This work aims to improve heat transmission a fundamental component of engineering and industrial processes, by examining entropy formation in magnetohydrodynamic natural convection inside an enclosure containing a saturated porous material under circumstances of local thermal non-equilibrium. The study utilizes an Al2O3–Cu/water hybrid nanofluid, with a cross-shaped obstacle and thermally elevated corners. The model employs a two-phase nanofluid methodology, the local thermal non-equilib rium approximation, and Darcy’s law to characterize the behavior of the porous medium. Numerical solutions to the governing partial differential equations are derived using the finite difference technique, with validation against prior work demonstrating strong concordance. The research investigates heat transfer rates and micropolar hybrid nanofluid flow by illustrating contours of nanofluid flow, isotherms for both fluid and solid phases, and distributions of stream function, temperature, and nanoparticle volume percent. Results demonstrate that positive heat sources (Q = 5) augment convective currents, whereas negative heat sinks (Q = − 15) diminish buoyancy effects and decrease efficiency. Moreover, elevating nanoparticle concentration (ϕ) enhances ther mal conductivity, markedly augmenting heat transfer efficiency in convection-dominated environments. The Cu-based hybrid nanoparticles demonstrated superior efficacy compared to Al2O3 by providing increased thermal conductivity, improved heat transfer, and less entropy production. The results underscore the need of optimizing heat transfer processes to reduce entropy generation and fluid friction irreversibility, thereby improving the efficiency of thermal systems.

Thecurrentmodeloutlinesthepropertiesofamicropolarhybridnanofluid(titaniumdioxide-copper/water)flowingthroughan inclined wavy porous cavity. The Cattaneo-Christov equation is utilized to describe the heated circular obstacle and heat flux within the cavity. Additionally, thermal radiation is taken into account. Buoyancy, which is affected by a consistent magnetic f ield(B0)atanangleandheatradiation(Rd),istheprimaryforcethatdrivestheflow.Thetemperatureoftheleftandrightwalls of the cavity is lower compared to the other sides, which are insulated and contain a heated circular obstacle. The governing partial differential equations (PDEs) are solved using the finite difference approach and are expressed in terms of streamlines, isotherms, iso-micro-rotations, vertical and micropolar velocity, average and local Nusselt number. The obtained results are confirmedwithpriornumericalinvestigations.Thepaperdiscussesseveralcharacteristics,includingtheheatsource,Hartmann number, thermal radiation, undulations, vortex viscosity parameter, and radius of the circular obstacle. As the heat-generating parameter rises, the vertical and horizontal walls observe a corresponding rise in the local Nusselt number. The vertical and micropolar velocities exhibit a diminishing trend as the Hartmann number (Ha) values increase. The average Nusselt number increases as the value of thermal radiation (Rd) rises. Wavy cavity analysis is employed in applications like cooling systems, building design, and cable systems.Thisresearchfacilitates innovative cooling technologies for high-performance computing, renewable energy systems, and next-generation automotive thermal managemen

Efficient heat transfer in inclined enclosures is critical for applications in thermal management, energy storage, and electronic cooling, yet the combined effects of micropolar nanofluids, porous media, and electromagnetic forces remain underexplored. This study investigates conjugate convective heat transfer in a porous inclined cavity filled with micropolar nanofluid under a tilted Lorentz force, where local thermal non-equilibrium is assumed between fluid and solid phases. The governing non linear equations are solved using the finite difference method (FDM), with adiabatic vertical walls and thermally conductive horizontal walls. To reduce computational cost, an artificial neural network (ANN) is trained on FDM-generated data to predict local Nusselt numbers. The results show that increasing the thickness of the solid wall from 0.05 to 0.3 reduces the maximum temperature by up to 84.28%, indicating improved thermal insulation characteristics. Additionally, higher solid volume fractions (up to 0.2) and stronger micropolar effects (vortex viscosity ratio up to 2.0) increase thermal resistance, resulting in a reduction in heat transfer of approximately 20%. Furthermore, enhancing the porosity of the medium from 0.1 to 0.9 leads to a 76.67% improvement in convective flow. This work advances the state of the art by coupling micropolar nanofluid dynamics, porous media, and tilted magnetic fields in inclined enclosures—an area not previously addressed with such detail. The integration of ANN with physics-based modeling offers a novel, high-fidelity, and computationally efficient framework for the optimization of complex thermal systems.

The significance of heat transfer and nanofluid flow in cavities with local heaters is investigated in the present study, crucial in numerous applications in engineering. The research focuses on the magnetohydrodynamic (MHD) with natural convection f low of Cu-water nanofluid inside a square cavity that includes a centrally positioned adiabatic block in square form. The enclosure features heated sections located proximate to all the corners (referred to as heated corners) with both the left and right wall sections being cooled. On the top and bottom walls, the remaining segments are adiabatic. This configuration sets the stage for exploring heat transfer dynamics and fluid behavior within the porous medium, offering insights into the thermal interactions within the cavity. The mathematical formulation of the problem is detailed in the subsequent section. Notably, it is clear that as heat source lengths increase, the local Nu number does as well (B) in all cases. The overall entropy generation is observed to diminish with a rise in the fraction of nanoparticle volume and the Rayleigh number. As the Hartmann number’s volume fraction rises, the average Nusselt number falls. Although the percentage of growth is higher for the rate of thermal performance, increasing the Darcy numbers improves the nanoparticle volume fraction. By raising the volume percentage of the nanoparticles, the total entropy creation is rising. The average Nu number falls with rising magnetic field strength

