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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 study aims to assess the heater and cooler positional impacts systematically using four different quadrantal cavities filled with hybrid nanofluid, keeping the curved surface adiabatic under the orientated magnetic fields. Both heat transfer and entropy generation analyses are performed for a hybrid nanofluid flow in a quarter circular cavity considering different orientations of magnetic fields. The investigation is focused to assess the heater and cooler positional impacts systematically using four different quadrantal cavities (first to fourth quadrantal cavities), keeping the curved surface always adiabatic. The impacts of pertinent variables like Rayleigh number, Hartmann number and volumetric concentration of hybrid nanofluid on heat transfer characteristics are in consideration with the second law of thermodynamics. The analysis includes the thermal, viscous and magnetic aspects of entropy generation.

After validating against the experimental results, the present work explores numerically following the Galerkin weighted finite element technique. The solution is obtained through an iterative process satisfying the convergence limit of 10⁻⁸ and 10⁻¹⁰ for the maximum residuals and the mass defect, respectively.

It revealed that the mutual exchange of heater-cooler positions on the adjacent straight edges of the quadrant cavity does not have any impact on the flow direction. Although the magnitude of flow velocity enhances, the sidewall plays a decision-making role in the formation of a single circulation vortex. It also shows that thermal entropy production is the main cause behind thermodynamic irreversibility. The second or third quadrantal arrangement could have been opted as the best configuration of the heater-cooler position for achieving superior heat transfer. The Lorentz force plays a great role to moderate the heat transfer process. The maximum entropy generation is located, as expected, at the heating-cooling junction point.

There are plenty of prospects for extension of the present research concept numerically or experimentally, adopting three-dimensional analysis, working fluids, boundary conditions, etc. In fact, the study could be carried out for unsteady or turbulent fluid flow.

As the position of the heated source and cold sink on the enclosure geometry can significantly alter the thermo-fluid phenomena, this kind of analysis is of utmost relevance for the further development of efficient heating/cooling arrangements and proper management of the devices subjected to magnetic field applications. This original contribution could be a potentially valuable source for future research and exploration pertaining to a thermal system or device, like heat exchangers, solar collectors, thermal storage, electronic cooling, food and drying technologies and others.

In the literature, an inadequate number of works have focused on a quadrantal cavity, mostly considering the first quadrant of the circle. However, during practical applications, it is possible that the cavity can take the shape of the other three quadrants too, and the corresponding knowledge on relative performance is still missing. Furthermore, the present investigation includes the existence of magnetic fields at various orientations. The impact analysis of this field-induced Lorentz force on the nanofluid thermal performance is another major contribution from the present work that would enrich the domain knowledge and could be useful for thermal system engineers.

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 focus on a thermo-fluid flow in a partially driven cavity (PDC) using Cu-water nanoliquid, magnetic field and porous substance. The cooling and sliding motion are applied on the upper half of the vertical walls and the bottom wall is heated. Thermal characteristics are explored to understand magnetohydrodynamic convection in a nanoliquid filled porous system from a fundamental viewpoint. The governing parameters involved to cater to the moving speed of the sidewalls and partial translation direction are the relative strength of thermal buoyancy, porous substance permeability, magnetic field intensity, nanoparticle suspension and orientation of the cavity.

The coupled transport equations of the problem are solved using an in-house developed finite volume-based computing code. The staggered nonuniform grids along the x and y directions are used. The SIMPLE algorithm technique is considered for the iterative solution of the discretized equations with the convergence check of the continuity mass defect below 10^–10.

The present study unveils that the heat transfer enhances at higher Ri with the increasing value of Re, irrespective of the presence of a porous substance or magnetic field or the concentration of nanofluid. Apart from different flow controlling parameters, the wall motions have a significant contribution to the formation of flow vortices and corresponding heat transfer. Orientation of the cavity significantly alters the transport process within the cavity. The upward wall velocity for both the sidewalls could be a better choice to enhance the high heat transfer (approximately 88.39% at Richardson and Reynolds numbers, respectively, 0.1 and 200).

