Adiabatic Wall Research Articles

Effect of Source-Sink Misalignment and Sink Cavity Aspect Ratio on the Thermal Performance of Gallium Heat Sinks

Herein, we numerically investigated methods to improve heat dissipation from the base of a phase-change material (PCM) heat sink exposed to high heat flux (15 W/cm2). The sink cavity exhibited a rectangular cross-section with two opposite vertical walls of high thermal conductivity. These walls serve as heat-dissipating fins. We used gallium, a metallic PCM with high thermal conductivity and a low melting point to improve heat dissipation by leveraging buoyancy-driven circulations within the molten gallium. We adopted a method to position the sink base on top of the heat source surface in such a way to augment temperature gradients within the liquid to induce imbalances in gallium density and consequent internal circulations. In this technique, one vertical wall is subjected to forced-convective heat exchange with the surroundings, while the other remains adiabatic. Subsequently, for the case which showed optimum performance, we relaxed the adiabatic thermal boundary condition applied at one of the vertical walls and replaced it with convective heat transfer condition, and assessed the sink performance based on that. Further, we analyzed the impact of various aspect ratios of the sink cavity on the induced internal circulations and base cooling. Sink cavities with aspect ratios of 1.33, 0.96, and 0.64 corresponding to sink heights of 20, 17, and 14 mm, respectively, were examined under a consistent heat flux applied across a 15-mm base length. We also investigated the precise positioning of the sink base relative to the heat source surface and explored its influence on temperature gradients and gallium density imbalances crucial for induced internal circulations. Results indicate that a sink cavity aspect ratio of 0.96 yields the optimal heat dissipation from the base. Further, aligning the left bottom edge of the sink base with the left edge of the heat source surface maximizes heat dissipation to the ambient surroundings, thereby prolonging latent-heat dumping into the sink before the gallium completely melts. Any misalignment between the sink base and the surface of the heat source may have a profound impact on the temporal evolution of induced internal circulations within the molten gallium, essentially affecting heat dissipation from the sink base.

Convective heat transfer parameters in the film cooling with thermal radiation

Thermal radiation is a large contributor to the total heat transfer of combustion systems so that it cannot be neglected, with the improvement of gas temperature and infrared stealth requirements. This paper deeply investigated the convective parameters in film cooling with thermal radiation through theoretical analysis and numerical simulation. A method to obtain the convective driving temperature under radiation was proposed and demonstrated. Research found that the film cooling effectiveness with radiation should be expressed by the mixing temperature rather than the adiabatic wall temperature. Although heat transfer and mass transfer under radiation cannot be theoretically analogized due to the radiant source term in the energy equation, the concentration cooling effectiveness without and with radiation remains approximately the same. The numerical results indicate that although conjugate coupling plays a crucial role in determining convective and radiative heat fluxes, the coupling of radiation and convective parameters is very weak. Radiation has little influence on the film cooling effectiveness (η) and the convective heat transfer coefficient (hf). Convective parameters can be decoupled from radiation with negligible loss of accuracy. This allows the non-radiation convective parameters η and hf to be directly used for calculating the convective heat flux under radiation, with relative deviations of less than 5%.

Comprehensive Experimental Assessment Of Unsteady Pressure And Heat Flux In A Small-Core Turbine Over-Tip Shroud

Abstract For novel high-speed small core turbines, with tip clearance below 0.5mm, even small blade-to-blade tip clearance variation is significant. The assessment of these complex flows is pertinent to the design of the next generation of small-core turbines. This manuscript provides a thorough experimental analysis of the shroud?s unsteady heat flux and static pressure in a small-core squealer-tip blade turbine. Atomic Layer Thermopile sensors and fast response pressure transducers were used to perform high-frequency acquisition at 2MHz around the 51% axial blade chord on the shroud. Measurements were taken at engine-representative conditions at several operational conditions and tip clearances. The signals were phase-locked averaged over the revolution period and synchronized to identify individual blade and row signatures. The linear relationship between the rotational tip Reynolds and the static pressure ratio across the blade tip reveals the transition point to reverse over-tip flows. Total heat flux is decomposed into different steady and unsteady heat flux contributions. It is demonstrated that the adiabatic wall temperature governs the unsteady heat flux and contributes to one third of the total surface heat flux. A linear trend was observed between the unsteady heat flux and the tip clearance measured at the pressure and suction side rims. Similar trends were observed between the local heat flux and the pressure ratio across the tip. A comparison with CFD predictions highlights some limitations on resolving the detached and secondary flows, evidencing the necessity of complementary experimental data.

