Local Nusselt Number Research Articles

Machine learning algorithms on predicting the turbulent mixed convection flow in a driven-cavity with two horizontal cylinders

Turbulent mixed convection flow and heat transfer properties in a driven cavity with two circular cylinders arranged one above another are analyzed numerically with the incorporation of a finite element scheme, based on the Galerkin method of weighted residuals. A comparison of streamlines, isotherms, and local, average Nusselt number is provided to illustrate how the Richardson number Ri, Reynolds number Re and the eddy viscosity ε affect the transport phenomena inside the cavity. The local and average Nusselt number have been evaluated and it is found that strong convection at the top wall causes the average Nusselt number to progressively rise with respect to Ri and ε, while steady or slightly varying profiles are seen with regard to Re. In order to predict the thermal distribution inside the cavity due to these hot cylinders, Artificial Neural Network (ANN) and Gaussian Process Regression (GPR) have been developed with these model parameters as input and average Nusselt Number as target values. Several plots have been depicted to come to a conclusion that both models have been trained very effectively with the minimal observed Mean Square Error (MSE) values of 0.0026018 and 0.0026428 for ANN and GPR, respectively. In support to these findings, the coefficient of determination R2 suggests that ANN (R2 = 0.89) outperforms GPR (R2 = 0.87) in testing accuracy, hence it is recommended for prediction task.

Magnetohydrodynamic double diffusion natural convection of power-law Non-Newtonian Nano-Encapsulated phase change materials in a trapezoidal enclosure

PurposeThe present numerical investigation examines the magnetohydrodynamic (MHD) double diffusion natural convection of power-law non-Newtonian nano-encapsulated phase change materials (NEPCMs) in a trapezoidal cavity.Design/methodology/approachThe governing Navier-Stokes, energy and concentration equations based on the Cartesian curvilinear coordinates are solved using the collocated grid arrangement’s finite volume method. The in-house FORTRAN code is validated with the different benchmark problems. The NEPCM nanoparticles consist of a core-shell structure with Phase Change Material (PCM) at the core. The enclosure, shaped as a trapezoidal hollow, features a warmed (Th) left wall and a cold (Tc) right wall. Various parameters are considered, including the power law index (0.6 ≤ n ≤ 1.4), Hartmann number (0 ≤ Ha ≤ 30), Rayleigh number (104 ≤ Ra ≤ 105) and fixed variables such as buoyancy ratio (Br = 0.8), Prandtl number (Pr = 6.2), Lewis number (Le = 5), fusion temperature (Θf = 0.5) and volume fraction (ϕ = 0.04).FindingsThe findings indicate a decrease in local Nusselt (Nu) and Sherwood (Sh) numbers with increasing Hartmann numbers (Ha). Additionally, for a shear-thinning fluid (n = 0.6) results in the maximum local Nu and Sh values. As the Rayleigh number (Ra) increases from 104 to 105, the structured vortex in the streamline pattern is disturbed. Furthermore, for different Ra values, an increase in n from 0.6 to 1.4 leads to a 67.43% to 76.88% decrease in average Nu and a 70% to 77% decrease in average Sh.Research limitations/implicationsThis research is for two-dimensioal laminar flow only.Practical implicationsPCMs represent a class of practical substances that behave as a function of temperature and have the innate ability to absorb, release and store heated energy in the form of hidden fusion enthalpy, or heat. They are valuable in these systems as they can store significant energy at a relatively constant temperature through their latent heat phase change.Originality/valueAs per the literature review and the authors’ understanding, an examination has never been conducted on MHD double diffusion natural convection of power-law non-Newtonian NEPCMs within a trapezoidal enclosure. The current work is innovative since it combines NEPCMs with the effect of magnetic field Double diffusion Natural Convection of power-law non-Newtonian NEPCMs in a Trapezoidal enclosure. This outcome can be used to improve thermal management in energy storage systems, increasing safety and effectiveness.

