Increase In Nusselt Number Research Articles

Twisted-tape inserts of rectangular and triangular sections in turbulent flow of CMC/CuO non-Newtonian nanofluid into an oval tube

Purpose This paper aims to study numerically the non-Newtonian solution of carboxymethyl cellulose in water along with copper oxide nanoparticles, which flow turbulently through twisted smooth and finned tubes. Design/methodology/approach The twisted-tape inserts of rectangular and triangular sections are investigated under constant wall heat flux and the nanoparticle concentration varies between 0% and 1.5%. Computational fluid dynamics simulation is first validated by experimental information from two test cases, showing that the numerical results are in good agreement with previous studies. Here, the impact of nanoparticle concentration, tube twist and fins shape on the heat transfer and pressure loss of the system is measured. It is accomplished using longitudinal rectangular and triangular fins in a wide range of prominent parameters. Findings The results show that first, both the Nusselt number and friction factor increase with the rise in the concentration of nanoparticles and twist of the tube. Second, the trend is repeated by adding fins, but it is more intense in the triangular cases. The tube twist increases the Nusselt number up to 9%, 20% and 46% corresponding to smooth tube, rectangular and triangular fins, respectively. The most twisted tube with triangular fins and the highest value of concentration acquires the largest performance evaluation criterion at 1.3, 30% more efficient than the plain tube with 0% nanoparticle concentration. Originality/value This study explores an innovative approach to enhancing heat transfer in a non-Newtonian nanofluid flowing through an oval tube. The use of twisted-tape inserts with rectangular and triangular sections in this specific configuration represents a novel method to improve fluid flow characteristics and heat transfer efficiency. This study stands out for its originality in combining non-Newtonian fluid dynamics, nanofluid properties and geometric considerations to optimize heat transfer performance. The results of this work can be dramatically considered in advanced heat exchange applications.

Turbulent convection in emulsions: the Rayleigh–Bénard configuration

This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh–Bénard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in dispersed-phase volume fractions, $0.0 \leq \varPhi \leq 0.5$ , and ratios of dynamic viscosity, $\lambda _{\mu }$ , and thermal diffusivity, $\lambda _{\alpha }$ , within the range $[0.1\unicode{x2013}10]$ . The Rayleigh, Prandtl, Weber and Froude numbers are held constant at $10^8$ , $4$ , $6000$ and $1$ , respectively. Initially, when both fluids share the same properties, a 10 % Nusselt number increase is observed at the highest volume fractions. In this case, despite a reduction in turbulent kinetic energy, droplets enhance energy transfer to smaller scales, smaller than those of single-phase flow, promoting local mixing. By varying viscosity ratios, while maintaining a constant Rayleigh number based on the average mixture properties, the global heat transfer rises by approximately 25 % at $\varPhi =0.2$ and $\lambda _{\mu }=10$ . This is attributed to increased small-scale mixing and turbulence in the less viscous carrier phase. In addition, a dispersed phase with higher thermal diffusivity results in a 50 % reduction in the Nusselt number compared with the single-phase counterpart, owing to faster heat conduction and reduced droplet presence near walls. The study also addresses droplet-size distributions, confirming two distinct ranges dominated by coalescence and breakup with different scaling laws.

Impacts of Buoyancy and Joule Heating on Unsteady MHD Fluid Flow Along a Semi‐Infinite Vertical Porous Plate With Dufour, Chemical Reaction, and Radiation Effect

ABSTRACTAn analytical solution for unsteady, incompressible, laminar MHD fluid flow involving mass and heat transfer along a semi‐infinite vertical moving flat plate in a porous medium have been studied in this paper. Effects of heat radiation and absorption, Joule heating, Dufour, thermal and solutal buoyancy, and first order chemical reaction of are discussed under suitable physical conditions. It is postulated that the plate will migrate in the fluid's motion's direction due to the presence of a uniform magnetic field normal to the porous surface. The regular perturbation technique is used to solve the dimensionless governing equations. The mathematical derivations for fluid velocity, temperature, and concentration are evaluated; apart from that, skin friction, rate of mass and heat transfer at the plate are also expressed. The present outcomes are compared with previously obtained results and are found to be in excellent agreement. It is observed that the fluid velocity and temperature enhanced with thermal and solutal buoyancy forces as well as the Dufour effect. Also, with an increase in chemical reaction parameter, there is a decrease in fluid velocity, temperature, and concentration. Skin friction and Nusselt number increase with higher heat absorption parameter values. Schmidt number and chemical reaction parameter both lead to a rise in Sherwood number. Applications for these models have been observed in a number of industrial and technical methods.