Heat Transfer and Entropy Generation on Free Convection Airflow inside a T-shaped Cavity Considering Inner Obstacles

In this study, a numerical analysis of heat and entropy generation on free convection of airflow is performed inside a T-shaped cavity with and without circular obstacles. The T-shaped cavity is formed with two symmetrically isothermal rectangular blocks. A cold temperature is maintained on the cavity's upper wall. The adiabatic walls are connected to heated wall at constant temperature. It is assumed that the flow is laminar, 2-D, and steadily incompressible. The finite element analysis is employed for solving the governing equations. The calculated results are compared and validated with the other published works. The dimensionless velocity (streamlines) and temperature (isotherms) are calculated and illustrated for varying Rayleigh numbers. It is found that the average Nusselt number at the heated walls and entropy generation inside the cavity increase with the increment of Rayleigh numbers. Moreover, the thermal performance effects on natural convection flow are investigated with circular obstacles inside the enclosure. Five cases without and with circular obstacles regarding the boundary conditions are investigated. It is found that the thermal performance of the cavity can be improved by adding two circular obstacles with cool boundary conditions. It is evident that the innovative structure by adding two circular obstacles with cool boundary conditions gives higher average Nusselt number and entropy generation whereas lower Bejan numbers for varying Rayleigh numbers. The study is performed for and . Jagannath University Journal of Science, Volume 11, Number 1, June 2024, pp. 186−202

Thermal spreading in a multilayer geometry with convective cooling along the side wall of each layer

Two-dimensional thermal conduction between a source/sink and a body of larger size results in thermal spreading and constriction, which are of much technological importance in problems such as semiconductor thermal management. While the traditional analysis of thermal spreading and constriction assumed adiabatic side walls, there is growing interest in convective heat removal from the side walls, such as in multilayer three-dimensional integrated circuits (3D ICs) and stacked Li-ion cells in a battery pack. This work presents theoretical analysis of thermal spreading in a multilayer body with distinct convective heat transfer coefficients along the side wall for each layer, in addition to anisotropic thermal conductivity in each layer and thermal contact resistance at interfaces between layers. A series solution for the temperature distributions in each layer is derived, with a unique set of eigenvalues for each layer. A set of linear algebraic equations that govern the coefficients of the series solutions is derived. Results are shown to agree well with past work for special cases, as well as with numerical simulations for general problems. The impact of source size, thermal anisotropy and Biot numbers of various layers is analyzed in detail. In particular, the interplay between Biot numbers along the sidewall and at the sink plane in determining total thermal resistance is investigated in detail. This work contributes towards a fundamental understanding of theoretical thermal conduction in problems of practical relevance, such as advanced microelectronics and Li-ion cells. Results may find application in the design and optimization of these and other engineering systems where thermal spreading or constriction play an important role.

CFD Analysis to Optimize Air Quality in Aeroponic Tower Garden

Aeroponic tower gardens represent an innovative approach to urban agriculture, utilizing vertical structures to cultivate plants without soil. Research highlights the efficiency of this method in optimizing resource usage, such as water and space, compared to traditional farming. Studies emphasize increased crop yields, faster growth rates, and reduced environmental impact. Additionally, aeroponic systems enable precise nutrient delivery to plants, fostering optimal growth conditions. While the technology shows promise, further investigations are needed to address potential challenges and optimize its application in diverse agricultural settings. The study presents the simulation of air temperature and humidity distribution in a closed chamber of the vertical farm for optimization purposes. The environmental conditions inside the chamber are optimized for plant growth, to maintain the temperature at a range of 18-24 °C temperature and the relative humidity at a range of 75-85 %. The paper also discusses the challenges, limitations, and future recommendations for improving the system. Simulation of the system, on the other hand, is crucial not only for prototype fabrication but also for the optimization of sensor locations. The simulation of the tower garden system was performed using ANSYS-FLUENT to portray how the airflow inside the tower garden's enclosed environment was distributed. The system parameters such as humidity and temperature were set to meet the plants' growth requirements, and the system was treated as the steady state with an adiabatic boundary. Based on the simulation results, the best design recommended is to use two humidity and temperature sensors, one at the top and the other at the core of the prototype. Hence, a complete mapping of temperature and humidity distribution that is critical for plant growth would be occurred.

