Darcy Number Research Articles

Investigation of the thermo-convective characteristics of a flow passing through a partially heated channel filled with a porous medium saturated with a hybrid nanofluid

As part of this study, we used three-dimensional numerical simulations to look into mixed thermal convection in a nanofluid that flows in a partially heated cylindrical channel without being able to be compressed. Our study specifically focused on two distinct configurations: the investigation of mixed thermal convection in the laminar regime using a hybrid nanofluid under both porous and nonporous conditions. The study adds to the scientific understanding of heat transfer processes in complex fluid–solid systems and contributes to the ongoing advancement of knowledge in the fields of thermal engineering and nanofluid research. This research involved investigations into varying nanoparticle volume fractions (0%–4%), Reynolds numbers within the range of 200–800, Richardson numbers between 1 and 2, and a fixed Darcy number of Da = 10 − 8 . Our analytical methodology involved a thorough assessment of temperature, velocity, and heat distributions within the hybrid nanofluid. The study we did showed that adding nanoparticles made the base fluid’s effective thermal conductivity much better. This made the transfer rate go up. Specifically, the thermal conductivity of the Al2O3-CuO-water hybrid nanofluid displayed noteworthy improvement. Furthermore, the incorporation of a porous matrix substantially enhanced the overall efficiency of the heat transfer process.

Variable thermal conductivity and mass diffusivity effects in a free convective flow of doubly stratified non-darcian porous medium over a vertical plate

The research in this article is carried out to study incompressible and unsteady free convective flow on a semi-infinite isothermal vertical plate in a doubly stratified non-Darcian porous media with variable mass diffusivity and variable thermal conductivity. The governing non-linear partial differential equations of flow were calculated by applying an implicit finite difference scheme of Crank-Nicolson type. Various parametric impacts on concentration profiles, temperature, velocity, as well Sherwood number, Nusselt number and skin friction, were examined and presented in graphs. It is examined that there exists a significant temperature decrease for high Darcy number in stratified fluids. Also, it is detected that the presence of stratification produces a considerable drop in skin friction while increases the mass and heat transfer rate. Comparison of current outcomes well agreed with the available solutions.

Impact of Local Thermal Non-Equilibrium and Gravity Fluctuations on the Onset of a Darcy-Brinkman Porous Convection

The numerical investigation of the Darcy-Brinkman convective problem with gravity fluctuations in a Local Thermal Nonequilibrium (LTNE) model is conducted. Utilizing linear stability analysis, the convective problem is explored, and the numerical values of the Rayleigh and wave numbers for onset convection are computed through the one-term Galerkin approach. Three distinct types of gravity fluctuations (linear, parabolic, and exponential) are considered. The results show the Darcy number and gravity parameter delay the onset of convection. The porosity-scald conductivity ratio and interface heat transfer coefficient have a significant effect on the stability of the configuration. Graphical representations depict the effects of various parameters, highlighting the significant impacts of incorporating gravity fluctuations and non-equilibrium conditions in determining convection stability thresholds.

Thermal Analysis of a Casson Boundary Layer Flow over a Penetrable Stretching Porous Wedge

This work aims to analyze the Casson thermal boundary layer flow over an expanding wedge in a porous medium with convective boundary conditions and ohmic heating. Moreover, the effects of porosity and viscous dissipation are studied in detail and included in the analysis. The importance of this study is due to its applications in biomedical engineering where the analysis of behavior of non-Newtonian blood flow in arteries and veins is desired. Within the context of blood flow, it is also applicable to many other fields, for instance, radiative therapy, MHD generators, soil machines, melt-spinning, and insulation processes. The modeled problem is a set of PDEs, which is nondimensionalized to derive a nonlinear boundary value problem (BVP). The obtained BVP is solved using the shooting technique, endowed with the order four Runge-Kutta and Newton methods. The impact of different parameters on the momentum and temperature fields is investigated along with two important parameters of physical significance, i.e., the Nusselt number and the surface drag force. Results are validated, and an excellent agreement is seen for the parameters of interest using MATLAB built-in function bvp4c. A significant finding is that by increasing the Casson liquid parameter, the velocity decreases as the wedge expands quicker than the free stream velocity at R=2. However, the velocity increases for the case when R=0.1. A decrease in the Darcy number increases the temperature profile. Furthermore, the convective parameter accelerated the heat transmission rate, and a rise in the Prandtl number thickens the thermal boundary layer. The findings of this investigation contribute to problems in fluid dynamics and heat transfer that involve studying the behavior of a non-Newtonian fluid with Casson rheological properties near a solid porous wedge surface.