Considering other multi-physical scenarios like porous layers, conducting block, microorganisms and the present investigation could be further extended to analyze a problem of complex flow physics.

In this study, the concept of partially driven wall motion has been adopted under the Cu-water nanoliquid, magnetic field, porous substance and oblique enclosure. All the involved flow-controlling parameters have been experimented with under a wide parametric range and associated thermo-flow physics are analyzed in detail. This outcome of this study can be very significant for designing as well as controlling thermal devices.

The convective process in a partially driven cavity (PDC) with the porous medium has not been investigated in detail considering the multi-physical scenarios. Thus, the present effort is motivated to explore the thermal convection in such an oblique enclosure. The enclosure is heated at its bottom and has partially moving-wall cold walls. It consists of various multi-physical conditions like porous structure, magnetic field, Cu–H₂O nanoliquid, etc. The system performance is addressed under different significant variables such as Richardson number, Reynolds number, Darcy number, Hartmann number, nanoliquid concentration and orientation of cavity.

The purpose of this study is to carry out a comprehensive analysis of magneto-hydrodynamics (MHD), nanofluidic flow dynamics and heat transfer as well as thermodynamic irreversibility, within a novel butterfly-shaped cavity. Gaining a thorough understanding of these phenomena will help to facilitate the design and optimization of thermal systems with complex geometries under magnetic fields in diverse applications.

To achieve the objective, the finite element method is used to solve the governing equations of the problem. The effects of various controlling parameters such as butterfly-shaped triangle vertex angle (T), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ ) on the hydrothermal performance are analyzed meticulously. By investigating the effects of these parameters, the authors contribute to the existing knowledge by shedding light on their influence on heat and fluid transport within butterfly-shaped cavities.

The major findings of this study reveal that the geometrical shape significantly alters fluid motion, heat transfer and irreversibility production. Maximum heat transfer, as well as entropy generation, occurs when the Rayleigh number reaches its maximum, the Hartmann number is minimized and the angle of the magnetic field is set to 30° or 150°, while the butterfly wings angle or vertex angle is kept at a maximum of 120°. The intensity of the magnetic field significantly controls the heat flow dynamics, with higher magnetic field strength causing a reduction in the flow strength as well as heat transfer. This configuration optimizes the heat transfer characteristics in the system.

Further research can be expanded on this study by examining thermal performance under different curvature effects, orientations, boundary conditions and additional factors. This can be accomplished through numerical simulations or experimental investigations under various multiphysical scenarios.

The geometric configurations explored in this research have practical applications in various engineering fields, including heat exchangers, crystallization processes, microelectronic devices, energy storage systems, mixing processes, food processing, air-conditioning, filtration and more.

This study brings value by exploring a novel geometric configuration comprising the nanofluidic flow, and MHD effect, providing insights and potential innovations in the field of thermal fluid dynamics. The findings contribute a lot toward maximizing thermal performance in diverse fields of applications. The comparison of different hydrothermal behavior and thermodynamic entropy production under the varying geometric configuration adds novelty to this study.

The purpose of this study is to investigate the influence of enclosure shape on magnetohydrodynamic (MHD) nanofluidic flow, heat transfer and irreversibility in square, trapezoidal and triangular thermal systems under fluid volume constraints, with the aim of optimizing thermal behavior in diverse applications.

The study uses numerical simulations based on a finite element-based technique to analyze the effects of the Rayleigh number (Ra), Hartmann number (Ha), magnetic field orientation (γ) and nanoparticle concentration (ζ) on heat transfer characteristics and thermodynamic entropy production.

The key findings reveal that the geometrical design significantly influences fluid velocity, heat transfer and irreversibility. Trapezoidal thermal systems outperform square systems, while triangular systems achieve optimal enhancement. Nanoparticle concentration enhances heat transfer and flow strength at higher Rayleigh numbers. The magnetic field intensity has a significant impact on fluid flow and heat transport in natural convection, with higher Hartmann numbers resulting in reduced flow strength and heat transfer. The study also highlights the influence of various parameters on thermodynamic entropy production.