Film hole layout optimization for multi-row film cooling plate in continuous parameter space under non-uniform inlet temperature distribution

Film cooling is an advanced external cooling technology for protecting gas turbine blades from excessive temperatures. To counteract non-uniform heat loads caused by hot streak and swirl effects at the combustion chamber outlet, fine design of film hole positions is necessary. However, the complexity due to the numerous film holes and their positional parameters presents challenges in the independent optimization of film hole positions in a continuous parameter space. This study proposed an optimization method grounded in the divide and conquer approach to address optimization for film hole layout. The film hole layout was decomposed into multiple single rows and optimized systematically by iteratively refining the single-row film hole layout along the streamwise direction using the expectation maximization algorithm. Optimized layouts for five different inlet temperature distributions were obtained using the proposed method and adiabatic wall temperature distributions were compared and analyzed for optimized and staggered layouts. Additionally, the cooling performance of the optimized layout was evaluated against the staggered layout under conjugate heat transfer conditions and the robustness of the optimized layout under various blowing ratios and peak temperature positions was tested. The results demonstrated that the proposed method can optimize the positions of 52 film holes within 0.3h, and it was generalized to various inlet temperature distributions. By enhancing lateral interactions among downstream film jets, the lifting effect of kidney vortex in the optimized layout was weakened, bringing the film jets closer to the wall and significantly increasing coolant coverage during streamwise development. Comparative analysis reveals the superior cooling performance of the optimized layout at the blowing ratio of 1.0, evidenced by a 15.1% reduction in total input heat transfer rate and a 12.3% enhancement in overall cooling efficiency relative to the staggered layout. Under conditions with blowing ratios ranging from 0.5 to 1.5 and peak temperature position deviations, the average wall temperature of the optimized layout consistently remained lower than the staggered layout, indicating the robustness of the optimized layout to variations in blowing ratio and hot streak position.

Research on multi-heat source arrangement optimization based on equivalent heat source method and reconstructed variational autoencoder

The variational autoencoder (VAE) architecture has significant advantages in predictive image generation. This study proposes a novel RFCNN-βVAE model, which combines residual-connected fully connected neural networks with VAE to handle multi-heat source arrangements. By integrating analytical solutions, polynomial fitting, and temperature field superposition, we accurately simulated the temperature rise distribution of a single heat source. We further explored the use of multiple equivalent heat sources to replace adiabatic boundary conditions. This enables the analytical method to effectively solve the two-dimensional conjugate convective heat transfer problem, providing a reliable alternative to traditional numerical solutions. Our results show that the model achieved high predictive accuracy. By adjusting the β parameter, we balanced reconstruction accuracy and latent space generalization. During the stable phase of the multi-heat source optimization iteration, 73.4% of the results outperformed the dense dataset benchmark, indicating that the model successfully optimized heat source coordinates and minimized peak temperature rise. This validates the feasibility and effectiveness of deep learning in thermal management system design. This research lays the groundwork for optimizing complex thermal environments and contributes valuable perspectives on the effective design of systems with multiple thermal sources or for applications like multi-beam lighting equalization.

Nonlinear stability analysis of thermal convection in a fluid layer with slip flow and general temperature boundary condition

The current article presents a comprehensive analysis of the influence of inconstant viscosity into thermal convection, incorporating the influence of generalized velocity (slip boundary condition) and temperature boundary conditions (physically represent imperfectly conducting boundary) within a fluid layer. Slip boundary conditions are often considered more practical than no-slip conditions (Neto et al. (2003)). Therefore, in the present work, slip boundary condition is used to discuss the effect of temperature and pressure dependent viscosity. Both linear and nonlinear stability analyses are explored, revealing a noteworthy finding: the precise alignment of the nonlinear stability boundary with the linear instability threshold. Additionally, the exchange of stability is illustrated, indicating that convection exclusively manifests in a stationary mode. The findings are derived across a spectrum of boundary scenarios, ranging from free-free to rigid-free, and rigid-rigid boundaries, encompassing both isothermal and adiabatic conditions. Notably, the slip length parameter exhibits a destabilizing effect, while convection is observed to occur more swiftly under adiabatic boundary conditions compared to isothermal conditions. The Chebyshev pseudo-spectral technique is applied to solve the eigenvalue problems obtained from linear and nonlinear stability analysis.