Instability in an anisotropic Brinkman layer due to downward or upward throughflow and purely due to internal heat generation

A linear stability analysis using normal mode technique is applied on an internally heated anisotropic Brinkman porous layer with vertical throughflow. Four internal heat source functions are considered to model the problem with same temperature at the bounding plates. The basic temperature profile due to pure internal heating is seen to be disturbed by throughflow (upward or downward) and the impact of through flow on these profiles is studied. Downward through flow, in particular, is seen to disturb the instability criterion for different profiles. Effect of anisotropy and modified Darcy number on onset of convection is also discussed.

LTNE effects on two‐layer configuration with throughflow

AbstractThe effect of throughflow on the beginning of convective motion in a fluid layer overlying a fluid‐saturated porous layer is examined theoretically in this article under the local thermal nonequilibrium model. We considered boundaries to be insulating to temperature perturbations. The normal mode approach is employed to analyze the governing equation for a composite configuration, with the solution sought through the regular perturbation technique to assess linear stability. The critical Rayleigh number, signifying the initiation of stationary convection, has been determined by solving the system of coupled equations. It is found that the system attains stability with increased porosity–conductivity ratios, regardless of the throughflow direction. This stability is consistently observed for depth ratios of 0.1 and 0.2. However, for higher depth ratios (0.5 and 1.0), the system exhibits dual nature stability when throughflow is present. Further, the stability of the system is enhanced by a graphical depiction illustrating how the throughflow parameter, porosity‐scaled conductivity ratio, depth ratio, Darcy number, and Prandtl number collectively influence the onset of convective motion.

Analytical simulation of Darcy–Forchheimer flow of hybrid nanofluid through cone with nonlinear heat source and chemical reaction

This paper intends to discuss the hybrid nanofluid flow through a cone in a Darcy–Forchheimer porous media, containing base fluid Methanol (CH3OH), nanoparticles of titanium oxide (TiO2) and copper (Cu). We have examined the flow under the influences of mixed convection, viscous dissipation, chemical reaction, and nonlinear heat source. In hybrid nanofluid flow, viscous dissipation and mixed convection play a crucial role in heat exchangers. By accounting for both mixed convection and viscous dissipation, the addition of nanoparticles into a base fluid improves the transfer of heat and optimizes the performance of the cooling system. Using the laws of conservation, governing equations have been constructed. The flow model is converted using the appropriate similarity transformations from partial differential equations to ordinary differential equations. The homotopy analysis method is used to solve the updated system of equations. When Forchheimer inertial drag parameter is increased, the velocity profile decreases, but it rises when the Darcy number is increased. As the value of exponential heat source parameter rises, the temperature profile increases as well. The result exposes that with an increment in nanoparticle volume fraction, temperature profile also rises but velocity profile decreases.

Investigation of free convection in a wavy trapezoidal porous cavity with MWCNT- Fe3O4/Water hybrid nanofluid under MHD effects: Galerkin finite element analysis

