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This paper aims to study the effect of concentric hot circular cylinder inside egg-cavity porous-copper nanofluid on natural convection phenomena.

The finite element method–based Galerkin approach is applied to solve numerically the set of governing equations with appropriate boundary conditions.

The effects of different range parameters, such as Darcy number (10–3 = Da = 10–1), Rayleigh number (103 = Ra = 106), nanoparticle volume fraction (0 = ϑ = 0.06) and eccentricity (−0.3 = e = 0.1) on the fluid flow represent by stream function and heat transfer represent by temperature distribution, local and average Nusselt numbers.

A comparison between oval shape and concentric circular concentric cylinder was investigated.

In the current numerical study, heat transfer by natural convection was identified inside the new design of egg-shaped cavity as a result of the presence of a circular inside it supported by a porous medium filled with a nanofluid. After reviewing previous studies and considering the importance of heat transfer by free convection inside tubes for many applications, to the best of the authors’ knowledge, the current work is the first study that deals with a study and comparison between the common shape (concentric circular tubes) and the new shape (egg-shaped cavity).

The purpose of this study is to analyse the magnetic field effect on Fe₃O₄/H₂O Ferrofluid flowing in a sudden expansion tube, which has specific behaviour in terms of rheology, with convex dimple fins. Because the investigation of flow separation is a prominent application in performance, the effect of magnetic field and convex dimple on the thermo-hydraulic performance of sudden expansion tube are examined, in detail.

During the solution of the boundary conditions of the sudden expansion tube, finite volume method was used. Analyses have been conducted considering the single-phase solution, steady-state, incompressible fluid and no-slip condition of the wall under forced convection conditions. In the analyses, it has been assumed that the flow was developing thermally and has been fully developed hydrodynamically.

The present study focuses on exploring the influence of the magnetic field, nanofluid concentration and convex dimple fins on the thermo-hydraulic performance of sudden expansion tube. The results indicate that the strength of the magnetic field, nanofluid concentration and convex dimple fins have a positive effect on the convective heat transfer in the system.

The authors conducted numerical studies, determining through a literature search that no one had yet investigated enhancing heat transfer on a sudden expansion tube using combinations of magnetic fields, nanofluids and convex dimple fins. The results of the numerical analyses provide valuable information about the improvement of heat transfer and system performance in electronic device cooling and heat exchangers.

This study aims to focus on understanding how different jet angles and Reynolds numbers influence the phase change materials’ (PCMs) melting process and their capacity to store energy. This approach is intended to offer novel insights into enhancing thermal energy storage systems, particularly for applications where heat transfer efficiency and energy storage are critical.

The research involved an experimental and numerical analysis of PCM with a melting temperature range of 22 °C–26°C under various conditions. Three different jet angles (45°, 90° and 135°) and two container angles (45° and 90°) were tested. Additionally, two different Reynolds numbers (2,235 and 4,470) were used to explore the effects of jet outlet velocities on PCM melting behaviour. The study used a circular container and analysed the melting process using the hot air inclined jet impingement (HAIJI) method.

The obtained results showed that the average temperature for the last time step at Ф = 90° and Re = 4,470 is 6.26% higher for Ф = 135° and 14.23% higher for Ф = 90° compared with the 45° jet angle. It is also observed that the jet angle, especially for Ф = 90°, is a much more important factor in energy storage than the Reynolds number. In other words, the jet angle can be used as a passive control parameter for energy storage.

This study offers a novel perspective on the effective storage of waste heat transferred with air, such as exhaust gases. It provides valuable insights into the role of jet inclination angles and Reynolds numbers in optimizing the melting and energy storage performance of PCMs, which can be crucial for enhancing the efficiency of thermal energy storage systems.

As data centres grow in size and complexity, traditional air-cooling methods are becoming less effective and more expensive. Immersion cooling, where servers are submerged in a dielectric fluid, has emerged as a promising alternative. Ensuring reliable operations in data centre applications requires the development of an effective control framework for immersion cooling systems, which necessitates the prediction of server temperature. While deep learning-based temperature prediction models have shown effectiveness, further enhancement is needed to improve their prediction accuracy. This study aims to develop a temperature prediction model using Long Short-Term Memory (LSTM) Networks based on recursive encoder-decoder architecture.

This paper explores the use of deep learning algorithms to predict the temperature of a heater in a two-phase immersion-cooled system using NOVEC 7100. The performance of recursive-long short-term memory-encoder-decoder (R-LSTM-ED), recursive-convolutional neural network-LSTM (R-CNN-LSTM) and R-LSTM approaches are compared using mean absolute error, root mean square error, mean absolute percentage error and coefficient of determination (R²) as performance metrics. The impact of window size, sampling period and noise within training data on the performance of the model is investigated.

The R-LSTM-ED consistently outperforms the R-LSTM model by 6%, 15.8% and 12.5%, and R-CNN-LSTM model by 4%, 11% and 12.3% in all forecast ranges of 10, 30 and 60 s, respectively, averaged across all the workloads considered in the study. The optimum sampling period based on the study is found to be 2 s and the window size to be 60 s. The performance of the model deteriorates significantly as the noise level reaches 10%.

The proposed models are currently trained on data collected from an experimental setup simulating data centre loads. Future research should seek to extend the applicability of the models by incorporating time series data from immersion-cooled servers.

The proposed multivariate-recursive-prediction models are trained and tested by using real Data Centre workload traces applied to the immersion-cooled system developed in the laboratory.

To present the detailed implementation processes of the IDEAL algorithm for two-dimensional compressible flows based on Delaunay triangular mesh, and compare the performance of the SIMPLE and IDEAL algorithms for solving compressible problems. What’s more, the implementation processes of Delaunay mesh generation and derivation of the pressure correction equation are also introduced.