Thecurrent contributionemphasizesentropygenerationdue tobio-convection(Cu?TiO2)/H2O-modifiednano-liquid flowthroughtheL-shapedcavitywiththreeobstaclesconsideringtheaspectofgyrotacticmicroorganisms.Theactive sectionsofthebottomhorizontalandleftverticalwallsarepreservedcoolwhiletheotherportionsoftheporouscavityare insulated.ThefinitemethodisadoptedtosimulatethedimensionlessPDEsofthemodel.Theresultsdemonstratedhowthe influenceofthebio-convectionfactorsincreasesthedensityofmotilemicroorganisms.Ithasbeennotedthatthelocaland averageheat transmissionrateshaveincreasedwithhighervaluesof thelengthofcoldparts(heatsink), theverticaland horizontalwalls’ crest lengths, andnanoparticlevolume fraction. Largevalues of theRayleighnumber diminish the thermalperformancerate.Entropygeneration,localNusseltandSherwoodnumbers,anddensityofmotilemicroorganisms arealsoargued.

Inclinedsquarecavitiesplayacritical role inengineeringapplications,partic ularlyinthermalmanagement,energystorageandelectroniccooling,whereinclinationangles in°uence convectiveheat transfer.This studyexamines conjugate convectiveheat transfer withinaninclinedsquarecavity¯lledwithmicropolarnano°uidsunderatiltedLorentzforce usinga two-phasenano°uidmodel.The systemincludes aheat-generatingporousmedium underthermalnonequilibrium, introducingcomplexdynamics.Factorssuchasthermalbuoy ancy,°uid{solidheattransfercoe±cientandmicropolar°uidpropertiesareanalyzedfortheir impact onheat transfer e±ciency.Methods:The studyuses the¯nitedi®erencemethod (FDM) to solvenonlinear equations governingconvective°owandheat transfer.Physica

This study investigates the thermal dynamics of a C-shaped, wavy, porous cavity filled with Al₂O₃-Cu/H₂O hybrid nanofluids, influenced by an inclined magnetic field and a heat source/sink. The governing equations are non- dimensionalized and resolved using the finite difference method in a proprietary MATLAB solver. The study investigates the influence of numerous dimensionless parameters such as length of heat position(B = 0.2, 0.4, 0.8), heat source/sink (Q = 4, 0, 1), Porosity ( ∈ =0.1, 0.3, 0.9), Rayleigh number(Ra = 10, 100, 10000), Hartmann number(Ha = 0, 25, 50),length of a cavity (H = 0.5, 10, 100), length of ED/H (L2 = 0.2, 0.4, 0.6) and distance of AD/H (L1 = 0.2, 0.4, 0.6)are analyzed. The findings demonstrate that an elevated Rayleigh number augments convection, whilst increased porosity promotes heat transfer efficiency. The Al₂O₃-Cu/H₂O hybrid nanofluids markedly improve heat transfer owing to their exceptional thermal conductivity. The average Nusselt number validates the efficacy of hybrid nanofluids in enhancing thermal performance. The results indicate that hybrid nanofluids enhance heat transfer, while magnetic fields hinder convection, and the cavity shape in f luences flow patterns. By limiting convective flow, an increased Hartmann number leads to heat transport that is dominated by conduction. Additionally, the length of the heater has a direct influence on the generation of vortices and the enhancement of localized heat and heat transfer.

Purpose– Thispaperaimstoexplore,through a numerical study, buoyant convective phenomena in a porous cavity containing a hybrid nanofluid, taking into account the local thermal nonequilibrium (LTNE) approach. The cavity contains a solid block in the shape of a cross (þ). It will be helpful to develop and optimize the thermal systems with intricate geometries under LTNEconditions for a variety of applications

Thisstudynumericallyinvestigatesinclinedmagneto-hydrodynamicnaturalconvectioninaporouscavityfilledwithnanofluid containinggyrotacticmicroorganisms.Thegoverningequationsarenondimensionalizedandsolvedusingthefinitevolume method. The simulations examine the impact of keyparameters suchas heat source lengthandposition, Peclet number, porosity,andheatgeneration/absorptiononflowpatterns, temperaturedistribution,concentrationprofiles,andmicroorganism rotation.Resultsindicatethatextendingtheheatsourcelengthenhancesconvectivecurrentsandheattransferefficiency,while optimizing the heat sourceposition reduces entropygeneration.Higher Peclet numbers amplify convective currents and microorganismdistribution complexity.Variations inporosityandheat generation/absorption significantly influence flow dynamics. Additionally, the artificial neural networkmodel reliably predicts themeanNusselt andSherwood numbers ( ) Nu Sh & ,demonstratingitseffectiveness for suchanalyses.Thesimulationresults reveal that increasingtheheat source lengthsignificantlyenhancesheat transfer, asevidencedbya15%increaseinthemeanNusseltnumber.