Our study focuses on numerically investigating natural convection within a three-dimensional trapezoidal cavity featuring a corrugated hot bottom wall, with a particular emphasis on enhancing heat exchange using a water-based hybrid nanofluid. Employing a steady-state regime assumption, the study considers laminar and incompressible three-dimensional flow. The Darcy-Forchheimer model is incorporated to account for inertial advection effects within the porous layer. Predictions of the thermal and hydrodynamic behaviors of the system are achieved by solving dimensionless equations utilizing the Galerkin Finite Element Method (GFEM). Notably, a range of influential parameters, including the volume fraction of nanoparticles (φ), Darcy number (Da) spanning from 10−5 to 10−2, Hartman number (Ha) across the range of 0–100, φ within the range of 0–0.08, porosity (ε) ranging from 0.2 to 0.9, and Rayleigh numbers (Ra) varying from 103 to 106 was explored. The investigation also evaluates the geometrical impact of the enclosure by considering undulation numbers (N) of the warm bottom ranging from 1 to 4. Our results provide novel quantitative insights. Specifically, we observe an inverse relationship between undulation number (N), Hartman number (Ha), and porosity (ε) with large Rayleigh (Ra) flows, significantly influencing effective heat transfer. Notably, this influence diminishes at lower Ra flows. At the highest Ra, we find that increasing Da, ε, and φ enhances the Nusselt number (Nuavg) by 26 %, 17 %, and 23.5 %, respectively. Conversely, increasing Ha and N reduces Nuavg by 13 % and 40 %, respectively. These findings highlight the nuanced interplay of parameters and offer valuable quantitative data for optimizing heat transfer processes in similar systems.

Numerical Investigation of Double-Diffusive Convection in an Irregular Porous Cavity Subjected to Inclined Magnetic Field Using Finite Element Method

Purpose—This study aims to perform an in-depth analysis of double-diffusive natural convection (DDNC) in an irregularly shaped porous cavity. We investigate the convective heat transfer process induced by the lower wall treated as a heat source while the side walls of the enclosure are maintained at a lower temperature and concentration, and the remaining wall is adiabatic. Various factors, such as the Rayleigh number, Darcy effects, Hartmann number, Lewis number and effects of magnetic inclination are evaluated for their influence on flow dynamics and heat distribution. Design/methodology/approach—After validating the results, the FEM (finite element method) is used to simulate the flow pattern, temperature variations, and concentration by solving the nonlinear partial differential equations with the modified Rayleigh number (104 ≤ Ra ≤ 107), Darcy number (10−4 ≤ Da ≤ 10−1), Lewis number (0.1≤Le≤10), and Hartmann number 0≤Ha≤40 as the dimensionless operating parameters. Findings—The finding shows that the patterns of convection and the shape of the isotherms within porous enclosures are notably affected by the angle of the applied magnetic field. This study enhances our understanding of how double-diffusive natural convection (DDNC) operates in these enclosures, which helps improve heating and cooling technologies in various engineering fields. Research limitations/implications—Numerical and experimental extensions of the present study make it possible to investigate differences in thermal performance as a result of various curvatures, orientations, boundary conditions, and the use of three-dimensional analysis and other working fluids. Practical implications—The geometry configurations used in this study have wide-ranging applications in engineering fields, such as in heat exchangers, crystallization, microelectronics, energy storage, mixing, food processing, and biomedical systems. Originality/value—This study shows how an inclined magnetic field affects double-diffusive natural convection (DDNC) within a porous system featuring an irregularly shaped cavity, considering various multiphysical conditions.

Optimization and sensitivity analysis of hydromagnetic convective heat transfer in a square cavity filled with a porous medium saturated by Ag-MgO/water hybrid nanofluid using response surface methodology