Research on the division of heat dissipation spaces for multiple heat sources based on the adiabatic characteristic of heat flow lines

Due to the pressing need for compact layouts, the spacing between high-power devices is gradually decreasing, making the mutual influence between multiple heat sources unavoidable. Therefore, this paper proposes a method based on the adiabatic characteristics of heat flow lines and their convergence positions to evaluate the rationality of the thermal space design of each heat source. This method has been validated for applicability in one-dimensional, two-dimensional, and three-dimensional multi-heat-source conjugate convection heat transfer. Heat flow lines have significant advantages in describing energy flow, as they align with the direction of the temperature gradient. In thermal spaces with adiabatic boundaries or mutual influences between multiple heat sources, heat flow lines converge at certain positions. The relationship between adiabatic boundaries and heat flow line convergence positions has been studied, and a more interpretative decoupling scheme for multi-heat-source systems has been proposed. The main feature of this scheme is the separation of each heat source in the same steady-state thermal space and assigning adiabatic boundaries to the solid partition surfaces, allowing efficient observation of the thermal conditions of individual heat sources and targeted layout optimization. Results indicate that this method can utilize changes in heat flow line convergence positions to assess current thermal conditions and can be used to compare the thermal performance of different shaped heat sinks. Simulation results show that under the same mass conditions, thin-fin heat sinks perform 47 % better than thick-fin heat sinks, providing a more comprehensive and intuitive assessment compared to metrics such as thermal resistance and average temperature. The proposed method offers new ideas for multi-heat-source layout optimization, heat flow control, multi-heat-source partitioned simulation, and abnormal heating detection in multiple heat sources.

Determination of Local Heat Transfer Coefficients and Friction Factors at Variable Temperature and Velocity Boundary Conditions for Complex Flows

Transient conjugate heat transfer measurements under varying temperature and velocity inlet boundary conditions at incompressible flow conditions were performed for flat plate and ribbed channel geometries. Therefrom, local adiabatic wall temperatures and heat transfer coefficients were determined. The data were analyzed using typical heat transfer correlations, e.g., Nu=CRemPrn, determining the local distributions of C and m. It is shown that they are closely linked. A relationship lnC=A−mB is observed, with A and B as modeling parameters. They could be related to parameters in log-law or power-law representations for turbulent boundary layer flows. The parameter m is shown to have a close link to local pressure gradients and, therewith, near wall streamlines as well as friction factor distributions. A normalization of the C parameter allows one to derive a Reynolds analogy factor and, therefrom, local wall shear stresses.

Adjoint-based optimisation of time- and span-periodic flow fields with Space–Time Spectral Method: Application to non-linear instabilities in compressible boundary layer flows

We aim at computing time- and span-periodic flow fields in span-invariant configurations. The streamwise and cross-stream derivatives are discretised with finite volumes while time and the span-direction are handled with pseudo-spectral Fourier-collocation methods. Doing so, we extend the classical Time Spectral Method (TSM) to a Space–Time Spectral Method (S-TSM), by considering non-linear interactions of a finite number of time and span harmonics. For optimisation, we introduce an adjoint-based framework that allows efficient computation of the gradient of any cost functional with respect to a large-dimensional control parameter. Both theoretical and numerical aspects of the methodology are described: evaluation of matrix–vector products with S-TSM Jacobian (or its transpose) by algorithmic differentiation, solution of fixed-points with quasi-Newton method and de-aliasing in time and space, solution of direct and adjoint linear systems by iterative algorithms with a block-circulant preconditioner, performance assessment in CPU time and memory. We illustrate the methodology on the case of 3D instabilities (first Mack mode) triggered within a developing adiabatic boundary layer at M = 4.5. A gradient-ascent method allows to identify a finite-amplitude 3D forcing that triggers a non-linear response exhibiting the strongest time- and span-averaged drag on the flat-plate. In view of flow control, a gradient-descent method finally determines a finite amplitude 2D wall-heat flux that minimises the averaged drag of the plate in presence of the previously determined non-linear optimal forcing.