Numerical study on heat transfer and pressure performance of different suspension nozzles

The drying process of the lithium battery pole pieces makes extensive use of the suspension nozzle. It is of great significance to study the heat transfer and pressure steady-state characteristics of the suspension nozzle and to select the appropriate nozzle structure for the production of pole pieces. Based on the SSTk-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{SST }}k - \\omega$$\\end{document} turbulence model, this article numerically simulates the impact jet process of suspension nozzles with slits, injection holes, and effusion holes. There is a qualitative and quantitative analysis of the distribution of their velocity field, temperature field, local Nusselt number, average Nusselt number, local pressure coefficient, and average pressure coefficient, and the comprehensive performance index of the nozzle is proposed. The results show that when the weight factor of heat transfer performance α is less than 21.61% and the weight factor of pressure performance β is more than 78.39%, the comprehensive performance of the traditional suspension nozzle with double slits is the best. As the α is increasing, the β is decreasing. The comprehensive performance of the suspension nozzle with effusion holes is the best. The turbulent intermittence, interaction between neighbouring jets, and edge effects affect the heat transfer and pressure uniformity of the suspension nozzle.

Jet array impingement heat transfer in a rectangular cavity with effusion holes

Various researchers have studied jet array impingement heat transfer in impingement/effusion cooling systems. However, there is a lack of research on impingement/effusion cooling systems installed within rectangular cavities that focus on the impact of the proximity of the jet hole to the cavity sidewalls on cooling performance. The main objective of this study is to investigate the flow and heat transfer characteristics of jet array impingement with effusion holes in a rectangular cavity, considering various spacings between the cavity sidewalls and the outermost jet hole. The design parameters in this study include the ratio of the jet hole pitch to jet hole diameter of 7.1, 10.0, and 16.7, and the ratio of the distance between the jet and impingement plates to jet hole diameter of 2, 6, and 10, with the Reynolds number based on the jet hole diameter ranging from 2500 to 15,000. Heat transfer characteristics in the stagnation region and wall jet region were examined using local Nusselt number distributions on the impingement surface, measured by liquid crystal thermography. The local Nusselt number was high in the stagnation region and decreased radially from the stagnation region as the wall jet region formed. The closer the outermost jet hole is to the sidewall, the higher the Nusselt number on the impingement surface near the sidewall. Moreover, the flow structure in the rectangular cavity was numerically investigated, and the velocity vectors and streamlines showed that primary and secondary vortices were generated in the middle of two neighboring jets and near the sidewall, respectively. This study also assessed previous average Nusselt number correlations. Based on experimentally determined average Nusselt number data with 54 center unit cells and 1296 side unit cells, new correlations to predict the average Nusselt number on the impingement surface in a rectangular cavity with effusion holes were developed.

Numerical investigation of fluid flow and heat transfer of a nanofluid around two circular cylinders arranged in tandem in horizontal duct

In this study, two-dimensional unsteady laminar convective heat transfer from two isothermal cylinders arranged in tandem in horizontal duct has been numerically investigated. The numerical study is performed by solving the governing equations (continuity and momentum) and energy equations using a finite volume-based code ANSYS Fluent. The present study was conducted using nano sized copper particles suspended in water. The Prandtl number Pr of the resulting suspension being equal to 7. The range of solid volume fractions studied is and the flow Reynolds number is equal to 100.The spacing ratio of the two cylinders was varied from 2 to 5 while the blockage ratio was kept constant β=0.25. A detailed discussion has been provided regarding the variation of flow structure and the characteristics of flow, including total drag and lift coefficients, as a function of the dimensionless parametersIn order to visualize the flow and heat transport, streamlines, vorticity contours and isotherms were generated. In addition, the local and average Nusselt numbers for the upstream and downstream cylinders are calculated. The results demonstrate that the force coefficients, the wake structure behind the cylinders, and the Nusselt number are significantly influenced by the value of the spacing ratio and the volume fractions of nanoparticles. The results demonstrate a significant enhancement in heat transfer efficiency relative to the base fluid. The aforementioned improvement is more pronounced in the case of higher gap ratios and higher nanoparticle volume fractions.