A computational exploration is presented to emphasis on optimization and sensitivity inspection of the unsteady free convective heat transfer flow of hybrid nanofluid in a square cavity under multidirectional periodic magnetic field with aluminum foam porous medium. The vertical walls of the cavity are maintained at constant low temperature whereas the constant as well as the variable thermal conditions on the bottom wall is considered and the top wall is considered as adiabatic. The finite element technique has been applied to solve the governing equations after changing them into dimensionless form. In the numerical simulations, the Ag-MgO/water hybrid nanofluid has been engaged to gain insight into the flow and thermal arenas. The obtained outcomes are exhibited in terms of streamlines, isotherms and average Nusselt number as well as plotting the response surface and contours. The average Nu is displayed in line graphs, response surface and contours graphs as well as tabular form for different flow parameters. Response surface methodology is applied to achieve an optimization procedure to search for the best situation in which the highest heat transfer rate occurs when the distinct model parameters namely Darcy number, porosity and hybrid nanoparticles volume fraction are treated as the sensitivity of the parameters. A correlation equation between the output response and input variables has been derived with the help of response surface methodology. The magnetic field and its path regime the flow decoration of hybrid nanofluid suggestively. The Ag and Ag-MgO nanomaterial with water flow arenas are compared. While considering Ag-H2O nanofluid, the average Nu increases 23.97 % at Ra = 107 with ϕhnp = 0.02 whereas the corresponding increases is 25.68 % if the Ag-MgO/H2O hybrid nanofluid is taken into account. The average Nu upsurges suggestively, as hybrid nanoparticles volume fraction, period number, magnetic field leaning angle, Darcy number and Rayleigh number rises but porosity and Hartmann number have inverse effect. The outcomes showed that the average Nu is more sensitive to the hybrid nanoparticles volume fraction rather than the porosity or Darcy number. Also, it is discovered that the optimum condition arises at Da = 0.001, ε = 0.2 and ϕhnp = 0.02 with the final Nuave = 2358.21.

Soret Effect on Mixed Convection of Casson Fluid Flow in Presence of Porous Media in a Porous Channel

The purpose is to investigate the impact of Soret on free and mixed convective Casson fluid flow in presence of amplification in a porous channel with magnetic field is carried out analytically. The obtained are coupled PDEs are highly nonlinear and are converted to an ODEs by similarity transformation and further solved by using perturbation technique to obtain velocity, concentration and temperature equations of the physical system. The influence of non-dimensional parameters such as Prandtl number Pr, Schmidt number Sc, thermal buoyancy parameter λ, Reynolds number R, chemical reaction rate γ, concentration buoyancy parameter N, Darcy number Da, Casson fluid parameter β, Hartmann number M2 , Soret effect Sr on velocity, thickness of fluid and heat have been discussed with graphs. The few important computational outcomes reveal that the Soret effect Sr enriches the concentration, fluid flow and temperature of fluid whereas Casson fluid parameter β diminishes the profiles. The earlier work and present work have been compared in the absence of Soret effect and is establishes to be good contract.

Adjoined ISPH method and artificial intelligence for thermal radiation on double diffusion inside a porous L-shaped cavity with fins

PurposeThe purpose of this study is to adapt the incompressible smoothed particle hydrodynamics (ISPH) method with artificial intelligence to manage the physical problem of double diffusion inside a porous L-shaped cavity including two fins.Design/methodology/approachThe ISPH method solves the nondimensional governing equations of a physical model. The ISPH simulations are attained at different Frank–Kamenetskii number, Darcy number, coupled Soret/Dufour numbers, coupled Cattaneo–Christov heat/mass fluxes, thermal radiation parameter and nanoparticle parameter. An artificial neural network (ANN) is developed using a total of 243 data sets. The data set is optimized as 171 of the data sets were used for training the model, 36 for validation and 36 for the testing phase. The network model was trained using the Levenberg–Marquardt training algorithm.FindingsThe resulting simulations show how thermal radiation declines the temperature distribution and changes the contour of a heat capacity ratio. The temperature distribution is improved, and the velocity field is decreased by 36.77% when the coupled heat Cattaneo–Christov heat/mass fluxes are increased from 0 to 0.8. The temperature distribution is supported, and the concentration distribution is declined by an increase in Soret–Dufour numbers. A rise in Soret–Dufour numbers corresponds to a decreasing velocity field. The Frank–Kamenetskii number is useful for enhancing the velocity field and temperature distribution. A reduction in Darcy number causes a high porous struggle, which reduces nanofluid velocity and improves temperature and concentration distribution. An increase in nanoparticle concentration causes a high fluid suspension viscosity, which reduces the suspension’s velocity. With the help of the ANN, the obtained model accurately predicts the values of the Nusselt and Sherwood numbers.Originality/valueA novel integration between the ISPH method and the ANN is adapted to handle the heat and mass transfer within a new L-shaped geometry with fins in the presence of several physical effects.