Evolution of Displacement Speed Statistics During Head-On Flame-Wall Interaction within Turbulent Boundary Layers

ABSTRACT The statistical behaviours of the density-weighted displacement speed and its curvature and strain rate dependence during head-on interaction of statistically planar premixed flames have been analysed based on Direct Numerical Simulations. The analysis has been conducted within turbulent boundary layers featuring inert walls, under both isothermal and adiabatic wall boundary conditions. The flame quenches due to heat loss when it reaches close to the wall in the case of isothermal wall boundary condition. By contrast, the flame can propagate all the way to the wall before extinguishing due to the consumption of reactants in the case of adiabatic wall boundary conditions. Thus, the effects of thermal expansion, quantified by dilatation rate, and flame normal acceleration during flame-wall interaction in the case of the isothermal wall are weaker than that in the case of the adiabatic wall case due to flame quenching. This gives rise to significant differences in the curvature and strain rate dependences of the reactive scalar gradient magnitude, which affects the statistical behaviours of the reaction and normal diffusion components of density-weighted displacement speed including their mean values, widths of their probability density functions, and their local strain rate and curvature dependences. It has been found that the interaction of near-wall vortical structures with flame surface increases the range of curvature variation during head-on interaction, which acts to widen the probability density function of the density-weighted displacement speed. This trend is relatively stronger for the isothermal wall boundary condition because of the larger variation of the reaction rate component of the density-weighted displacement speed due to local flame quenching, which also acts to widen the range of the density-weighted displacement speed variation in comparison to that in the case of adiabatic wall boundary conditions. Although the qualitative nature of curvature, strain rate, and stretch rate dependences of the density-weighted displacement speed remain unaffected by the wall boundary condition, the strength of the correlation changes with the progress of head-on interaction. It has been found that the negative correlation between the density-weighted displacement speed and flame curvature weakens with the progress of head-on interaction, which gives rise to a reduction in the strength of the correlation between the density-weighted displacement speed and flame stretch rate. Similarly, the correlation between the tangential strain rate and the density-weighted displacement speed weakens with the progress of head-on interaction. Detailed physical explanations are provided for these behaviours, and their modeling implications are indicated.

Melting and heat management of phase change material using smart ternary-hybrid coolant

This research investigates the effectiveness of using a smart ternary-hybrid nanofluid to enhance the melting rate and convective behavior of electrically conducting tin (Sn) in a rectangular enclosure under the influence of a uniform magnetic field. The enclosure has adiabatic vertical walls with hot and cold temperatures on the bottom and top walls. The finite element method (FEM) is used to solve the governing equations with appropriate boundary conditions using Galerkin's weighted residual approach. The study focuses on applying tin as the phase change material (PCM), with the highest temperature of 508 K, the lowest temperature of 503 K, and the melting interface temperature of 505 K. To enhance the heat transfer performance, tin-based ternary (graphene (G), silicon carbide (SiC), and nickel (Ni)) hybrid smart coolant is applied into the system. To investigate the mechanism of the melting and convective thermal transfer process, the results of the present study are reported with time for various values of the magnetic field (Ha) and solid concentration of ternary hybrid nanoparticle (ϕ). This study represents the streamlines, isothermal lines, melting interface, melting fraction, and heat transfer for the above-mentioned parameters. The results show that increasing the magnetic field reduces the rate of thermal transport by 38.96 % at t = 4000s. However, at a particular time of 2500s, increasing the solid volume fraction of nanoparticles enhances the melting fraction by approximately 8.34 %. Two regression equations are derived for the Nusselt number and melting fraction, with multiple response variables. This article improves understanding of natural convective heat transport during phase change processes for various coolants in different engineering applications.