Lid driven flow and heat transfer due to various positions of slit in a square cavity: FEM approach

A detailed analysis of flow and heat transfer due to moving slit within the various positions of the square cavity is discussed. The slit is strategically positioned and examined at three distinct locations within the square cavity i.e. left, middle and right. Constraints of the square cavity are defined for horizontal and vertical walls. The top horizontal wall is considered to be adiabatic while the other three walls of the cavity are cold. The upper surface of slit is heated and movable towards the left side of the square cavity while the other three walls are immovable and cold. The fluid flow dynamics and heat transfer within the enclosed cavity are governed by fundamental principles of mass, momentum and energy conservation. These governing principles manifest as intricate mathematical equations, specifically nonlinear partial differential equations accompanied with boundary conditions. The key parameters under consideration include the Reynolds number (250≤Re≤1500) and Richardson number (0.01≤Ri≤5) at a fixed Prandtl number (Pr=6.2). These parameters are analysed through variations in velocities, temperature profiles, isotherms and streamlines. In the computational framework, the momentum and temperature equations are addressed through quadratic interpolation, while linear interpolation is applied to handle the pressure equation. The numerical solution, utilizing Newton's technique and the PARADISO solver, is rigorously validated against existing research methodologies, establishing its methodological reliability. Higher Reynolds numbers shift the primary vortex towards the middle and create corner recirculation zones, more uniform heat distribution, while higher Richardson numbers increase buoyancy forces, reducing isotherm contours and affecting heat distribution. The local Nusselt number increases with the increase in Reynolds numbers but shows small changes with the increase in Richardson number. The value of Nusselt number decreases as the position of slit changes from left to right.

Non-similar solution of Casson fluid flow over a curved stretching surface with viscous dissipation; Artificial neural network analysis

PurposeThe main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.Design/methodology/approachThe non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.FindingsThe results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.Originality/valueAI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

Influence of Rotation and Viscosity on Parallel Rolls of Electrically Conducting Fluid

Rayleigh–Bénard convection is a fundamental fluid dynamics phenomenon that significantly influences heat transfer in various natural and industrial processes, such as geophysical dynamics in the Earth’s liquid core and the performance of heat exchangers. Understanding the behavior of conductive fluids under the influence of heating, rotation, and magnetic fields is critical for improving thermal management systems. Utilizing the Boussinesq approximation, this study theoretically examines the nonlinear convection of a planar layer of conductive liquid that is heated from below and subjected to rotation about a vertical axis in the presence of a magnetic field. We focus on the onset of stationary convection as the temperature difference applied across the planar layer increases. Our theoretical approach investigates the formation of parallel rolls aligned with the magnetic field under free–free boundary conditions. To analyze the system of nonlinear equations, we expand the dependent variables in a series of orthogonal functions and express the coefficients of these functions as power series in a parameter ϵ. A solution for this nonlinear problem is derived through Fourier analysis of perturbations, extending to O(ϵ8), which allows for a detailed visualization of the parallel rolls. Graphical results are presented to explore the dependence of the Nusselt number on the Rayleigh number (R) and Ekman number (E). We observe that both the local Nusselt number and average Nusselt number increase as the Ekman number decreases. Furthermore, the flow appears to become more deformed as E decreases, suggesting an increased influence of external factors such as rotation. This deformation may enhance mixing within the fluid, thereby improving heat transfer between different regions.