Programming completely in C++.

Five compressible examples are used to test the SIMPLE and IDEAL algorithms, and the comparison with measurement data shows good agreement. The IDEAL algorithm has much better performance in both convergence rate and stability over the SIMPLE algorithm.

The detail solution procedure of implementing the IDEAL algorithm for compressible flows based on Delaunay triangular mesh is presented in this work, seemingly first in the literature.

Financial mathematics is one of the most rapidly evolving fields in today’s banking and cooperative industries. In the current study, a new fractional differentiation operator with a nonsingular kernel based on the Robotnov fractional exponential function (RFEF) is considered for the Black–Scholes model, which is the most important model in finance. For simulations, homotopy perturbation and the Laplace transform are used and the obtained solutions are expressed in terms of the generalized Mittag-Leffler function (MLF).

The homotopy perturbation method (HPM) with the help of the Laplace transform is presented here to check the behaviours of the solutions of the Black–Scholes model. HPM is well known for its accuracy and simplicity.

In this attempt, the exact solutions to a famous financial market problem, namely, the BS option pricing model, are obtained using homotopy perturbation and the LT method, where the fractional derivative is taken in a new YAC sense. We obtained solutions for each financial market problem in terms of the generalized Mittag-Leffler function.

The Black–Scholes model is presented using a new kind of operator, the Yang-Abdel-Aty-Cattani (YAC) operator. That is a new concept. The revised model is solved using a well-known semi-analytic technique, the homotopy perturbation method (HPM), with the help of the Laplace transform. Also, the obtained solutions are compared with the exact solutions to prove the effectiveness of the proposed work. The different characteristics of the solutions are investigated for different values of fractional-order derivatives.

This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results.

This paper considered theoretical and numerical methodologies.

This paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures.

The novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.

This paper aims to investigate the thermal performance of equivalent square and circular thermal systems and compare the heat transport and irreversibility of magnetohydrodynamic (MHD) nanofluid flow within these systems.

The research uses a constraint-based approach to analyze the impact of geometric shapes on heat transfer and irreversibility. Two equivalent systems, a square cavity and a circular cavity, are examined, considering identical heating/cooling lengths and fluid flow volume. The analysis includes parameters such as magnetic field strength, nanoparticle concentration and accompanying irreversibility.

This study reveals that circular geometry outperforms square geometry in terms of heat flow, fluid flow and heat transfer. The equivalent circular thermal system is more efficient, with heat transfer enhancements of approximately 17.7%. The corresponding irreversibility production rate is also higher, which is up to 17.6%. The total irreversibility production increases with Ra and decreases with a rise in Ha. However, the effect of magnetic field orientation (γ) on total EG is minor.

Further research can explore additional geometric shapes, orientations and boundary conditions to expand the understanding of thermal performance in different configurations. Experimental validation can also complement the numerical analysis presented in this study.

This research introduces a constraint-based approach for evaluating heat transport and irreversibility in MHD nanofluid flow within square and circular thermal systems. The comparison of equivalent geometries and the consideration of constraint-based analysis contribute to the originality and value of this work. The findings provide insights for designing optimal thermal systems and advancing MHD nanofluid flow control mechanisms, offering potential for improved efficiency in various applications.

The research focused on analysing a unique type of heat exchanger that uses swirling air flow over heated tubes. This heat exchanger includes a round baffle plate with holes and opposite-oriented trapezoidal air deflectors attached at different angles. The deflectors are spaced at various distances, and the tubes are arranged in a circular pattern while maintaining a constant heat flux.

This setup is housed inside a circular duct with airflow in the longitudinal direction. The study examined the impact of different inclination angles and pitch ratios on the performance of the heat exchanger within a specific range of Reynolds numbers.

The findings revealed that the angle of inclination significantly affected the flow velocity, with higher angles resulting in increased velocity. The heat transfer performance was best at lower inclination angles and pitch ratios. Flow resistance decreased with increasing angle of inclination and pitch ratio.

The average thermal enhancement factor decreased with higher inclination angles, with the maximum value observed as 0.94 at a pitch ratio of 1 at an angle of 30°.

This paper aims to establish a lattice Boltzmann (LB) method for solid-liquid phase transition (SLPT) from the pore scale to the representative elementary volume (REV) scale. By applying this method, detailed information about heat transfer and phase change processes within the pores can be obtained, while also enabling the calculation of larger-scale SLPT problems, such as shell-and-tube phase change heat storage systems.

Three-dimensional (3D) pore-scale enthalpy-based LB model is developed. The computational input parameters at the REV scale are derived from calculations at the pore scale, ensuring consistency between the two scales. The approaches to reconstruct the 3D porous structure and determine the REV of metal foam were discussed. The implementation of conjugate heat transfer between the solid matrix and the solid−liquid phase change material (SLPCM) for the proposed model is developed. A simple REV-scale LB model under the local thermal nonequilibrium condition is presented. The method of bridging the gap between the pore-scale and REV-scale enthalpy-based LB models by the REV is given.

This coupled method facilitates detailed simulations of flow, heat transfer and phase change within pores. The approach holds promise for multiscale calculations in latent heat storage devices with porous structures. The SLPT of the heat sinks for electronic device thermal control was simulated as a case, demonstrating the efficiency of the present models in designing and optimizing SLPT devices.

A coupled pore-scale and REV-scale LB method as a numerical tool for investigating phase change in porous materials was developed. This innovative approach allows for the capture of details within pores while addressing computations over a large domain. The LB method for simulating SLPT from the pore scale to the REV scale was given. The proposed method addresses the conjugate heat transfer between the SLPCM and the solid matrix in the enthalpy-based LB model.