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This study aims to undertake a comprehensive examination of heat transfer by convection in porous systems with top and bottom walls insulated and differently heated vertical walls under a magnetic field. For a specific nanofluid, the study aims to bring out the effects of different segmental heating arrangements.

An existing in-house code based on the finite volume method has provided the numerical solution of the coupled nondimensional transport equations. Following a validation study, different explorations include the variations of Darcy–Rayleigh number (Ra_m = 10–10⁴), Darcy number (Da = 10^–5–10^–1) segmented arrangements of heaters of identical total length, porosity index (ε = 0.1–1) and aspect ratio of the cavity (AR = 0.25–2) under Hartmann number (Ha = 10–70) and volume fraction of φ = 0.1% for the nanoparticles. In the analysis, there are major roles of the streamlines, isotherms and heatlines on the vertical mid-plane of the cavity and the profiles of the flow velocity and temperature on the central line of the section.

The finding of a monotonic rise in the heat transfer rate with an increase in Ra_m from 10 to 10⁴ has prompted a further comparison of the rate at Ra_m equal to 10⁴ with the total length of the heaters kept constant in all the cases. With respect to uniform heating of one entire wall, the study reveals a significant advantage of 246% rate enhancement from two equal heater segments placed centrally on opposite walls. This rate has emerged higher by 82% and 249%, respectively, with both the segments placed at the top and one at the bottom and one at the top. An increase in the number of centrally arranged heaters on each wall from one to five has yielded 286% rate enhancement. Changes in the ratio of the cavity height-to-length from 1.0 to 0.2 and 2 cause the rate to decrease by 50% and increase by 21%, respectively.

Further research with additional parameters, geometries and configurations will consolidate the understanding. Experimental validation can complement the numerical simulations presented in this study.

This research contributes to the field by integrating segmented heating, magnetic fields and hybrid nanofluid in a porous flow domain, addressing existing research gaps. The findings provide valuable insights for enhancing thermal performance, and controlling heat transfer locally, and have implications for medical treatments, thermal management systems and related fields. The research opens up new possibilities for precise thermal management and offers directions for future investigations.

This study aims to numerically investigate heat transport in a trapezoidal cavity using hybrid nanoparticles (Ag-$Al_2O_3$). Unlike previous studies, this one covers magnetohydrodynamics, joule heating with viscous dissipation, heat absorption and generation. The left and right sides of the chasm are frigid. The upper wall heats, whereas the bottom wall remains adiabatic.

After reducing the system of dimensional equations to dimensionless equations, the authors use the Galerkin finite element method to solve them numerically. Geometric parameters affect heating efficiency; thus, the authors use flow metrics such as the Reynold number Re, magnetic parameter M, volume fraction coefficient, heat absorption and Eckert number Ec. The authors use the finite volume method to solve the governing equations after converting them to dimensionless form. The authors also try the artificial neural network method to predict the innovative cavity’s heat response in future scenarios. Transition state charts, regression analysis, MSE and error histograms accelerate, smooth and accurately converge solutions.

As the magnetic parameter and Eckert number increase, the enclosure emits more heat. As Reynold and volume fraction coefficients rise, the Nusselt number falls. It rose as magnetic, Eckert and heat absorption characteristics increased. The average Nusselt number rises with Reynolds and volume fraction coefficients. The magnetic, Eckert and heat absorption characteristics have inverse values.

This study numerically investigates heat transport in a trapezoidal cavity using hybrid nanoparticles (Ag-$Al_2O_3$). Unlike previous studies, this one covers MHD, joule heating with viscous dissipation, heat absorption and generation. The left and right sides of the chasm are frigid. The upper wall heats, whereas the bottom wall remains adiabatic.

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 purpose of this paper is to investigate the effects of gravitational modulation on natural convection in a square inclined porous cavity filled by a fluid containing copper nanoparticles.

The present study uses a system of equations that couple hydrodynamics to heat transfer, representing the governing equations of fluid flow in a square domain. The Boussinesq–Darcy flow with Cu-water nanofluid is considered. The dimensionless partial differential equations are solved numerically using finite difference method based on alternating direction implicit scheme. The cavity is differentially heated by constant heat flux, while the top and bottom walls are insulated. The authors examined the effects of gravity amplitude (λ), vibration frequency (σ), tilt angle (α) and Rayleigh number (Ra) on flow and temperature.