Numerical heat transfer analysis of steam injection into subcooled water

Steam direct contact condensation (DCC) into subcooled water may be encountered in different important industrial process applications, such as steam jet pumps, steam ejectors, pressurizers, and emergency cooling systems of nuclear reactor core. In this work, a numerical simulation study has been done for injection of steam into a tank full of subcooled water. In the simulations, the Eulerian multiphase flow in addition to a realizable k-epsilon turbulence model has been utilized. Moreover, a DCC model has been used for condensation capturing. Fluent software with a user-defined function (UDF) for the DCC model was employed for simulations. The results obtained from simulations were validated with experimental results, and a fair agreement was observed. This study considered the local Nusselt number (LNN) the most suitable parameter for investigating the heat transfer rate (HTR) at the computational cell level. Therefore, the contours of the LNN, its axial distribution, and radial distribution were studied with respect to the inlet pressure of injected steam, temperature of tank water, and location along the axis of the nozzle. The results reveal the fact that the value of the LNN reaches a maximum at the nozzle exit along the axis of the nozzle at 323 K tank water temperature. LNN decreases by increasing or decreasing the tank water temperature beyond 323 K. It is claimed that the heat transfer (HT) study at such a local scale has been conducted for the first time to the best of our knowledge, and it unfolds various crucial facts regarding steam-water interaction.

Rheological analysis of pressure-driven Jeffrey fluid flow between corrugated porous curved walls with slip constraints

Pressure-driven movement is a fundamental concept with numerous applications in various industries, scientific disciplines, and fields of engineering. Its proper execution is vital for promoting revolutionary innovations and providing solutions in numerous sectors. Therefore, this article scrutinizes the pressure-driven flow of a magnetized Jeffrey fluid between two curved corrugated walls. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity and temperature taking the corrugation amplitude as the perturbation parameter. Furthermore, the volumetric flow rate, skin friction coefficient, and local Nusselt numbers are precisely calculated numerically for a variety of parameters, with the results presented comprehensively in tabular form. The impact of dissimilar parameters, such as the curvature parameter, wave number, magnetic parameter, Darcy number, thermal radiation, heat source/sink parameter, Jeffery fluid parameter, and amplitude parameter, on the flow fields is analyzed through graphical and tabular forms and discussed in detail. The results show that the velocity profile increases due to the curvature parameter and the Jeffrey fluid parameter. However, it decreases due to the magnetic parameter. The temperature distribution rises with the thermal slip and heat source/sink parameters. Meanwhile, it declined for the radiation parameter and the curvature parameter. The model can be used to simulate blood flow in arteries with varying geometries and magnetic fields, aiding in the study of cardiovascular diseases and the design of medical devices such as stents.

Investigation on numerical simulation models for heat transfer characteristics of lead-bismuth eutectic

The liquid lead-bismuth eutectic (LBE) has distinct thermal and physical properties that challenge the effectiveness of traditional RANS turbulence models and turbulent Prandtl number (Prt) models for accurately simulating its flow and heat transfer characteristics. This study aims to investigate numerical simulation models of LBE based on existing experimental data. Simulations are conducted using different combinations of three turbulence models and four Prt models, and comparisons are made with experimental data. The local and overall heat transfer characteristics of LBE are analyzed, and the applicability of each model combination is evaluated. Results indicate that for simulating local heat transfer characteristics, the SST k-ω turbulence model combined with the Prt model proposed by Cheng et al. yields the highest accuracy. Additionally, the empirical correlation for heat transfer proposed by Kutateladze provides the best prediction of the local Nusselt number. For overall heat transfer characteristics, the combination of the SST k-ω turbulence model and the Prt model introduced by Reynolds et al. demonstrates the highest accuracy and applicability. This investigation might offer a pivotal benchmark for the discernment of appropriate computational fluid dynamics (CFD) models for liquid metal breeder reactor (LMBR) applications utilizing lead-bismuth eutectic (LBE) as coolant.

Turbulent impinging air jet for cooling the heated surface

The present work deals with the experimental and numerical study of steadystate conjugate heat transfer during impingement of turbulent air jet over a heated stainless steel. The plate is heated using copper heater located at the middle. The temperature field is measured using an infrared camera and compared with the numerical simulations. Numerical simulations are performed using three-dimensional finite volume based formulation. The turbulence shear-stress transport (SST) is modeled using k−ω model based on the Reynolds averaged Navier Stokes (RANS) equations. The numerical simulations are in good agreement with the experimental data with marginal discrepancy in the steel plate region due to the contact thermal resistance between steel and copper. It is observed that the local Nusselt number increased in the stagnation region with increasing velocity of the impinging turbulent flow and practically unaltered in the region of the steel plate.

