Local Nusselt Number Research Articles

Effect of thermal radiation on unsteady magneto-hybrid nanofluid flow in a π -shaped wavy cavity saturated porous medium

The present investigation deals with the natural convection (NC) of Al2O3-Cu-water hybrid nanofluid (HNF) within a “ π”-shaped cavity under the influence of an externally applied magnetic field (MF). Also we studied the porous media with radiative effect as well as common heat transfer for better fitting to real industrial problems. The inverse U shaped-cavity design includes upper walls that are partially heated and wavy right and left walls designed for cooling purposes, while the remaining walls are maintained as adiabatic. A FORTRAN home code using finite difference method-based approach is adopted to solve the governing equations. A verification is performed by comparing with previous numerical investigations to substantiate the precision of the established numerical model. The findings are expressed in term of stream function, isotherms, and local and averaged Nusselt number. It was found that by increasing amplitude (A), location of the heater (D), thermal radiation parameter (Rd) and wavelength (λ) about 140%, 94%, 775%, and 28% Nuavg increases, respectively. In addition, by increasing Dimensionless of heat source/sink length (B), Ha, and heat generation/absorption coefficient (Q) about 20%, 1.1% and 28% Nuavg decreases, respectively. Also, Nuavg first decreases and then increases by increasing Ra.

Numerical study on fluid flow and heat transfer characteristics of supercritical CO2 in horizontal tube under various non-uniform heating conditions

Supercritical CO2 (sCO2) is deemed the potential working medium for thermodynamic cycles in the next generation of power machinery. In this paper, the flow and heat transfer characteristics of highly buoyant turbulent sCO2 in horizontal tubes are numerical studied under the non-uniform heating conditions. The tube with a typical internal diameter of 10 mm is selected with mass flux equaling to 300 kg/(m2·s), effective heat fluxes ranging from 20 to 60 kW/m2, and pressure equaling to 8 MPa. The results confirmed that the heat transfer of sCO2 inside the horizontal tube in the circumferential or axial non-uniform heating conditions is greatly deteriorated by 13 %-68 % compared to the uniform heating. The overall heat transfer performance of semi-circumferential axial non-uniform heating is about 2.5 % higher than that of bottom semi-circumferential uniform heating, while the axial temperature difference of the bottom surface exceeds 150 K. Screening three representative heating positions, the bottom heating has the best temperature uniformity. The corresponding turbulent streamlines featured by unique helical structures can substantially improve the circumferential and radial heat transfer over 10 %, enhancing the heat transfer performance of the smooth tube close to that of rifled tubes. Based on the numerical data, viable correlations were developed for calculating the axial local Nusselt number of forced convection heat transfer of sCO2 in horizontal tubes considering the effects of cross-sectional vorticity, secondary flow intensity, and buoyancy-natural convection, and the prediction values are in good agreement with experimental data.

Reversible esterification process in Casson nanofluids: A numerical analysis of non-newtonian hydromagnetic flow