Investigating the Influence of Square Size Vanes on Heat Transfer in porous media: An In-depth Nusselt distribution

Abstract This research provides an extensive analysis with various γ on natural convection, thermal entropy generation, fluid flow, and temperature distribution in the porous cavity. On the thermal performance, the studying impact effective factors entailing geometrical parameters, Ha, Da, Pr, γ, and ε are analyzed meticulously. The finite element method (FEM) is carried out to analyze fluid flow and heat distribution in the present porous media. The innovation of this research is considered key parameters constitute Ha, Da, Pr, γ, and ε for substantial assesses average Nusselt number in porous media with different square size vanes at the corners and effect variable cooled size at the corners of the square porous cavity for an in-depth analysis of the thermal performance. In validation, the calculation of the results was adapted accurately to the finite element method's fluid flow, temperature distribution, and average Nusselt number. Numerical results revealed that various γ affected widely in the generation of entropy. Also, square-size vanes at the corners of the porous cavity markedly influenced fluid flow trend hot and cold temperature distribution. The Hartman number is the most important influence on the average Nusselt number, which observed a sharp increase in the average Nusselt number. Moreover, as the Darcy number grew, the average Nusselt number rose apart from in γ = 1 in porous media with size vanes 0.2.

Twisted tapes in solar chimney-earth air heat exchangers for equipment downsizing and passive cooling

Harnessing solar and geothermal energy in hot and arid climates is an effective strategy to reduce building energy consumption. This research investigates integrating Twisted Tapes (TT) into Earth Air Heat Exchanger (EAHE) pipes within a Solar Chimney (SC)-EAHE system, aiming to reduce EAHE pipe length while meeting ventilation requirements and decreasing cooling demand. Two key innovations are introduced: first, this study pioneers the integration of TT into a SC-EAHE system; second, it comprehensively explores TT geometry optimization, analyzing the effects of width ratio and rotation rate across 77 configurations. Numerical simulations are conducted in ANSYS Fluent using the k-ε RNG turbulence model to investigate thermal performance and airflow characteristics. Findings reveal that TT integration results in a 153 % increase in Nusselt number. Additionally, it is shown that a 1 m SC diameter achieves ventilation of 4.8 Air Changes per Hour (ACH) using TT with a width ratio and rotation rate of 0.5, while reducing EAHE pipe length by 2.6 %. Increasing the SC diameter to 1.25 m, with a TT width ratio of 0.6 and rotation rate of 1.25, leads to a 13 % (35 m) reduction in EAHE pipe length while meeting a minimum outlet temperature of 290.15 K and ACH requirements. However, the benefit diminishes beyond a 1.25 m SC diameter. This study contributes to understanding of integrating TT into SC-EAHE systems, addressing the critical need for sustainable energy solutions and offering a novel and energy-efficient approach for passive cooling in extreme climates.

Analysis of hydrodynamics and thermal–hydraulic performance of twisted angle fins within an annular conduit

AbstractThis paper investigated the influence of various twisted angles of fin inserts integrated on the inner heated pipe wall of a double-pipe heat exchanger by analysing the thermal–hydraulic performance through numerical simulations. Results showed twisted angle fin (TAF) induced turbulent fluid flow phenomena, generating transverse and longitudinal vortices, along with swirling flow. This collaboration between the vortices and swirling flow effectively prevents heat trapping and enhances heat transfer from the inner pipe wall through the intensive fluid mixing. Despite longitudinal swirling vortices and turbulence significantly enhance local and global heat transfer performance, they led to increased pressure drop. However, TAF twisting reduces pressure drop by streamlining flow. The performance evaluation criterion (PEC) value is a dimensionless quantity that facilitates the comprehensive evaluation of optimal configurations by comparing the increment in Nusselt number and the increment in friction factor. PEC values greater than 1 indicate that the increase in Nusselt number exceeded the increase in friction factor. Among tested configurations, the twisted fin angles of 60° (TAF60) exhibited the highest improvement in Nusselt number and friction factor, also achieving the highest PEC of 1.59712 at Reynolds number of 1194.71. TAF40 and TAF50 were identified as optimal configurations for enhancing the thermal–hydraulic efficiency, with average PEC values of 1.26893 and 1.27030, respectively. Overall, the study indicated a consistent enhancement trend with increasing twisted angles and emphasizes the significant thermal performance improvement of TAF configurations compared to the smooth conduit. Furthermore, the results showed a converging tendency across all TAF configurations in the percentage improvement in Nusselt number and friction factor, as well as PEC compared to the baseline No fin configuration with increasing Reynolds number, suggesting that future improvements in thermal–hydraulic performance are more dependent on geometric angles than fluid flow velocity.