Experimental and numerical studies of detailed heat transfer and flow characteristics in the rib turbulated annulus of a double pipe heat exchanger

An enhancement in the overall heat transfer between the fluids in a Double pipe heat exchanger (DPHE) can be achieved through various active or passive techniques. The present study focuses on the passive heat transfer enhancement in the annular region of a DPHE by incorporating circular ribs on the outer surface of the inner pipe. The primary objective is to investigate the influence of the ribs on the local distribution of heat transfer and fluid flow in the annulus of the heat exchanger. The local Nusselt number (Nu) distribution was determined experimentally using a test section specially designed with a provision to measure the wall temperature distribution of the inner pipe with an IR thermal imaging camera. The pressure drop across the channels with the ribs was also measured in the experimental studies. Numerical studies are employed to gain insights into the flow characteristics in the annular region in the presence of ribs. Studies comprise various rib diameters (e/Dh = 0.08, 0.14), rib-to-rib pitches (P/e = 6, 12, 18), and Reynolds number values (Re = 5000, 7500, and 10000). The heat transfer behaviour from the experimental study is discussed based on the flow mechanism observed using numerical techniques. The flow separation and reattachment due to the rib and the induced recirculation zone cause large variations in the Nusselt number distribution between the ribs. The peak Nusselt number value between adjacent ribs is observed at the location of reattachment of the flow to the ribbed wall. Acquired data also shows that the flow and heat transfer characteristics differ significantly with changes in the P/e ratio. The rib configuration with e/Dh = 0.14 and P/e = 12 is identified as optimal, achieving a balanced improvement in heat transfer while showing a relatively lower pressure drop.

Analysis of flow and heat transfer in bend pipe with different smoothing

This research employs a numerical approach to comprehensively analyze fluid flow and forced convection heat transfer phenomena within a bent pipe. The finite difference method obtains numerical results, and simulations are conducted across a Reynolds number range of 100≤Re≤800, at constant Prandtl number (Pr=1). The study explores three inclination angles (ϕ=30°45°70°) and incorporates three smoothing phases of the bending angles. The results are presented through streamline and isotherm and local Nusselt numbers. Notably, vortices near the pipe bend positively correlate with Reynolds number and inclination angle, enhancing heat transfer. At the same time, an inverse relationship is observed between vortex length and bend smoothness. Furthermore, higher local Nusselt numbers are identified at elevated inclination angles, and Reynolds numbers are on the wall bend in the channel. Overall, this investigation underscores the significant influence of inclination angle on heat transfer characteristics, providing valuable insights for applications in thermal engineering and fluid dynamics.

Application of Box-Behnken design with RSM to predict the heat transfer performance of thermo-magnetic convection of hybrid nanofluid inside a novel oval-shaped annulus enclosure

The study of flow around a stationary or rotating circular cylinder holds substantial importance in numerous engineering disciplines, including building, bridge, and structural engineering. This knowledge is utilized to manage flow-induced vibrations, implement blowing or suction techniques, control moving surfaces, and develop acoustic thrusters and synthetic jets. The current aims to analyze the numerical and RSM optimization with Box–Behnken design (BBD) for the buoyancy driven convective flow and heat management features of Magneto Fe3O4−MWCNTs/water hybrid nanofluid filled inside a novel oval-shaped annulus enclosure with concentric hot circular cylinder. The water used as base fluid and iron oxide and Multiwall carbon nanotubes as nanoparticles. The finite element method is employed to solve numerically the coupled equations. The RSM optimization with Box–Behnken design (BBD) is applied to optimize the heat transfer rate across different three factors. The stream lines, isotherms and line graphs are design for different flow parameters effect. The results indicated that heat transfer is enhanced by using of hybrid nanofluid. The velocity is reduced via increment in Hartmann number. The local Nusselt number is increases with increment in the values of the Rayleigh number. Furthermore the Heat transfer rate is boosted up with increases the concentration of nanoparticles.