A computational mechanism has been formulated to scientifically analyze the phenomenon of combined convection in the occurrence of magnetohydrodynamic flow behavior of Casson nanofluid. This study emphasizes the trajectory of the nanofluid along a stretching sheet with nonlinear permeability, while considering additional physical effects such as reversible chemical reaction, thermal radiation, energy source/sink, suction and viscous dissipation. In this study, we have additionally integrated the nanofluid paradigm proposed by Buongiorno, which encompasses the repercussion of thermophoresis along with Brownian motion. The utilization of appropriate similarity renovations serves the purpose of recasting the dominant multivariate differential equations to a collection of nonlinear differential equations in single variable. The Runge–Kutta shooting mechanism is implemented for the intention of numerically determining the unknown boundary conditions. The solution to the dominant equations was obtained by employing the fourth-order Runge–Kutta technique and to ensure the dependability of the outcomes, the bvp4c method was employed. The graphical and tabulated observations are presented herein to facilitate a comprehensive analysis of the underlying physical characteristics inherent in the problem at hand. The utilization of the Casson parameter has been found to be advantageous in the reduction of shear stress rate, along with the enhancement of mass and energy transfer rates. Additionally, the application of suction has been observed to be beneficial in the enhancement of Sherwood number and energy transfer rate. Within the scope of the context of the esterification process, the purpose of this proposal is to evaluate the impact that numerous arithmetical values exert on the temperature field, the velocity profile and the volumetric concentration. An in-depth graphical analysis that takes into account the relevant physical consequences is used to evaluate the most important factors that relate to the physical quantities that describe the contours of temperature, velocity and concentration. In addition to being accompanied by their respective explanations, the tabular portrayal of the local Sherwood number, shear stress rate along with local Nusselt number all feature in this paper. There is a clear distinction that can be made between irreversible and reversible flows in the evaluation of the local Sherwood number, rate of shear stress and local Nusselt number. This differentiation is brought about by taking into analysis thermophoresis parameter, Brownian motion parameter and suction parameter. The results that were produced from the theoretical simulations have significant repercussions for a variety of fields that are related to energy engineering. The findings derived from the analysis indicate a negative correlation between the Brownian motion parameter and both irreversible and reversible flow in terms of rate of energy transfer and shear stress rate. It is imperative to highlight that reversible flow holds greater significance in comparison to irreversible flow.

Shape factor and thermal radiation effects on convective MHD flow of Casson blood ternary hybrid nano‐fluid through a stretched rotating rigid disk

AbstractThe mathematical modeling of blood flow with the incorporation of ternary hybrid nanoparticles (i.e., titania, silica, and alumina nanoparticles) is the focus of this work. The flow of blood is simulated using the Casson fluid model. The impacts of ternary hybrid nanoparticles, shape factor, and Geometry of solid nanoparticles are visualized and investigated. The momentum and thermal characteristics of a flowing liquid are determined by considering magnetization, porosity, and nonlinearized radiating thermal flux. The basic partial differential equations resulting from mathematical modeling are turned into non‐linear ordinary differential equations using suitable velocity transforms. The derived nonlinear equations are then numerically calculated using the 4th‐5th order Runge‐Kutta‐Fehlberg method with the shooting technique and analytically solved by the Adomian decomposition method (ADM). The effects of the factors involved on the dimensionless profiles produced are fully addressed. It is found that the Skin friction factor and heat transfer rate in the radial direction upsurge with the augment of both rotation parameter and nanoparticles volume fraction; however, the Skin friction factor drops in the azimuthal direction. Also, results obtained reveal an enhancement in the local Nusselt number with the upsurge in the magnitude of radiation parameter, Rd, solid nanoparticles concentration, , shape factor value, s, and disk temperature, . For validation, the outcomes of this inquiry were compared to the outcomes of the HAM‐based Mathematica software. In addition, the acquired analytical DRA data are compared to numerical RKF45 values and those given in the literature.

Flow and heat transfer characteristics of low water content jet fuel in U-bend tubes: A numerical study using LES and DPM approaches

This study provides an in-depth analysis of the flow and heat transfer behavior of low-water-content jet fuel (α ≤ 2 %) in U-bend tubes, utilizing Large Eddy Simulations (LES) and Discrete Phase Models (DPM). The research focus on the influence of radii of curvature ratio (r/D), flow rates (Qtp) and α on flow dynamics and heat transfer mechanisms. Flow fields for r/D = 1 and r/D ≥ 2.5, where distinct secondary flow structures, play a critical role in shaping internal flow behavior. These vortices significantly enhance flow mixing and heat transfer, especially on the inner wall, through complex multi-level vortex interactions. The local wall Nusselt number shows a close correlation with vorticity trends, initially increasing and then decreasing, with notable deviations near the inlet and outlet regions. This non-uniform heat transfer is primarily driven by the interaction of secondary flow structures and adverse pressure gradients near the inner wall, while higher Qtp and smaller r/D can improve heat transfer uniformity under certain flow conditions. The presence of droplets increases the total wall Nusselt number by 4 % to 60 % compared to single-phase jet fuel flow, due to two-phase interaction and boundary layer disruption. Finally, the study proposes modified correlations for pressure drop gradients and total wall Nusselt numbers, accounting for effects of r/D and multiphase heat transfer processes. These correlations, validated with RRMSEs of 3.54 % and 6.80 % respectively, provide valuable insights for improving heat transfer efficiency in fuel systems and form a theoretical foundation for real-time monitoring technologies in aircraft fuel lines.