Entropy generation analysis and thermal performance of absorber tube in parabolic trough solar collector inserted with eccentric structure insert

To address the issue of uneven heat transfer in parabolic trough solar collectors, this study introduces an innovative insert (composed of vortex generators) layout. The vortex generators are strategically placed in areas with high heat flux density, while their number is reduced in regions with low heat flux density. By adjusting the position of the central rod, the inserts are defined as three different layout strategies (central structure, low eccentric structure, and upper eccentric structure), and their thermal performance is analyzed. The differences in fluid flow and heat transfer induced by different structures are also compared. The results show that the upper eccentric structure can induce unevenly distributed high-intensity mixing vortices, and through the ejection and sweeping movements of these vortices, the high-temperature fluid in areas with high heat flux density is transported to positions with low geothermal flow. Among all the studied configurations, the upper eccentric structure achieves a Nusselt number increase ranging from 1.16 to 2.34 times and a friction number value increase between 1.47 and 5.38 times. In terms of heat transfer performance, the highest value is 1.43 when the number of vortex generators is 6 and Reynold number is 13,750. Additionally, the thermal performance of the inserted tubes is analyzed using the field synergy principle and entropy generation method.

Modeling of turbulent flows through annuli with smooth and rough walls; drag reduction and heat transfer

A model of a turbulent flow in an annular channel with rough walls is developed. An effect of roughness on hydraulic resistance of the channel is accounted for through the formal dimensionless negative velocity shift at the wall by using an empirical function linking this velocity shift to the dimensionless sandgrain wall roughness. The developed annular flow model is validated by experimental data found in literature for both smooth walls, both rough walls, smooth outer wall and rough inner wall as well as vice versa. The same flow model is applied also to a polymer solution turbulent flow in annular channel with hydraulically smooth walls. A turbulent drag reduction effect, observed in this case, is accounted for by a positive velocity shift at the wall determined for a certain drag reduction chemical from experiments in a round cross-section pipe. Also, an engineering approach for modeling heat transfer through either outer or inner wall of an annular channel with rough walls is suggested. This approach is based on the known analogy of heat transfer in a hydraulically smooth annular channel and a pipe. This analogy is extended to an annular channel with rough walls by using the developed flow model. The heat transfer model developed is validated, discussed and illustrated by calculation examples. Key attention is paid to analyzing an effect of the Reynolds number on both a Nusselt number increase and an efficiency change for different wall roughening cases.

Second law of thermodynamics, heat transfer, and pumping power analyses of water and ionic liquid mixture based MXene nanofluids in a shell and helical coil heat exchanger

Heat exchangers are extensively employed across diverse sectors for efficient thermal (heat)transfer between two fluids, specifically from a hot fluid to a cold fluid. Nanofluids are promising heat transfer fluids that exhibit exceptional thermal performance in heat exchangers. The present study examines the thermodynamic second law efficiency analysis of a shell and helical coil heat exchanger utilizing MXene/80:20% water+[MMIM][DMP] (mass percentage) based ionanofluids. An analytical investigation was conducted on the heat transfer coefficient, entropy generation rate, and exergy efficiency of a shell and helical coil heat exchanger, considering particle weight loadings from 0.2% to 1.0%, Reynolds numbers from 500 to 4300, and flow rates from 0.5 to 3.5 L/min. In the base fluid, at 1.0 wt.% and at a Reynolds number of 3598, the increase in heat transfer, Nusselt number, friction factor, pressure drop, effectiveness, and frictional entropy generation are 45.59%, 28.27%, 15.19%, 12.56%, 17.20%, and 16.21%, respectively. Concurrently, thermal entropy generation, and total exergy destruction were reduced by 46.23% and 20.08%, respectively. The second law (exergy) efficiency and thermal performance factor are improved by 34.04% and 1.384-times, respectively, at 1.0 wt.% and at a Reynolds number of 3598, compared to the base fluid. The data from the current study is corroborated by existing literature. New correlations were developed from the computed data points to estimate the Nusselt number and friction factor.