Further research can explore additional geometries, parameters and boundary conditions to expand the understanding of enclosure shape effects on MHD nanofluidic flow and heat transfer. Experimental validation can complement the numerical simulations presented in this study.

This study provides valuable insights into the impact of enclosure shape on heat transfer performance in MHD nanofluid flow systems. The findings contribute to the optimization of thermal behavior in applications such as electronics cooling and energy systems. The comparison of different enclosure shapes and the analysis of thermodynamic entropy production add novelty to the study.

This study aims to investigate the influence of wall curvature in a semicircular thermal annular system on magneto-nanofluidic flow, heat transfer and entropy generation. The analysis is conducted under constant cooling surface and fluid volume constraints.

The mathematical equations describing the thermo-fluid flow in the semicircular system are solved using the finite element technique. Four different heating wall configurations are considered, varying the undulation numbers of the heated wall. Parametric variations of bottom wall undulation (f), buoyancy force characterized by the Rayleigh number (Ra), magnetic field strength represented by the Hartmann number (Ha) and inclination of the magnetic field (γ) on the overall thermal performance are studied extensively.

This study reveals that the fluid circulation strength is maximum in the case of a flat bottom wall. The analysis shows that the bottom wall contour and other control parameters significantly influence fluid flow, entropy production and heat transfer. The modified heated wall with a single undulation exhibits the highest entropy production and thermal convection, leading to a heat transfer enhancement of up to 21.85% compared to a flat bottom. The magnetic field intensity and orientation have a significant effect on heat transfer and irreversibility production.

Further research can explore a wider range of parameter values, alternative heating wall profiles and boundary conditions to expand the understanding of magneto-nanofluidic flow in semicircular thermal systems.

This study introduces a constraint-based analysis of magneto-nanofluidic thermal behavior in a complex semicircular thermal system, providing insights into the impact of wall curvature on heat transfer performance. The findings contribute to the design and optimization of thermal systems in various applications.

The purpose of this paper is to characterise the failure model of a system that is covered by a two‐dimensional warranty, one dimension depicting time and the other usage. Specifically, the authors study the effect of use‐rate on system life when each constituent component life is described by an accelerated‐failure‐time (AFT) type model.

The paper evaluates the effect of use‐rate on the expected failure time of a system having different internal configurations involving components. Firstly, the coherent structure as well as modules with redundant structures (standby and load‐sharing) are analysed, whereby component failures are assumed to be conditionally independent. Study systems of some basic configurations with a general dependence structure among component failure instances are also studied.

The results strongly indicate that, irrespective of the internal component‐configuration of the system, the models should posses the property that the expected failure time given the use‐rate is a non‐increasing function of use‐rate. The study also reveals that dependence among components arises quite naturally due to variability in use‐rate, even when all other factors of the usage environment are held constant.

The findings of this paper are the outcome of a theoretical investigation. Although they are supported by some real‐life cases as cited from the literature, it is important that they are validated through more examples.

The results would find a direct application in the analysis of two‐dimensional warranty policies as well as the reliability assessment of consumer durables.

The proposed approach to the characterisation of a bivariate failure model (indexed by time and usage) is quite realistic. This investigation may lead to the development of a more suitable model.

This study aims to investigate the impact of different heater geometries (flat, rectangular, semi-elliptical and triangular) on hybrid nanofluidic (Cu–Al₂O₃–H₂O) convection in novel umbrella-shaped porous thermal systems. The system is top-cooled, and the identical heater surfaces are provided centrally at the bottom to identify the most enhanced configuration.

The thermal-fluid flow analysis is performed using a finite volume-based indigenous code, solving the nonlinear coupled transport equations with the Darcy number (10^–5 ≤ Da ≤ 10^–1), modified Rayleigh number (10 ≤ Ra_m ≤ 10⁴) and Hartmann number (0 ≤ Ha ≤ 70) as the dimensionless operating parameters. The semi-implicit method for pressure linked equations algorithm is used to solve the discretized transport equations over staggered nonuniform meshes.