Numerical Simulation of MHD Oldroyd-B Fluid with Thermal Radiation and Chemical Reactions Using Chebyshev Wavelets

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partial differential equations, which then give rise to a set of highly nonlinear coupled ordinary differential equations using similarity transformations. The nonlinearity in the differential equations is dealt with quasilinearization technique. The resultant equations are numerically solved using Chebyshev wavelet collocation method. The effects of magnetic field, radiation, chemical reaction and buoyancy parameters are investigated. The numerical values of local skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated and analyzed. We observe that the increase in buoyancy parameters enhances the velocity profiles and larger values of magnetic field decrease the velocity profiles but increases the temperature and concentration profiles. Error analysis has been done to check the convergence of the numerical scheme.

Comparative analysis of inlet and outlet cavity designs on the thermal-hydraulic performance of compact heat exchangers for combustion engine exhaust heat recovery

ABSTRACT Improving the Internal Combustion Engines (ICEs) overall thermal efficiency is crucial to reduce fuel consumption and emissions. To achieve this goal, waste heat recovery from exhaust gases remains the most promising strategy, which involves the utilization of compact heat exchangers. This study evaluates the performance of novel Monolithic Integrated Thermal Exchange Matrixes (MITEMs) designs for recovering exhaust heat from a 70 hp diesel engine, focusing on the impact of inlet/outlet cavities. Computational Fluid Dynamics simulations were employed to analyze the heat transfer rate, pressure drop, and overall thermal-hydraulic performance of different MITEM designs. The Rectangular Channels with Large Cavities (RCLC) design exhibited superior performance, enhancing the heat transfer rate by 14.7% compared to the baseline design while limiting pressure drop increase to 9.2%. The RCLC design increased local Nusselt numbers and heat transfer coefficients by up to 60%, achieving peak velocities of 98 m/s within cross-sectional planes. These findings provide valuable insights for optimizing exhaust heat recovery systems in diesel engines.

Natural convection magneto hydrodynamic filled with TiO2 nanofluid with a right-angled triangle obstacle within square cavity

The goal of this study is to examine the result of natural convection, magnetohydrodynamics, and nanofluids within a square cavity with an obstacle of a right-angle triangle within it. Among the various nanoparticles, TiO2 nanoparticles blended with water have shown promise in improving heat transfer. The Finite Element Method is used for the simulation. By utilizing the commercial software 'COMSOL Multiphysics 6.1' graphical illustrations, the influence of prominent parameters on streamline, isotherm contours and the local Nusselt number is effectively portrayed. The key factors that play a dominant role include the Prandtl number (Pr = 6.2) and Rayleigh number (104 <= Ra <= 106), Hartmann number (Ha = 0, 30, 50), and the heat source/sink (Q = -6, 0, 6) employed. The result confirms that the decline in fluid velocity and convective heat transfer is due to the enhancement of the Lorentz force. This outcome of the study affirms that the appropriate amalgamation of nanoparticles significantly improves the transmission of heat properties of fundamental fluids. The discoveries of this investigation could aid in comprehending the hydrothermal aspects of thermal systems, including electronic cooling, solar power and the utilization of nanofluid to regulate liquid movement and thermal exchange attributes within the annular space.

