterized with topological analyses, spectral analyses, attractors, Lyapunov exponents, and fractal dimensions. Furthermore, the heat and mass transfer in the cuboid pool have been investigated.

Investigating combined effects of varying gravity and heat flux direction on the melting dynamics of phase change material in space

The present work investigates the combined effect of varying gravity and heat flux direction with respect to gravity on the melting dynamics of Phase Change Material. Similar conditions are relevant to applications in space, at different space infrastructures, such as orbiting satellites, as well as various extraterrestrial surface assets, landers, and rovers. The numerical simulations are performed to study the melting dynamics of a paraffin-based phase change material with Prandtl number Pr ≈ 71 and Stefan number Ste ≈ 0.33 inside a differentially heated square enclosure. The mathematical model employs a control volume-based enthalpy porosity approach to simulate the melting process inside enclosure. The direction of the incoming heat flux relative to the gravity vector is defined in terms of an orientation angle, which is varying circularly with a step of 45°, whereas the gravity level is ranging from the terrestrial surface value g to 0.2g to analyze the melting process over a wide range of Rayleigh number 100 ≤ Ra ≤ 107. The study provides a detailed insight into the attributes of heat transfer, flow dynamics, and energy storage, along with a quantitative analysis of the transition between various melting regimes and temporal fluctuations in the performance parameters. The findings demonstrate that the mutual orientation between the directions of incoming heat flux and gravity, as well as the value of the latter, significantly affect features of the convective motion in the liquid phase, as well as the entire thermally driven heat transfer within the domain. In particular, for the oppositely directed gravity and heat flux, the melted fluid closely resembles Rayleigh-Bénard convection with the presence of multicellular flow structures, while at other orientation angles, except for a co-directed gravity and heat flux case, a circular convective motion of the melted fluid takes place. The results of numerical simulations reveal declining melting rates as the mutual orientation of gravity and heat flux changes from opposite to co-directed and vice versa. The low gravity conditions delay the onset of convection-driven melting, reducing the melting rate significantly.

Conjugate transient flow and thermal analysis of non-isothermal rubber curing process in autoclave system

Autoclave manufacturing under high pressure and elevated temperature was required to vulcanize the rubber compound applied in the aerospace industry. Nevertheless, few works have comprehensively explored the transient effect of flowing factors on curing efficiency, thermal uniformity, and exergy destruction in autoclave processing. In this study, the three-dimensional model and non-isothermal vulcanization of an autoclave with a built-in combustion chamber were solved by combining the finite volume method and the proposed mixed kinetic model, and exergy destruction was determined to estimate the energy consumption using a direct method. Variations in the Reynolds number (Re), gas pressure (P), temperature, rate of temperature change, and Prandtl number (Pr) were analyzed to improve the unstable thermo-vulcanization and reduce energy consumption in autoclave processing. The results demonstrate that increasing the inlet Re can significantly increase the curing rate while decreasing the temperature difference in the rubber area, and a reduction of 41.89 %−46.62 % for the complete vulcanization time is achieved by changing Re from 105 to 2 × 106; however, adjusting P and temperature has only a minor effect on the heat transfer under constant higher Re. Furthermore, changing the rate of temperature change and Pr is also advantageous for optimizing the curing process and reducing exergy destruction. A minimal non-dimensional exergy destruction rate arises for a given P, rate of temperature change, or Pr when the Re is raised. The knowledge gathered from this research could provide a theoretical foundation for reducing energy consumption and boosting productivity during autoclave curing.

Numerical investigation of thermal and entropy generation characteristics in a sinusoidal corrugated channel under the influence of sinusoidal wall temperature

The corrugated channels play a vital role in many engineering applications, such as electronic cooling and heat exchanger devices; thus, forced convection heat transfer and entropy generation within the corrugated channels are important subjects to investigate. This study numerically investigated the laminar forced convection heat transfer and entropy generation of water flow within a sinusoidal corrugated channel. The channel walls were subjected to sinusoidal wall temperature heating while varying the wave parameters. The finite element method had been employed to solve the governing equation, and the simulation results were conducted for Reynolds number 5 ≤ Re ≤ 500, dimensionless wall temperature wavelength 0.25 ≤ λth ≤ 2.25, and Prandtl number Pr = 6.93. The main findings were depicted in terms of Nusselt number, skin friction coefficient, heat transfer effectiveness, total entropy generation, and Bejan number contours, as well as the results being compared with the results of uniform heating. In addition, the results demonstrated that sinusoidal heating significantly improved heat transfer compared to uniform heating for λth < 1.75 and all ranges of Reynolds number, while a critical Reynolds number was found, where the uniform heating showed a higher heat rate compared to non-uniform heating at λth ≥ 1.75 . Besides that, it is found that the sinusoidal wall temperature has lower entropy generation than uniform heating, except with λth = 0.25. This investigation recommends that sinusoidal wall temperature heating is more effective in heat transfer than uniform heating by 7.5, 2.78, 1.9, 1.52, and 1.34 factors at λth = 0.25, 0.75, 1.25, 1.75 and 2.25, respectively.