The numerical simulations, in the form of streamlines, isotherms, Nusselt number and maximum stream function for different values of amplitude, frequency, tilt angle and Rayleigh number, have revealed an oscillatory behavior in the development of flow and temperature under gravity modulation. An increase of amplitude from 0.5 to 1 intensifies the flow stream (from |ψ_max| = 21.415 to |ψ_max| = 25.262) and improves heat transfer (from Nu¯ = 17.592 to Nu¯ = 20.421). Low-frequency vibration below 50 has a significant impact on the flow and thermal distributions. However, once this threshold is exceeded, the flow weakens, leading to a gradual decrease in heat transfer rate. The inclination angle is an effective parameter for controlling the flow and temperature characteristics. Thus, transitioning the tilt angle from 30° to 60° can increase the flow velocity (from 22.283 to 23.288) while reducing the Nusselt number (from 16.603 to 13.874). Therefore, by manipulating the combination of vibration and inclination, it is founded that for a fixed frequency value of σ = 100 and for increased amplitude (from 0.5 to 1), the flow intensity at inclination of 60° is boosted, and an increase of the heat transfer rate at inclination of 30° is also observed. Convective thermal instabilities may arise depending on the different key factors.

To the best of the authors’ knowledge, this study is original in its examination of the combined effects of modulated gravity and cavity inclination on free convection in nanofluid porous media. It highlights the crucial roles of these two important factors in influencing flow and heat transfer properties.

This study aims to delve into the coupled mixed convective heat transport process within a grooved channel cavity using CuO-water nanofluid and an inclined magnetic field. The cavity undergoes isothermal heating from the bottom, with variations in the positions of heated walls across the grooved channel. The aim is to assess the impact of heater positions on thermal performance and identify the most effective configuration.

Numerical solutions to the evolved transport equations are obtained using a finite volume method-based indigenous solver. The dimensionless parameters of Reynolds number (1 ≤ Re ≤ 500), Richardson number (0.1 ≤ Ri ≤ 100), Hartmann number (0 ≤ Ha ≤ 70) and magnetic field inclination angle (0° ≤ γ ≤ 180°) are considered. The solved variables generate both local and global variables after discretization using the semi-implicit method for pressure linked equations algorithm on nonuniform grids.

The study reveals that optimal heat transfer occurs when the heater is positioned at the right corner of the grooved cavity. Heat transfer augmentation ranges from 0.5% to 168.53% for Re = 50 to 300 compared to the bottom-heated case. The magnetic field’s orientation significantly influences the average heat transfer, initially rising and then declining with increasing inclination angle. Overall, this analysis underscores the effectiveness of heater positions in achieving superior thermal performance in a grooved channel cavity.

This concept can be extended to explore enhanced thermal performance under various thermal boundary conditions, considering wall curvature effects, different geometry orientations and the presence of porous structures, either numerically or experimentally.

The findings are applicable across diverse fields, including biomedical systems, heat exchanging devices, electronic cooling systems, food processing, drying processes, crystallization, mixing processes and beyond.

This work provides a novel exploration of CuO-water nanofluid flow in mixed convection within a grooved channel cavity under the influence of an inclined magnetic field. The influence of different heater positions on thermomagnetic convection in such a cavity has not been extensively investigated before, contributing to the originality and value of this research.

This investigation delves into the rationale behind the preferential applicability of the non-Newtonian nanofluid model over alternative frameworks, particularly those incorporating porous medium considerations. The study focuses on analyzing the mass and heat transfer characteristics inherent in the Williamson nanofluid’s non-Newtonian flow over a stretched sheet, accounting for influences such as chemical reactions, viscous dissipation, magnetic field and slip velocity. Emphasis is placed on scenarios where the properties of the Williamson nanofluid, including thermal conductivity and viscosity, exhibit temperature-dependent variations.

Following the use of the OHAM approach, an analytical resolution to the proposed issue is provided. The findings are elucidated through the construction of graphical representations, illustrating the impact of diverse physical parameters on temperature, velocity and concentration profiles.

Remarkably, it is discerned that the magnetic field, viscous dissipation phenomena and slip velocity assumption significantly influence the heat and mass transmission processes. Numerical and theoretical outcomes exhibit a noteworthy level of qualitative concurrence, underscoring the robustness and reliability of the non-Newtonian nanofluid model in capturing the intricacies of the studied phenomena.

Available studies show that no work on the Williamson model is conducted by considering viscous dissipation and the MHD effect past over an exponentially stretched porous sheet. This contribution fills this gap.

In this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the combined power of deep learning (DL) and physics-based methods (PBM) to create an active virtual replica of the physical system.