Features of microorganism and two-phase nanofluid in a tangent hyperbolic Darcy-Forchhiemer flow induced by a stretching sheet with Lorentz forces

This work examines the two-dimensional tangent hyperbolic flow over a stretching sheet with a uniform magnetic field. The Buongiorno model is utilized to analyze and explain the spread of uneven coefficients in the presence of gyrotactic microorganisms. The concept of microorganisms and the resulting bioconvection enhance the stability of the nanoparticles. The impacts of thermal radiation, heat sources, convective heating, and chemical reactions are also evaluated. The suggested mathematical problem results in a nonlinear set of partial differential equations (PDEs), which are subsequently reduced to ordinary differential equations (ODEs) by applying the appropriate transformation. The resultant highly nonlinear ordinary differential equations (ODEs) are numerically solved using MATLAB's built-in package known as bvp4c. An in-depth investigation into the changes in the velocity field, the temperature profile, the concentration of nanoparticles profile, and the motile density profile is analyzed through graphs against various influencing parameters. Additionally, computations of engineering interest quantities such as skin friction, local Nusselt number, local Sherwood number, and molecular density are presented in both graphical and tabular formats for further examination. It has been explored that with greater values of the Weissenberg number, the fluid velocity upsurges when n<1, whereas the opposite behavior is noticed when n>1. It is also noted that an increment in the Peclet number decreases motile density for both dilatants n>1 and pseudoplastic n<1 fluids. The computed results are compared with existing literature in limiting cases and found good agreement.

An experimental study on heat transfer using electrohydrodynamics (EHD) over a heated vertical plate.

The Corona effect offers significant potential for improving heat transfer efficiency in air. This study thoroughly examined how a single corona discharge affects heat transfer on a heated vertical flat plate. Key parameters tested included corona voltage, the aspect ratio of the vertical plate (y/L), and the inter-electrode discharge gap ratio (x/d). The findings revealed that increasing the corona voltage and decreasing the discharge gap enhanced heat transfer efficiency along the vertical surface. A predictive formula for the local Nusselt number was developed to characterize heat transfer on the plate. Additionally, Particle Image Velocimetry (PIV) was used to analyze the corona wind generated by the discharge. The study observed that the corona wind formed a vortex in the upstream region, which resulted in lower heat transfer rates upstream compared to the downstream region.

A computational study of Eyring‐Powell fluid model over a rotating cone with magnetic field and joule heating effect

AbstractIn this research, we investigate mixed convection transport of mass and heat transfer in the unsteady boundary layer flow of the Eyring‐Powell fluid around a rotating cone in the presence of Brownian and thermophoresis effects. Rotating cones are widely used in conical diffusers, medical devices, Aerospace Engineering and a variety of rheometric and viscosimetry applications. Specifically, we focus on the flow of the Eyring‐Powell fluid around the cone in the presence of magnetohydrodynamics and nanofluid. The modeled momentum, energy, and concentration equations of the problem are transformed into nonlinear dimensionless, nonlinear ordinary equations by utilizing the similarity variables. These nonlinear coupled ordinary differential equations are solved numerically via Bvp4c, and the outcomes for important physical parameters on momentum, energy, and concentration equations are presented graphically. The computational outcomes of physical parameters for skin friction coefficient, local Nusselt number, and Sherwood are also presented in tabular form.

Numerical analysis on performance evaluation of photovoltaic thermal systems using ternary hybrid nanofluids and forced convection around copper cylinders