Heat transfer and fluid flow analysis of a solar air heater using conical jet impingement with sine-wave corrugation on absorber plate

In the pursuit of renewable energy solutions, solar air heaters emerge as a promising technology to efficiently harness solar thermal energy for diverse applications such as space heating, agricultural drying and industrial process heating. However, the system’s efficiency is often limited by the low heat transfer capability of air and the formation of laminar sub-layer over the absorber plate. This study addresses the issue by investigating the innovative use of conical jet impingement combined with sine wave corrugations on the absorber plate to enhance heat transfer in solar air heaters. The design parameters include wave amplitude ratio (0.079–0.314), throat jet diameter ratio (0.063–0.141), base jet diameter ratio (0.126–0.251), and Reynolds number (3200–19200) as the operational parameter. The computational fluid dynamics simulations are employed to solve the Reynolds-Averaged Navier-Stokes equations coupled with RNG k-ɛ turbulence model to assess the heat transfer and frictional characteristics, followed by experimental validation. The findings demonstrate a significant improvement in the system’s heat transfer rate with the Nusselt number increase by a factor of 6.71 times compared to a smooth solar air heater, while the friction factor increase by 13.87 times. Furthermore, the highest thermo-hydraulic performance parameter is found to be 2.79 corresponding to Reynolds number of 3200, wave amplitude ratio of 0.079, throat and base jet diameter ratios of 0.126 and 0.220, respectively. The proposed geometry will be helpful for academic researchers and can be adopted by the industries for various applications.

Flow and sensitivity analysis of MHD radiative hybrid nanofluid flow across a permeable wedge with slip condition: Response surface methodology

AbstractThis current paper has been written to investigate the effect of a hybrid Tiwari and Das nanofluid model along with optimizing the flow using sensitivity analysis. Heat transfer rates and skin friction assessments were examined with the supplementation of external effects like heat source, thermal radiation, buoyancy forces, velocity slip as well as magnetic effect with spherical‐shaped nanoparticles. The mathematical modeling was formulated using a system of nonlinear PDE. Similarity transformations were implemented in the governing equations for obtaining the final set of nondimensional equations which were then solved using bvp4c code in MATLAB. The results obtained were in close agreement with published results. Some of the significant results obtained included an increase in Nusselt number by 2.26% for an increase in velocity ratio parameter () from to 0.3 along with an increase in skin friction coefficient by 0.77% with magnetic () parameter to . The heat transfer profile was augmented by 0.79% with increasing radiation parameter to while an increase of 18.84% was observed for skin friction profile values recorded for the hybrid model as compared to the base fluid model. Nusselt number reduced by 0.51% for a transition to nanofluid model from regular fluid and by 1.76% for the hybrid model compared to the nanofluid model The unblocked face‐centered central composite design (CCD) was used for analyzing the sensitivity analysis of independent, continuous input parameters on the response parameters, skin friction coefficient, and Nusselt number. The high values for , and , for Nusselt number and skin friction coefficient values, respectively, validate the ANOVA results obtained using response surface methodology (RSM). Only shows positive sensitivity for both the Nusselt number and skin friction responses. The present hybrid nanofluid model finds extensive applications in bio‐toxicity studies, manufacturing of water heaters, and forging of hot exhaust valve heads.

Enhancing heat transfer with a hybrid vortex generator combining delta wing and winglet designs: A numerical study using the GEKO turbulence model