Quasi-CJ rotating detonation with partially premixed methane-oxygen injection: Numerical simulation and experimental validation

The efficiency gain of rotating detonation depends on several loss factors related to the chamber geometry, the injection principle, the propellants and their mass flow rates, and the equivalence ratio. Numerical simulation can help quantify these losses, and this work presents a Large Eddy Simulation (LES) of rotating detonation in an annular chamber and its validation against experiments. The simulation captured the mixing processes, the overall dynamics of the detonation, the deflagration, and the burnt gas expansion. The injection device was numerically designed to ensure partial premixing of the propellants before injection into the chamber. The chamber had a length of 110 mm, an outer diameter of 80 mm, and a radial width of 10 mm. The mixture consisted of gaseous CH4 and O2 with an equivalence ratio of 1.2 and a mass flow rate of 160 g/s. Combustion kinetics was modeled using a skeletal mechanism with 62 reactions and 16 species. The boundary conditions were adiabatic slip walls. The results reproduce well the detonation velocity (within 1% deviation) and the pressure variation behind the wave. The simulated OH* chemiluminescence compares well with experimental high-speed imaging of the outlet and side of the chamber. The simulation results indicate that 65% of the propellant mass is well mixed in front of the wave whereas 15% of the mixture is burned by deflagration. They show that CH4 and O2 do not axially stratify because they have similar injection dynamics between periodic perturbations induced by the rotating detonation. Good propellant mixing and low deflagration losses explain the high experimental detonation velocity, about 90% of DCJ, and a high combustion efficiency of 98%. These agreements between the computational and experimental results indicate that the simulation is capable of capturing the physical scales relevant to RDC operation and producing reliable results for RDC design.

An adiabatic boundary condition with cylindrical perfect conductors for improved approximations from heat-pulse measurement near the soil-atmosphere interface

The cylindrical-perfect-conductors (CPC) theory, which assumes an infinite and homogeneous soil medium, can be used to analyze heat pulse (HP) measurements to estimate soil thermal property values. However, when a HP sensor is positioned near the soil surface, the CPC theory is not valid because of the change in media properties at the soil-atmosphere interface. In this study, a CPC solution considering an adiabatic boundary condition (CPC-ABC) is presented to account for the soil-atmosphere interface effect. Compared with the results from numerical simulations, the CPC-ABC solution gave more accurate soil temperature values at the sensing probe than did a CPC model. When a HP sensor was positioned horizontally at a depth of 1 mm below a sand soil surface, the relative errors (RE) of CPC estimated thermal property values were as large as 52%, while the RE values based on the CPC-ABC solution were about 8%. Results from numerical simulations and laboratory experiments both showed that the CPC model worked well for horizontally positioned HP sensors with probe lengths of 70-mm at burial depths greater than 15 mm. Soil-atmosphere interface effect was largely dependent on HP sensor dimensions and measurement volumes. Overall, the extended CPC-ABC theory provided accurate soil thermal property estimates by considering the effects of finite probe properties and the presence of the soil-atmosphere interface.

A SUPERPOSITION TECHNIQUE FOR PREDICTING OVERALL EFFECTIVENESS WITH MULTIPLE SOURCES OF INDIVIDUALLY CHARACTERIZED INTERNAL AND EXTERNAL COOLANT FLOWS

Abstract Gas turbine engines rely on intricate cooling schemes to protect turbine components from the high temperature freestream gas. Determining the optimal placement of film cooling holes while remaining mindful of the consumption of coolant air is therefore a design challenge. For several decades a method of superposition has been in use that provides a reasonable prediction of the adiabatic effectiveness in a region influenced by multiple rows of film cooling holes acting together if the adiabatic effectiveness distributions resulting from individual rows are already known. This classical superposition technique has been used to provide a first cut at determining where coolant holes might be placed. A shortcoming of the method is that it strictly applies only to prediction of adiabatic effectiveness which is indicative of the adiabatic wall temperature, not the actual surface temperature. The overall effectiveness, which is indicative of the actual surface temperature is somewhat more complicated as it is influenced not only by the external cooling, but also internal cooling. In the present work, a method of superposition of overall effectiveness data is proposed, allowing prediction of the actual surface temperature distribution on a component. Experimental results show that it is possible to use knowledge of the overall effectiveness distributions resulting from individual internal cooling and associated film cooling holes acting alone to determine how they are likely going to act when combined. This technique shows promise for a turbine designer to use superposition for actual surface temperature prediction and therefore higher quality initial cooling designs.