Buoyancy-driven nano-suspension subject to interstitial solid/nanofluid heat transfer coefficient: Role of local thermal non-equilibrium (LTNE)

BackgroundBecause of the prominent temperature discrepancy between fluid and solid in porous material, local thermal equilibrium (LTE) is not suitable in case of high-conductivity foams and electronic equipment. In view of above situation, Darcy-Brinkman-Forchheimer model subject to local thermal non-equilibrium (LTNE) is implemented. LTNE technique finds real world applications include groundwater pollution, geothermal extraction, microwave heating, industrial separation process, and transpiration cooling featuring with porous structure. The present study aims at the investigation of the entropy and hydrothermal characteristics of buoyancy-driven TiO2-H2O nanofluid inside a cross-shaped domain embodying two hot and cold rings influenced by LTNE. MethodsFinite element method (FEM) has been considered to solve the dimensionless form of governing equations. Significant findingsAmplification of interstitial solid/nanofluid heat transfer coefficient accounts for the intensification of streamlines, velocities, and diminution of isothermal lines in both nanofluid and solid matrix phases under the influence of LTNE. Strengthening of medium porosity whittles down entropy due to thermal effects in both nanofluid and solid phases, and that ameliorates entropy due to fluid friction and porous medium irreversibilities. Local and average Nusselt numbers in nanofluid phase reduce by 29.31 %, 20.72 %, 17.16 %, and 14.78 % while that in solid phase decays by 13.18 %, 7.63 %, 4.9 %, and 2.8 % for rise in εfrom 0.1 to 0.3, 0.3 to 0.5, 0.5 to 0.7, and 0.7 to 0.9, respectively. Introduction of Darcy-Brinkman-Forchheimer model subject to LTNE yielded better results in hydrothermal behavior of TiO2-H2O nanofluid inside a cross-shaped domain emplacing two hot and cold rings than earlier published results.

Hybrid ferrofluid flow on a stretching sheet with Stefan blowing and magnetic polarization effects in a porous medium

PurposeThis study investigates the behavior of viscous hybrid ferromagnetic fluids flowing through plain elastic sheets with the magnetic polarization effect. It examines flow in a porous medium using Stefan blowing and utilizes a versatile hybrid ferrofluid containing MnZnFe2O4 and Fe3O4 nanoparticles in the C2H2F4 base fluid, offering potential real-world applications. The study focuses on steady, laminar and viscous incompressible flow, analyzing heat and mass transfer aspects, including thermal radiation, Brownian motion, thermophoresis and viscous dissipation with convective boundary condition.Design/methodology/approachThe governing expression of the flow model is addressed with pertinent non-dimensional transformations, and the finite element method solves the obtained system of ordinary differential equations.FindingsThe variations in fluid velocity, temperature and concentration profiles against all the physical parameters are analyzed through their graphical view. The association of these parameters with local surface friction coefficient, Nusselt number and Sherwood number is examined with the numerical data in a table.Originality/valueThis work extends previous research on ferrofluid flow, investigating unexplored parameters and offering valuable insights with potential engineering, industrial and medical implications. It introduces a novel approach that uses mathematical simplification techniques and the finite element method for the solution.