This paper presents a numerical study on the enhancement of heat transfer in a solar air heater (SAH) duct with Hybrid Vortex Generators (HVG) placed periodically along the flow direction on its heated wall (absorber plate) for fluid flow and convection heat transfer at Reynolds numbers between 4121 and 25,365. HVGs consist of a trapezoidal winglet (TWL) for HVG-winglet-base-angles θ = 45° and 30°, or a combination of a delta winglet (DWL) with a delta wing (DWG) for angles θ = 26°, 18° and 12°. The angle of attack for the winglet (TWL or DWL) in the HVG is set at 30°, while the merging angle with the DWG is 45°, and the relative height BR = e/H = 0.48 remains constant. Initially, the effects on heat transfer and friction factor of Trapezoidal Winglet Vortex Generator (TWVG) and HVG45 (θ = 45°) obtained by basic modification on TWVG are investigated under the same flow conditions for PR = 1.5 and Re = 11,205. Subsequently, parametric studies are performed for five different HVG-winglet-base-angles (θ = 45°, 30°, 26°, 18° and 12°) and three different longitudinal pitch ratios (PR = PL/H = 1.0, 1.5 and 2.0). The calculations are performed with ANSYS Fluent 2021R2 based on the finite volume method. In order to model turbulent flow, the GEKO (GEneralized K-Omega) turbulence model recently developed by ANSYS and based on the k-ω formulation is used. HVG45, obtained by basic modification on TWVG, produces slightly stronger and more effective longitudinal vortices compared to TWVG, showing a 3.87 % decrease in friction factor and a 4.11 % increase in Nusselt number and thus a 5.43 % increase in Thermal Enhancement Factor (TEF). Parametric investigations are conducted across a range of values for both θ and PR. The highest rise in friction factor is attained at the lowest Reynolds number, reaching a value of f/f0 = 54.52, while the most significant enhancement in heat transfer rate is noted at the highest Reynolds number, with Nu/Nu0 = 5.86 for θ = 45° and PR = 1.0. The TEF reaches 2.42 at the lowest Reynolds number for the HVG18 with a winglet-base-angle of 18° and a longitudinal pitch ratio of 1.5. The resulting findings not only offers a new approach to improve the thermal performance of solar air heaters but also hints at the potential success of the GEKO model in predicting turbulent flow and heat transfer analysis.

Synergistic effects of magnetic fields and Y-obstacles on a nanofluid-based split lid-driven thermal system

This study investigates the complex hydrothermal behavior in a novel split-driven square cavity filled with CuO-water nanofluid and featuring a Y-shaped obstacle. The research explores the interplay among mixed convection, magnetohydrodynamics (MHD), and geometric factors in a previously unexamined configuration. The upper wall is split into two isothermally heated, translating sections, while the bottom wall and Y-shaped obstacle provide cooling boundaries. Using finite element analysis, we examine the effects of Reynolds number (Re = 10-200), Rayleigh number (Ra = 103-106), Hartmann number (Ha = 0-70), and magnetic field inclination (λ = 0-150°) on flow patterns, heat transfer, and entropy generation. Energy flux vectors are utilized to analyze thermal energy transport dynamics. Key findings are as follows. (1) Increasing Re enhances fluid mixing, resulting in up to a 65% increase in the average Nusselt number (Nu). (2) Nu peaks at Ra ≈ 105, then slightly decreases due to complex force interactions. (3) Increasing Ha suppresses convection, reducing Nu by up to 30%. (4) Optimal heat transfer occurs at λ ≈ 75°. (5) The Y-shaped obstacle enhances heat transfer by up to 30%. These results provide insights for optimizing thermal management in applications requiring precise temperature control, potentially improving energy efficiency in advanced heat transfer systems.

Numerical simulation of thermal enhancement in pulsating inflow grooved channel based on hydrodynamic instability

In this paper, a numerical simulation study of flow and heat transfer in a grooved channel consisting of ten rectangular grooves with steady and pulsating flow is carried out. Numerical simulations of the steady flow with small perturbations applied at Re = 800, 1200, 1600, and 2000 show that the same intrinsic frequency fN exists at different positions, amplitudes, and durations, and it disappears gradually with the development of the flow. A sinusoidal pulsating flow with different frequencies is applied to the grooved channel with the dimensionless amplitude A fixed at 0.2. The flow and heat transfer properties of the grooved channel are investigated in the case of pulsating inflow, and it is found that there exists a vortex periodic formation–development–convergence–dissipation process inside each groove. The results show that the increase in the time-averaged Nusselt number is 44.12%, 57.75%, 53.21%, 52.93%, the time-averaged friction factor is increased by 58.23%, 133.04%, 140.80%, 151.26%, and the PECs is decreased with the increase in Reynolds number to be 1.24, 1.19, 1.14, and 1.12, respectively, when compared with the constant flow. When the forcing frequency is equal to the hydrodynamic instability frequency, the time-averaged Nusselt number of the grooved channel will reach its maximum value. Also, the dynamic mode decomposition analysis shows that the pulsation mode energy is maximum when the forcing frequency is equal to the hydrodynamic instability frequency. It shows that the applied pulsating flow has a positive effect of enhanced heat transfer, and the positive effect decreases with the increase in Reynolds number.