This study evaluates the performance of a photovoltaic thermal (PV/T) system using forced convection and ternary hybrid nanofluids, comprising water with cobalt, zinc, and silver. The PV/T system includes a glass absorber, polycrystalline silicon, and a flow channel with eight copper cylinders, positioned at 20 %, 40 %, 60 %, and 80 % along the channel, both above and below the flow path for optimal thermal conductivity. The working fluid is modeled under turbulent, steady-state conditions using the κ−ε turbulence model.Numerical simulations via COMSOL Multiphysics 6.0 evaluate the system's thermal and fluid dynamics, focusing on local Nusselt numbers and photovoltaic cell thermal efficiency compared to a baseline. The investigation spans Reynolds numbers from 10,000 to 100,000, nanoparticle volume fractions of 1 %–20 %, and aspect ratios of 0.1–0.3. The aspect ratio in this study is defined as the ratio of the height of a square obstacle within the flow channel to the total height of the flow channel. A supervised machine learning framework develops predictive regression models for system analysis. Results show fluid force at the outlet increases by about 1200 % and 1300 % for aspect ratios of 0.1 and 0.3 as the Reynolds number rises. The Nusselt number enhances by 420 % and 466 % at a 20 % nanoparticle volume fraction for aspect ratios of 0.1 and 0.3, respectively, with a 9 % improvement in photovoltaic cell efficiency. This work uniquely applies machine learning to derive regression equations for fluid force, Nusselt number, and electrical efficiency, an approach not previously explored in laminar flow studies.

Artificial intelligence and numerical study of the heat transfer and entropy generation analysis of NEPCM-MWCNTs-Water Hybrid Nanofluids inside a quadrilateral enclosure

In the present investigation, the primary objective is to assess the synergistic impact of a novel hybrid nanofluid composed of nano-enhanced phase change material, multi-walled carbon nanotubes, and water. The governing equations are transformed into dimensionless forms for a more generalized analysis. To solve the problem, the Galerkin finite element method is employed, offering a robust numerical approach. A dataset of 1000 records was created by numerically solving the model for various combinations of control parameters. Using the dataset, a neural network was trained to learn the relationship between control parameters and heat transfer rate. The evaluation outcomes are comprehensively illustrated through key parameters, including local and average Nusselt numbers, total entropy generation, contours, and streamlines in the range of 103<Rayleigh number<105, 0<nanotube concentration<0.025, 0<nano capsule concentration <0.025, and 0.1<non-dimensional fusion temperature <0.7. Remarkably, the results indicate a substantial improvement in the heat transfer rate of the suspension for a hybrid concentration of 5%, showcasing an impressive 13% enhancement in contrast to the water host fluid's performance. Notably, the observed rise in entropy generation is relatively moderate, only a 5% increase.

Non-similar analysis of heat generation and thermal radiation on Eyring-Powell Hybrid nanofluid flow across a stretching surface

This paper portrays a two-dimensional mathematical model developed for the analysis of Eyring-Powell hybrid nanofluid flow, incorporating variable temperature and velocity profiles. This study investigates the flow through a porous media with a mixture of hybrid nanoparticles (copper dioxide, magnetite) integrated into ethylene glycol ([Formula: see text]) across a stretching sheet. The model takes magnetic effects, heat generation, and thermal radiation into account. Additionally, nonsimilar partial differential equations (PDEs) are transformed into ordinary differential equations using the local nonsimilarity approach. These equations are then numerically solved using the built-in Matlab function bvp4c. To examine the effects of adjusting parameters on heat, mass transfer, and skin friction, the results are displayed graphically. With an increase in the given values of magnetic field [Formula: see text], the velocity profile [Formula: see text] is seen to decay. Moreover, it is observed that the hybrid nanofluid density and dynamic viscosity increase as the volume fraction rises. It is estimated that the thermal conductivity and viscosity of the [Formula: see text] hybrid nanofluid are expected to increase to 4.1% and 12.35%, respectively, and to 71.55% and 78.01%, respectively, for volume concentrations ranging from 0.02% to 0.05%. It is also concluded that the local skin-friction coefficient has the opposite trend while the local Nusselt number rises monotonically with both the slip velocity parameter and the surface convection parameter. This research has broad applications In the glass and polymer industries, metallic plate cooling, plastic sheet contractions, etc.