Laminar flow and convective heat transfer of ferrofluid in a tube under oscillating magnetic fields: Effect of magnetic phase shift

In this study, laminar flow and forced convective heat transfer of water-based ferrofluids flowing through a uniformly heated pipe are experimentally investigated under the presence of phase-shifted oscillating magnetic fields. To investigate the effect of phase shift on heat transfer, electromagnets are positioned along the tube, and oscillating magnetic fields are applied with various phase shift angles between opposing magnetic poles. Experiments are conducted for different Reynolds numbers (400 to 1000), magnetic field frequencies (0 Hz, 1 Hz, and 5 Hz), phase shift angles (0°, 90°, and 180°), and nanoparticle volume fractions (0.5 % and 1 %). For each parameter set, local and average Nusselt numbers, as well as pressure drop values, are determined, and the effect of applied magnetic fields on the heat transfer rate is extensively discussed. Results showed that, applying an external magnetic field resulted in significant enhancements in the forced convective heat transfer of ferrofluid. Under an oscillating magnetic field with 0° phase shift, maximum of 40 % and 20.6 % enhancements were observed in local and average Nusselt numbers respectively under the investigated parameters. Furthermore, applying oscillating magnetic fields with a phase shift between opposing poles caused significant fluctuations in the fluid, led to remarkable improvements in convective heat transfer rates. For 90° and 180° phase shifts, enhancements in local and average Nusselt numbers were observed to increase up to 73 % and 36 %, respectively.

Comparative characterization of heat transfer and entropy generation of micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade binary nanofluids in PTSCs settings

AbstractIn this paper, we delve into the behavior of binary micropolar nanofluids, specifically micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade, within the parabolic trough solar collector (PTSC) configurations. The primary objective is to enhance the collective efficiency of this device by means of a comprehensive comparison amongst the three aforementioned nanofluids. The governing equations, including continuity, linear momentum, angular momentum, and energy equations, were systematically formulated. Subsequently, the introduction of suitable similarity variables facilitated the transformation of the intricate partial differential equations into manageable ordinary differential equations. These resultant equations were then tackled utilizing the shooting method via the bvp4c numerical package in MATLAB. The study critically examines the influence of diverse parameters that dictate the flow dynamics of the nanofluids. This encompasses nanofluid velocity, angular velocity, temperature distribution, entropy generation, skin friction coefficient, and local Nusselt number. Remarkably, the research uncovers that the maximum temperature levels experienced enhancements of 12.1134%, 12.0616%, and 11.0645% for the micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade nanofluids, respectively. These results imply that the introduction of these binary micropolar nanofluids leads to notable thermal enhancements in the PTSCs settings.

An in‐depth comparative analysis of entropy generation and heat transfer in micropolar‐Williamson, micropolar‐Maxwell, and micropolar‐Casson binary nanofluids within PTSCs

AbstractSolar energy holds promise as a sustainable and environmentally friendly source of power. In this study, we focus on improving the thermal efficiency of parabolic trough solar collectors (PTSCs) by investigating the performance of three different binary micropolar nanofluids – micropolar‐Casson, micropolar‐Maxwell, and micropolar‐Williamson – when used as heat transfer fluids within these collectors, with engine oil as the base fluid. The problem studied revolves around enhancing the heat transfer characteristics within PTSCs, crucial for maximizing energy conversion efficiency in solar power generation. By exploring the behavior of these nanofluids under various flow conditions, we aim to optimize the design and operation of PTSC systems for improved performance and sustainability. The importance of this research lies in its potential to significantly enhance the efficiency of solar energy harvesting, thereby contributing to the transition toward cleaner energy sources and reducing dependence on fossil fuels. Additionally, the findings have implications for diverse applications, including solar aviation, solar‐powered maritime vessels, solar thermal power plants, industrial process heating, and solar‐driven water pumping mechanisms, where improved heat transfer efficiency is paramount for enhancing overall system performance and reducing operational costs. Furthermore, the investigation delves into the influence of various factors governing the flow of these binary micropolar nanofluids within PTSC setups, including aspects such as velocity, thermal characteristics, entropy generation, skin friction, drag force, and local Nusselt number. The results notably reveal substantial enhancements in thermal efficiency, with maximal relative enhancements quantified as 22.1768%, 19.3662%, and 17.7349% for micropolar‐Casson, micropolar‐Maxwell, and micropolar‐Williamson nanofluids, respectively.