Performance Analysis of Corrugated Twisted Tape Inserts for Heat Transfer Augmentation

This study explores the impact of wavy corrugated twisted tape inserts on enhancing heat transfer and reducing pressure drop in a double pipe heat exchanger. Cu inserts with twist ratios of 3.2, 4.2, and 5.2 were used to create turbulence in the inner tube. Varying water flow rates and measuring bulk mean temperatures at different points revealed significant improvements in heat transfer over smooth tubes. The insert with a 3.2 twist ratio achieved the highest Nusselt number increase (185%) and a 36.33% rise in the friction factor. These results highlight the effectiveness of wavy corrugated twisted tape inserts for optimizing heat transfer, with a 3.2 twist ratio identified as the most effective. Across Reynolds numbers from 4000 to 18000, Nusselt number increases were 77.75% for a 5.2 twist ratio, 167% for a 4.2 twist ratio, and 185% for a 3.2 twist ratio. Friction factors rose by approximately 10.42% for a 5.2 twist ratio, 32.54% for a 4.2 twist ratio, and 36.33% for a 3.2 twist ratio, demonstrating the relationship between twist ratio, heat transfer enhancement.

Novel 2D Layered MXene Nanofluids for Enhancing the Convective Heat Transfer Performance of Double-Pipe Heat Exchangers.

This paper proposes a new class of novel 2D layered structured materials, such as MXene (MX), for the synthesis of innovative nanofluids as coolants to evaluate the convective heat transfer performance of a double-pipe heat exchanger (DPHE). Convective heat transfer experiments were successfully conducted in lab-scale fabricated DPHE using low-concentration MXene nanofluids by varying the volume concentration of MXene nanoparticles (0.01-0.05 vol %) in different base fluids. The influence of the MXene nanofluids on various convective heat transfer parameters, such as LMTD, Nusselt number, heat transfer coefficient, and heat transfer rate without using any inserts in the DPHE was experimentally investigated. The results of the experiments revealed that the heat transfer coefficient and Nusselt number increase with increasing Reynolds number (Re) and concentration of MXene nanoparticles in the base fluids. Maximum enhancement in heat transfer coefficient (126%) was achieved for methanol-based MXene nanofluids at 0.05 vol %. Moreover, the Nusselt number exhibits a maximum enhancement of ∼50% for methanol- and water-based MXene nanofluids. In contrast, the thermal performance factor was also estimated, and it was observed that water- and methanol- based MXene nanofluids showed higher values than castor oil- and silicone oil-based MXene nanofluids. Finally, the LMTD and heat transfer coefficients were successfully validated using Aspen HYSYS 12.1 software.

Convective heat transfer in porous channel with multi-layer fractures under Local thermal non-equilibrium condition

Based on Brinkman-extended-Darcy model and Local thermal non-equilibrium (LTNE) model, analytical solutions of velocity and temperature fields, pressure drop and Nusselt number of porous channels containing different number of fracture layers are obtained. The characteristics of fluid flow and heat transfer in multi-layer parallel fractured channels are further studied. Results show that for a single-layer or multi-layer fractured channel, the pressure drop changes sensitively at small hollow ratio and increases as the number of fracture layers increases with decreasing increase degree, but the pressure drop tends to be consistent regardless of the number of fracture layers when Darcy number is high. For small ratio of effective thermal conductivity, LTE model is valid regardless of Biot number, and the heat transfer intensity in multi-layer fractured channels is always higher than that in single-layer fractured channel at any hollow ratio, but the heat transfer intensity is still low. For large ratio of effective thermal conductivity, increasing Biot number or fracture layer number makes the Nusselt number increase under very small hollow ratio for both single and multiple fracture cases, and when both the ratio of effective thermal conductivity and Biot number are high, there is an intersection point occurs at hollow ratio near 0.1, which makes same heat transfer effect under different fracture numbers.

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.