Effect of Finite Thermal Conductivity Bounding Walls on Darcy–Bénard Convection

Abstract Natural convection in fluid-saturated, horizontal porous-media is quintessential to many applications like geothermal reservoirs and solar thermal storage systems. Researchers have dedicated substantial effort over the years in pursuit of altering natural convection within a horizontal porous-media (Darcy–Bénard) system. Although significant research efforts have been directed toward understanding the effects of bounding walls in horizontal (Rayleigh–Bénard) convection systems, similar investigations for Darcy–Bénard convection systems are still lacking. Therefore, this study examines the effect of thermal properties of horizontal bounding plates on porous-media Nusselt number at high Rayleigh–Darcy numbers (105−107). Numerical simulations are performed by employing Darcy–Forchheimer model within a three-dimensional cylindrical computational domain to emulate Darcy–Bénard systems for two aspect ratios (1 and 2) and six different plate materials having nondimensional plate thicknesses of 0.02, 0.08, and 0.16. Polypropylene and compressed CO2 gas are chosen as solid and fluid phases for the porous media, respectively, that encompass a range of Darcy numbers (10−6−10−3). Findings reveal that when the ratio of thermal resistances of porous layer and plates falls below 4.61, the corrected Nusselt number deviates by more than 10% from the corresponding ideal Nusselt number with infinitely conducting bounding plates. The study also proposes a correction factor to estimate this deviation, which shows a good agreement with numerical results.

Rayleigh–Bénard Convection in a Gas-Saturated Porous Medium at Low Darcy Numbers

Abstract Natural convection heat transfer is measured in a horizontal enclosure filled with a gas-saturated porous medium composed of glass spheres. The height-to-pore scale ratio (H/d) is in the range of 25–150, yielding a low Darcy number (5.87×10−8≤Da≤1.94×10−6), which satisfies the porous medium assumption more rigorously. The maximum values attained for the modified Rayleigh numbers (Ra* up to 6150) and fluid Rayleigh numbers (Raf up to 2.5×1011) at these low Darcy numbers enable access to both the Darcy and Forchheimer flow regimes. The heat transfer relationship just beyond the onset of convection is in good accordance with theory and previous experiments, varying linearly with the modified Rayleigh number. For higher modified Rayleigh numbers, the data diverge as a function of the Darcy number, depending on both Da and the modified Rayleigh number. Transition points between the Darcy and Forchheimer regimes are estimated. At the highest fluid Rayleigh numbers, the data with the largest pore scales show some evidence of moving toward a regime similar to that of Rayleigh–Bénard convection, where boundary layer and plume length scales are small enough that the details of the porous medium cease to matter. It is argued that even in this regime, the boundary layer length scales are not diminished enough to make the contribution of Brinkman drag significant.

Numerical analysis to investigate the effect of a porous block on MHD mixed convection in a split lid-driven cavity with nanofluid

In this study, numerical analysis of a porous block influence on the mixed convection in a cavity filled with nanfluid has been investigated. The cavity is curvilinear shaped, in which the cold side is the top which is split to move in two directions on the same plane. The base is partially heated and connected to a block of porous media, while other walls are adiabatic. The complex governingequations are solved numerically using the finite element technique. For the assessment of the thermal performance, the considered variables which are Richardson number (from 0.15 to 10), Reynolds number (from 25 to 200), Darcy number (from 10−5 to 10−1), Hartmann number (from 0 to 62), ma magnetohydrodynamic's inclination angle (from 0° to 90º) and nanoparticles concentration (from 0 to 0.08). The height of the porous block is also investigated. The results’ main finding stated that the heat transfer could be enhanced due to the rise in Reynolds number, Richardson number, and the volume concentration while decreasing with the rise of Hartmann number. Also, value of Nuavg and the streams’ strength increase with the increase in Darcy number.