To achieve this goal, we introduce a deep neural network (DNN) as the digital twin and a Finite Element (FE) model as the physical system. This integrated approach is used to address the challenges of controlling an unsteady heat transfer problem with an integrated feedback loop.

The results of our study demonstrate the effectiveness of the proposed digital twinning approach in regulating the maximum temperature within the system under varying and unsteady heat flux conditions. The DNN, trained on stationary data, plays a crucial role in determining the heat transfer coefficients necessary to maintain temperatures below a defined threshold value, such as the material’s melting point. The system is successfully controlled in 1D, 2D and 3D case studies. However, careful evaluations should be conducted if such a training approach, based on steady-state data, is applied to completely different transient heat transfer problems.

The present work represents one of the first examples of a comprehensive digital twinning approach to transient thermal systems, driven by data. One of the noteworthy features of this approach is its robustness. Adopting a training based on dimensionless data, the approach can seamlessly accommodate changes in thermal capacity and thermal conductivity without the need for retraining.

The purpose of this paper is to analyze the mechanism of nanofluid enhanced heat transfer in microchannels and promote the application of nanofluids in industrial processes such as solar collectors, electronic cooling and automotive batteries.

The two-phase lattice Boltzmann method was used to calculate the flow and heat transfer characteristics of Al₂O₃ nanofluids in a microchannel at Re = 50. By comparing the simulation results of pure water, nanofluids without calculated nanoparticle-fluid interaction forces and nanofluids with calculated nanoparticle-fluid interaction forces, the effects of physical properties improvement and interaction forces on flow and heat transfer are quantified.

The findings show that the nanofluid (φ = 3%, R = 10 nm) increases the average Nusselt number by 22.40% at Re = 50. In particular, 16.16% of the improvement relates to nanoparticles optimizing the thermophysical parameters of the base fluid. The remaining 6.24% relates to the disturbance of the thermal boundary layer caused by the interaction between nanoparticles and the base fluid. Moreover, the nanoparticle has a negligible effect on the average Fanning friction factor. Ultimately, we conclude that the nanofluid is an excellent heat transfer working medium based on its performance evaluation criterion, PEC = 1.225.

To the best of the authors' knowledge, this research quantifies for the first time the contribution of nanoparticle-liquid interactions and nanofluids physical properties to enhanced heat transfer, advancing the knowledge of the nanoparticle's behavior in liquid systems.

The purpose of this study is to numerically investigate the geometric influence of different corrugation profiles (rectangular, trapezoidal and triangular) of varying heights on the flow and the natural convection heat transfer process over isothermal plates.

This work is an extension and finalization of previous studies of the leading author. The numerical methodology was proposed and experimentally validated in previous studies. Using OpenFOAM® and other free and open-source numerical-computational tools, three-dimensional numerical models were built to simulate the flow and the natural convection heat transfer process over isothermal corrugation plates with variable and constant heights.

The influence of different geometric arrangements of corrugated plates on the flow and natural convection heat transfer over isothermal plates is investigated. The influence of the height ratio parameter, as well as the resulting concave and convex profiles, on the parameters average Nusselt number, corrected average Nusselt number and convective thermal efficiency gain, is analyzed. It is shown that the total convective heat transfer and the convective thermal efficiency gain increase with the increase of the height ratio. The numerical results confirm previous findings about the predominant effects on the predominant impact of increasing the heat transfer area on the thermal efficiency gain in corrugated surfaces, in contrast to the adverse effects caused on the flow. In corrugations with heights resulting in concave profiles, the geometry with triangular corrugations presented the highest total convection heat transfer, followed by trapezoidal and rectangular. For arrangements with the same area, it was demonstrated that corrugations of constant and variable height are approximately equivalent in terms of natural convection heat transfer.

The results allowed a better understanding of the flow characteristics and the natural convection heat transfer process over isothermal plates with corrugations of variable height. The advantages of the surfaces studied in terms of increasing convective thermal efficiency were demonstrated, with the potential to be used in cooling systems exclusively by natural convection (or with reduced dependence on forced convection cooling systems), including in technological applications of microelectronics, robotics, internet of things (IoT), artificial intelligence, information technology, industry 4.0, etc.

To the best of the authors’ knowledge, the results presented are new in the scientific literature. Unlike previous studies conducted by the leading author, this analysis specifically analyzed the natural convection phenomenon over plates with variable-height corrugations. The obtained results will contribute to projects to improve and optimize natural convection cooling systems.