Analysis of magneto-natural convection and second law of thermodynamics of Cu-Al2O3-hybrid nanofluid in a vertical wavy cabinet having a localized non-uniform heat source

Improvements in thermal transference rate and minimization of entropy generation are critical issues in many industrial and engineering applications where heat transfer coefficient is essential to achieve optimal performance and minimal energy consumption. In the present investigation, a computational analysis has been conducted to analyze the impact of magnetic field on magneto-free convection and entropy generation inside a vertical wavy cabinet filled by Cu-Al2O3/H2O hybrid nanosuspension. In the geometry of this model, vertical boundaries of the chamber are designed as wavy and kept as cooled temperature (Tc), whereas the horizontal boundaries are modeled as square and are designed to be thermally adiabatic, except the centrally heated portion on the bottom wall. The centered bottom heated section is supposed to be isothermal with linearly changing temperature, and it changes linearly from Th1 to Th2, whereas it is modelled as a non-isothermal condition. The main focus, in this investigation, is on the entire chamber filled with the combination of hybrid nanoparticles regarded the volumetric concentration of copper and alumina nanoparticles (Cu-50 %+Al2O3-50 %) along with base liquid (H2O). The transformed dimensionless partial differential equations were solved by using finite volume method (FVM) with power law differencing scheme. The simulated flow and temperature fields are scrutinized by streamlines, isotherms, entropy formations, total entropy generation and average convective Nusselt number associated with varying number of undulations (0 ≤ N≤3) volume fraction of hybrid nano liquid (0 ≤ φ ≤ 0.04) magnetic orientation angles (0° ≤ ς ≤ 135°), Hartmann number (Ha = 0 and 50), and dimensionless temperature drop (Ω = 0.001–0.1). From this study, it is found that the average Nusselt number and entropy generation increase as the solid volume fraction of hybrid nanoadditives increases, while opposite trend is observed when the values of Hartmann number rises. The findings show that growth of undulation number (N) causes the reduction of convective heat transfer rate as well as average entropy production intensity. The obtained outcomes concluded that hybrid nano liquid is more effective and finest choice for the improvement of cooling of heat transfer process and minimal energy loss than single nanoliquid. According to the new proposed criterion (TPC), the results show that square-shaped enclosure (N=0) manifests the better cooling performance among the considered governing parameters. The novelty of this study is to scrutinize the flat/ vertical wavy boundaries of the cabinet which can be represented as a model of heat transfer controller, in which it manages the thermal and flow field characteristics. Predominantly, the isothermal line source is used to boost the overall convective heat transfer which is applied in buildings and fluid-mounted heaters. Additionally, many investigators have focused only on the enhancement of heat transfer. As it is known, to increase the thermodynamic efficiency of a system, optimization of entropy generation is an excellent tool which reduces the loss of energy. Hence, it recently does a good engineering sense to highlight an entropy irreversibility.

Finite element simulations to explore thermofluidic transport mechanism in permeable medium by using Darcy Brinkman-Forchheimer model

Diversified utilizations of permeable domains are found in cooling systems, gas recovery, and insulation engineering. Therefore, this research focused on investigating the heat transport aspects imparted by the buoyantly driven flow of a viscous fluid saturated in a permeable L-shaped enclosure. Darcy Brinkman-Forchheimer model is considered in the present pagination to envision permeability aspects. In addition, entropy generation is considered to encapsulate the disordered form of the system. In this study, an l-shaped domain with heated steps and insulated horizontal boundaries was entertained, while the vertical walls are kept cold. Non-persistent buoyancy forces are employed to elucidate the impact of the gravitational forces. The mathematical formulation of the problem is examined in the form of a dimensionless coupled partial differential system after normalizing the variables. Subsequently, the Galerkin finite element method was implemented using a commercial multigrid software (COMSOL) to find a solution to the constructed problem. The influence of the included parameters on the related distributions and quantities of interest in a comparative sense is evaluated using sketches and tables. A comparison of the results along with a grid-independent test is also performed to ensure the reliability of the computational procedure and computed outcomes. It is inferred that the total entropy and averaged Nusselt number increase as the Darcy number increases by 21.39% and 10.76%, respectively, whereas the Bejan number exhibits the opposite trend. Raising the aperture ratio of the enclosure results in a reduction of the heat flux coefficient, and the ECOP also indicates a reduction in entropy.