Study of hybrid nanofluid flow in a porous medium over an exponentially stretching sheet under Joule heating and thermal radiation: Finite difference

The significant purpose of present investigation of the behavior of a nanofluid's in magneto-hydrodynamics (MHD), mass transfer, Joule heating, and boundary layer transfer characteristics over an exponentially stretching sheet in a porous medium and thermal radiation effects. The article's goal is to look at the fluid flow and heat transmission characteristics from a sheet of hybrid nanoparticles. The partial differential equations (PDEs) that were derived for the mathematical model were converted using the proper similarity transformation into ordinary differential equations (ODEs). The hybrid nanofluid composed of 97 % of ethyl glycol (EG) and the volume concentration of Magnetite (Fe3O4) and Copper(Cu) are ranging from 0.5 % to 2.5 % both respectively. The effects of thermal radiation, stretching rate, Joule heating, porous medium permeability, and nanoparticle volume fraction on the flow and heat transmission properties are investigated by numerical simulations using the finite difference method (FDM). The analysis reveals that the inclusion of nanofluids enhance the thermal conductivity and enhance the heat transfer rate. Additionally, the influence of variable viscosity on the flow behavior and thermal characteristics are examined graphically. The effects of variable viscosity and thermal conductivity are examined, as it has significance in optimizing system under various thermal and magnetic effects. This study offers a pathway to develop more efficient thermal management solutions, by contributing to technological advancement and energy saving. The key findings of present study reveal that the temperature profile rises significantly due to Joule heating effects. The Nusselt number reveal an improvement of about 12 % when the volume fraction of nano particles is increased by 1–4 % indicating the enhancement in heat transfer efficiency. Similarly, the velocity profile was influenced by porous medium permeability as 11 % increase in porosity result a 18 % decrease in velocity profile.By using parametric research, the role of physical parameters in determining the local skin-friction coefficient, temperature, nanoparticle volume percentage, and longitudinal velocity profiles, local Nusselt number, and local Sherwood number are thoroughly examined. A graphic representation of the velocity, temperature, and concentration distribution findings is presented.

A Numerical Study on the Influence of Confining Walls on Drag and Heat Transfer Coefficients in Single‐Particle Lab‐Scale Reactors

AbstractSingle‐particle reactors in lab‐scale are a promising technology to gain an in‐depth understanding of the intricate reaction and transport processes that occur in catalyst particles under operando conditions. It is not described whether the effect of the bounding walls in such narrow flow channels influence the processes at the particle. Therefore, this work applies three‐dimensional (3D) computational fluid dynamics (CFD) simulations to analyze the drag coefficient CD alongside the local and average particle Nusselt number Nup as characteristic local and integral quantities in the range of particle Reynolds numbers 10 ≤ Rep ≤ 103. An equation is derived to correct for the wall effects on CD and Nup and assist the experimenter in the interpretation of measured results.

Thermal and velocity slip conditions together with thermal radiative effects on Joule heating mixed convection MHD hybrid nanofluid flow induced by an exponentially shrinking or stretching sheet

ABSTRACT The present study analyzes the mixed convection with magnetohydrodynamic (MHD) flow, Joule heating, and heat transfer in hybrid nanofluids on exponentially stretching or shrinking sheets. The study aims to optimize heat transfer and fluid dynamics properties in engineering and industrial applications. The governing partial differential equations are converted into ordinary differential equations by employing appropriate similarity transformations and then solved using the BVP4C MATLAB tool. In this study, the effects of silver volume fraction, velocity slip, thermal slip, magnetic field, heat generation, Eckert number, and thermal radiation on the skin friction coefficient, Nusselt number, velocity profile, and temperature profile are examined and graphically discussed. The base fluid water contained 2% silver (Ag) and 0.1% titanium oxide (TiO2) nano-particles in this hybrid model. The dual solution was present for a shrinking sheet ( λ < 0 ) when λ ≥ λ c . The skin friction coefficient values decreased by approximately 37%, while the local Nusselt number increased by approximately 3.1% when the velocity slip increased in the first solution. The Nusselt number increased by approximately 0.28% and 12% when the Eckert number and radiative parameter increased, respectively, but decreased by approximately 7.5% and 0.20% when the thermal slip and heat generation increased, respectively.