Thermal analysis of hybrid nanoliquid contains iron-oxide (Fe3O4) and copper (Cu) nanoparticles in an enclosure

The major aim of this work is to analyze the thermophysical properties of hybrid nanoliquid inside a square lid driven enclosure under the effect of applied magnetic field and mixed convection. The Hybrid nanofluid is considered a suspension of Iron-oxide (Fe3O4) and Copper (Cu) nanoparticles into water. The cavity walls have varying properties such as top adiabatic wall is moving continuously while the lower wall is maintained at a high constant temperature, in addition, the vertical walls are kept at a low fixed temperature. The magnetic field is applied to the right vertical wall in a horizontal direction. Additionally, the effects of buoyancy forces caused by temperature gradients and shear forces caused by continuous lid motion are considered. The mathematical modelling of problem with all assumptions yields the nonlinear partial differential system. First this system is transferred into non-dimensional form and then transformed system is solved by using Galerkin finite element method (GFEM) along with Gaussian elimination method. Results for isotherms, streamlines and average Nusselt number are obtained versus Richardson number (0.1 ≤ Ri ≤ 15), Grashof number (10 ≤ Gr ≤ 10000), Hartmann number (0 ≤ Ha ≤ 100), volume fractions of solid nanoparticles (0.005 ≤ ϕ1 ≤ 0.02) and (0.005 ≤ ϕ2 ≤ 0.02). It is observed that the Richardson number and Grashof number have significant impacts on both flow velocity and temperature. In addition, concentration of hybrid nanoparticles improves the heat transfer performance. The obtained results may be crucial for thermal management in the cooling of electronics, heat exchangers, solar thermal collectors, industrial operations, medical equipment, HVAC systems, food processing, and renewable energy systems.

Boundary-Layer Transition-Onset Variation Under Wide Range of Mach Numbers and Wall Temperature Ratios

Linear stability analysis is carried out for the boundary layer under a wide range of Mach numbers (4<Mae<16) and wall temperature ratios (0.1<Tw/Taw<1.0), and for the first time, the characteristics of the third mode are analyzed under different Mae and Tw/Taw. It is found that the unstable third mode appears at Mae=10 with an adiabatic wall, and its growth rate first increases and then decreases with increasing Mae. As the wall becomes colder, the unstable third mode is enhanced and appears at lower Mae. The transition-onset variations are investigated by the eN method. As Mae reaches 14, the third mode begins to promote the transition. The transition-onset Reynolds number of the third mode can be reduced by 11.4% compared to that of the second mode at Mae=16. The transition-onset momentum thickness Reynolds number Reθt varies significantly under different Mae and Tw/Taw. At 4<Mae<10, Reθt is around 800–2000 and increases with increasing Tw/Taw significantly. At 10<Mae<16, Reθt rises to 2000–3800 and is less sensitive to the change of Tw/Taw. Therefore, it is necessary to consider the effects of Mae and Tw/Taw on Reθt in transition prediction modeling for hypersonic boundary layers.

Study on heat transfer and pressure steady-state characteristics of a floating nozzle under a moving wall

This work considers the flow field as two-dimensional turbulent flow and studies the steady-state properties of heat transfer and the pressure of the suspension nozzle. An adiabatic wall parallel to the moving wall and two slit entrances at either end of the adiabatic wall make up the rectangular flow field. The SST k-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k - \\omega$$\\end{document} turbulence model is used in the turbulence computation. Both qualitative and quantitative analyses are conducted on the distribution of the flow field, temperature field, local Nusselt number, local pressure coefficient, average Nusselt number, and average pressure coefficient under various combination conditions. The findings indicate that when the suspension nozzle's flow field varies greatly, wall-jet velocity ratio is 0.1. A rise in Jet inclination angle is not helpful for the wall's suspension, and it has minimal effect on the flow field. The flow field is greatly influenced by separation space-slit width ratio. Larger separation space-slit width ratio values are advantageous for the wall's heat transmission but unfavorable for the wall's suspension. The flow field is most influenced by wall-jet velocity ratio. The wall's ability to convey heat is stronger the higher the wall-jet velocity ratio, but its ability to support weight falls.