Computational study of magneto-convective flow of aqueous-Fe3O4 nanoliquid in a tilted cylindrical chamber partially layered by porous medium: Entropy generation analysis

In various industrial applications, the main objective is to enhance thermal efficiency by minimizing the generation of entropy. Specifically, achieving optimal thermal efficiency in a tilted cylindrical chamber poses significant challenges due to the combined effects of tangential and normal gravity components. Our study focuses on the flow dynamics, thermal transport, and entropy generation of Fe3O4/H2O nanoliquid within a cylindrical annular enclosure by incorporating the synergistic effects of magnetic force, geometric inclination angle, and thickness of the porous region. The Brinkman–Forchheimer-extended Darcy model for ferrofluid motion and the one-equation model for heat transfer are applied in the porous region, while the conventional Navier–Stokes and energy equations are used in the fluid-only region. A series of computations is performed for various key parameters, such as Hartmann number (0≤Ha≤60), Darcy number (10−5≤Da≤10−1), porous layer thickness (0.1≤ε≤0.9), and angle of inclination (−60°≤γ≤60°). Our results reveal that the heat transport rate is enhanced by 48.6% with an increase in the Darcy number from 10−5 to 10−1. Moreover, the flow circulation and heat transport can be optimized by tilting the enclosure anticlockwise. It has been found that 91.8% of flow strength can be enhanced by rotating the enclosure from −60° to 60°. Finally, this study suggests that the inclination angle of 30° and a porous layer thickness of 0.3 emerge as the ideal configuration to obtain optimal performance, particularly for lower Hartmann and higher Darcy numbers. Our findings will provide insight into optimizing thermal processes in nanoliquid-filled enclosures subjected to magnetic force.

Linear and nonlinear stability analyses of micropolar fluid flow in horizontal porous layers

The linear and nonlinear stability analyses of micropolar fluid flow in a horizontal porous layer heated from below in the presence of throughflow is numerically investigated. The Brinkman model is considered to govern the micropolar fluid flow within the porous region. The main purpose of the present study is to investigate the behavior of the subcritical region for micropolar fluid parameters in the presence of throughflow. The energy approach is used to analyze nonlinear stability, whereas the normal mode scheme is used to investigate linear stability. The obtained eigenvalue problems related to linear and nonlinear stability analyses are solved numerically using the bvp4c routine in MATLAB. Finally, the critical thermal Rayleigh number is determined for the given values of the governing parameters. It is observed that the subcritical area decreases as the Darcy number (Da), micropolar parameter (m), and absolute value of throughflow parameter (|Pe|) decrease. Furthermore, there is no subcritical gap in the absence of the throughflow effect for micropolar fluid flow, which is a good agreement for the linear and nonlinear thresholds.

Intelligent prediction of non-Newtonian hybrid nanoparticle-enhanced fluid flow and heat transfer behaviours in a trapezoidal enclosure: Integrated simulation approach

This study investigates the utilization of a trapezoidal cavity with a corrugated bottom wall containing a Carreau hybrid nanofluid composed of water, aluminum, and copper nanoparticles. A heated, rotating cylinder is placed at the center of the enclosure in the presence of an external magnetic field. The impact of Forchheimer and Brinkman porous medium models on the hybrid nanofluid is examined. Three different inlet–outlet placement configurations are considered to investigate their influence on heat transfer. The governing equations for fluid flow and heat transfer are solved numerically. Through simulations, a range of flow-controlling variables is systematically adjusted, including the Darcy number, Reynolds number, Hartmann number, nanoparticle volume fraction, undulation on the hot bottom wall, power law index, and rotational speed of the inner heated cylinder. The results demonstrate that the hybrid nanofluid and rotating cylinder significantly enhance heat transfer within the trapezoidal cavity. Higher values of the Darcy number, Reynolds number, and nanoparticle volume fraction lead to increased heat transfer rates. The placement configuration of the inlet and outlet ports also affects heat transfer performance, with the bottom-top configuration yielding the best results. Furthermore, a comparative analysis of flow profiles and heat distribution is conducted using the multiple expression programing technique. The proposed model accurately predicts the flow and heat transfer characteristics in the trapezoidal cavity, as validated through comparison with provided data sets.