Simulation of Bingham–Papanastasiou model within trapezoidal cavity with mixed convection effects

The study of Bingham–Papanastasiou fluids is conducted in lid-driven cavity with consideration of viscous dissipation. The upper and left wall of the cavity is cold while other walls are insulated. Numerical simulations are conducted to study the isotherms, temperature profile, local and average Nusselt number. The main focus of work is to analyse the behaviour of heat transfer within trapezoidal cavity. The governing system of nonlinear dimensionless partial differential equations is analysed by using PDE solver of finite element method in COMSOL. The analysis is carried out for different parameters like Reynolds number, Bingham parameter, stress growth parameter, Eckert number and Prandtl number. It is observed that impact of Bingham parameter on temperature variation is negligible while the impact of stress parameter leads to the reduction in temperature within cavity. The novelty of this work is that no work is done for the case of trapezoidal cavity where Bingham–Papanastasiou fluid behaviour is observed under the consideration of viscous dissipation and mixed convection.

Neural network approach to investigate heat transfer in SWCNTs nanofluid within trapezoidal cavity with varied corrugated rod amplitudes

This article presents Artificial Neural Networks (ANN) for convective heat transfer in a trapezoidal cavity subjected to corrugated heated rod inside it. The LevenbergMarquardt algorithm is utilized to optimize the Neural Networks. The trapezoidal cavity has low-temperature inclined walls and adiabatic upper and lower walls compared to the corrugated heated rod. Single-wall carbon (SWCNTs) nanomaterials are submerged in the base liquid water. The flow of SWCNTs-water is generated due to the temperature gradient in the cavity. The system of dimensional partial differential equations has been formulated for the physical setup under investigation. The dimensional system has been converted into a non-dimensional form using dimensionless variables. Finite element is used for the solutions. The dimensionless functions velocity, temperature, and heat transfer rates are studied against the Rayleigh number (Ra). The outcomes are presented in the form of isotherms, contours, tabular values, and graphs. The data for Artificial Neural Networks (ANN) has been generated by FEM against the Nusselt number. The ANN has been trained for a specific amplitude of the rod and predicted heat transfer against a larger amplitude. The results show good agreement for both training and testing data. The outcomes of analysis reveals that convection caused by temperature gradient is dominant for higher values of the Rayleigh number (Ra). Local Nusselt number has been discussed against different amplitudes, and predicted enhancement for the larger amplitude of the rod.

Numerical Study on the Impact of the Richardson Number on Convection in an Enclosure, with Moving Sidewalls for Three Aspect Ratios: A = 1, 2 and 0.5

Using mathematical models, this research investigation seeks to explore how varying aspect ratios and the Richardson number impact the mixing effectiveness, fluid flow velocity, and heat transfer characteristics in a rectangle-shaped space where cooling occurs along the sides and warm with a steady temperature exists throughout the 80% of the bottom section's center. Discretizing the governing equations through the finite volume approach, we solved them iteratively using the Tri-diagonal Matrix Algorithm, where pressure-velocity coupling was successfully implemented via the SIMPLER procedure. Innovative approaches for convection and diffusion terms involved employing a power-law difference scheme alongside a central differential scheme. In various simulations with specified parameters (Re = 100, Pr = 0.71), we visualized results in forms like streamlines, isothermal lines, and temperature/velocity profiles, along with local and average Nusselt numbers. We observe five unique structure formations during flow behavior by analyzing how Richardson numbers impact heat transmission within a specific geometric configuration (enclosure size A = 1). A change in aspect ratio leads to improved control over fluid movement while minimizing structural distortion. A subtle rise in heat transmission emerged as the average Nusselt number and Richardson number intersection strengthened force convection's domination while experiencing significant escalation under conditions conductive to natural convection. Decreasing the aspect ratio increased heat transfer efficiency when the Richardson number rose.