The study demonstrates that altering the heater surface geometry improves heat transfer by up to 224% compared with a flat surface configuration. The triangular-shaped heating surface is the most effective in enhancing both heat transfer and flow strength. In general, flow strength and heat transfer increase with rising Ra_m and decrease with increasing Da and Ha. The study also proposes a mathematical correlation to predict thermal characteristics by integrating all geometric and flow control variables.

The present concept can be extended to further explore thermal performance with different curvature effects, orientations, boundary conditions, etc., numerically or experimentally.

The present geometry configurations can be applied in various engineering applications such as heat exchangers, crystallization, micro-electronic devices, energy storage systems, mixing processes, food processing and different biomedical systems (blood flow control, cancer treatment, medical equipment, targeted drug delivery, etc.).

This investigation contributes by exploring the effect of various geometric shapes of the heated bottom on the hydromagnetic convection of Cu–Al₂O₃–H₂O hybrid nanofluid flow in a complex umbrella-shaped porous thermal system involving curved surfaces and multiphysical conditions.

This study aims to numerically examine the influence of various geometric parameters of a novel W-shaped porous cavity undergoing hybrid nanofluid-based magnetohydrodynamic mixed convection. The W-shaped cavity is modified from the classical trapezoidal cavity by constructing a triangular shape at its bottom. This cavity is isothermally active at the bottom, with different numbers and heights of the triangular peak (or undulation). The heated hybrid nanofluid (Cu–Al₂O₃–H₂O) flow is cooled through the translating top wall. Inclined sidewalls are thermally insulated. To compare the impacts of change in geometric parameters, a square cavity under similar boundary conditions is also simulated. This study is carried out systematically addressing the various influences from a range of parameters like side angles (γ), number (m) and height (λ) of the bottom undulation, Reynolds number (Re), Richardson number (Ri), Darcy number (Da), Hartmann number (Ha), hybrid nanoparticles volume fraction (φ) on the overall thermal performance of the cavity.

Applying the finite volume approach, the transport equations involving multiphysical conditions like porous substance, hybrid nanofluid, magnetic field and shearing force are solved numerically by using a written FORTRAN-based code following the SIMPLE algorithm. The algebraic equations are solved over all the control volumes in an iterative process using the alternate direction implicit scheme and the tri-diagonal matrix algorithm. The converged solution of the iterative process is obtained when the relative error levels satisfy the convergence criterion of 10^–8 and 10^–10 for the maximum residuals and the mass defect, respectively.

It is revealed that an increase in the bottom undulation height always improves the thermal energy transfer despite the reduction of fluid volume. Thermal energy transfer significantly depends on the heating and cooling surface lengths, fluid volume in the cavity and the magnitude of the bottom undulation height of the W-shaped cavity. With the increase in bottom undulation height, effective heating length increases by ∼28%, which leads to a ∼15% reduction in the effective volume of the working fluid and a gain in heat transfer by ∼56.48%. In general, the overall thermal energy transport is improved by increasing Re, Ri and Da; whereas it is suppressed by increasing Ha.

There are many opportunities for future research experimentally or numerically, considering different curvature effects, orientations of the geometry, working fluids, boundary conditions, etc. Furthermore, this study could be extended by considering unsteady flow or turbulent flow.

In many modern systems/processes pertaining to materials processing, continuous casting, food processing, chemical reactors, biomedical applications, etc. fine control in the transport process is a major concern. The findings of this analysis can effectively be useful for other applications for getting more control features in terms of achieving the operational objectives. The approach of the system analysis (considering geometrical size parameters to delve into the underlying transport physics) and the obtained simulated results presented in the work can usefully be applicable to similar thermal systems/devices such as materials processing, thermal mixing, chemical reactors, heat exchangers, etc.

From the well-documented and vast pool of literature survey, it is understood that there exists no such investigation on the considered geometry and study. This study contributes a lot to understanding magnetic field moderated thermofluid flow of a hybrid nanofluid in a porous medium filled W-shaped cavity, in consideration of different geometrical shape parameters (undulation peak numbers at bottom wall, peak heights, side angles and heating and cooling length). Findings brought by this study provide great insights into the design and operation under various ranges of multiphysical thermofluid-flow processing phenomena.