Bioconvection flow of NEPCM and oxytactic microorganisms within a porous circular cylinder containing a circular cylinder fin using an artificial neural network in conjunction with the ISPH method

This article investigates the bioconvection flow within a porous circular cylinder filled with oxytactic microorganisms and incorporating nano-encapsulated phase change materials (NEPCMs). The circular cylinder, equipped with T-fins, is situated within the cylinder’s domain. The governing equations are solved using the ISPH method based on a time-fractional derivative. An ISPH simulation, coupled with an artificial neural networks (ANN) model, is employed to predict the values of the average Nusselt number ( Nu ¯ ). Utilizing bioconvection flow within a porous circular cylinder containing oxytactic microorganisms and integrating NEPCMs presents opportunities for progress in thermal management, environmental engineering, energy storage, and materials science. During the conducted simulations, we have investigated the impacts of Darcy, Lewis, Peclet, Rayleigh, and bioconvection Rayleigh numbers on a range of parameters, encompassing isotherms, heat capacity ratio, concentration profiles of oxygen and microorganisms, velocity field, and Nu ¯ . The results obtained highlight the significant influence of changes in the inner cylinder’s radius and fin length on regulating the intensity of bioconvection flow and improving heat transfer within a cavity. Additionally, the fusion temperature causes a shift in the heat capacity ratio toward the heat sources located within the cavity. The velocity field decreases by 97.39 % as the Darcy number decreases from 10 − 2 to 10 − 5 due to the challenges posed by porous media. Increasing the length of the T-fin enhances the cooling area, causing the isotherms to contract and altering the heat capacity ratio. In comparison to the target values, the ANN model demonstrates accurate prediction of Nu ¯ , bolstering confidence in its predictions.

Comparative analysis of entropy generation and heat transfer in a tilted partially heated square enclosure using the finite difference method

PurposeIn recent times, there has been a growing interest in buoyancy-induced heat transfer within confined enclosures due to its frequent occurrence in heat transfer processes across diverse engineering disciplines, including electronic cooling, solar technologies, nuclear reactor systems, heat exchangers and energy storage systems. Moreover, the reduction of entropy generation holds significant importance in engineering applications, as it contributes to enhancing thermal system performance. This study, a numerical investigation, aims to analyze entropy generation and natural convection flow in an inclined square enclosure filled with Ag–MgO/water and Ag–TiO2/water hybrid nanofluids under the influence of a magnetic field. The enclosure features heated slits along its bottom and left walls. Following the Boussinesq approximation, the convective flow arises from a horizontal temperature difference between the partially heated walls and the cold right wall.Design/methodology/approachThe governing equations for laminar unsteady natural convection flow in a Newtonian, incompressible mixture is solved using a Marker-and-Cell-based finite difference method within a customized MATLAB code. The hybrid nanofluid’s effective thermal conductivity and viscosity are determined using spherical nanoparticle correlations.FindingsThe numerical investigations cover various parameters, including nanoparticle volume concentration, Hartmann number, Rayleigh number, heat source/sink effects and inclination angle. As the Hartmann and Rayleigh numbers increase, there is a significant enhancement in entropy generation. The average Nusselt number experiences a substantial increase at extremely high values of the Rayleigh number and inclination.Practical implicationsThis numerical investigation explores advanced applications involving various combinations of influential parameters, different nanoparticles, enclosure inclinations and improved designs. The goal is to control fluid flow and enhance heat transfer rates to meet the demands of the Fourth Industrial Revolution.Originality/valueIn a 90° tilted enclosure, the addition of 5% hybrid nanoparticles to the base fluid resulted in a 17.139% increase in the heat transfer rate for Ag–MgO nanoparticles and a 16.4185% increase for Ag–TiO2 nanoparticles compared to the base fluid. It is observed that a 5% nanoparticle volume fraction results in an increased heat transfer rate, influenced by variations in both the Darcy and Rayleigh numbers. The study demonstrates that the Ag–MgO hybrid nanofluid exhibits superior heat transfer and fluid transport performance compared to the Ag–TiO2 hybrid nanofluid. The simulations pertain to the use of hybrid magnetic nanofluids in fuel cells, solar cavity receivers and the processing of electromagnetic nanomaterials in enclosed environments.