Governing Flow Equations Research Articles

Computational simulation of Casson hybrid nanofluid flow with Rosseland approximation and uneven heat source/sink

This article candidly presents the magnetohydrodynamics Casson hybrid nanofluid flow over a stretching surface. In the present study, we added a nonuniform heat source or sink and non-linear thermal radiation. We considered Al2O3 and copper nanoparticles to have antibacterial and antiviral properties without any harmful impacts and used water as the host fluid. We simplified the governing flow equations by using suitable self-similarity variables, which are used to convert PDEs to ODEs. The mathematical equations are numerically solved by using the bvp5c technique in the MATLAB software. Additionally, with higher values of the magnetic field and Casson fluid parameters the velocity profile decreased. The temperature profile is enhanced by increasing the magnetic field and thermal radiation parameters. Increasing the Casson fluid and radiation parameters enhances the skin friction and Nusselt number profiles. Alumina nanoparticles find applications in cosmetic fillers, polishing materials, catalyst carriers, analytical reagents. Copper nanoparticles have high electrical conductivity, which has many uses in electrical circuits and biosensors.

Characteristics of discharge of skew side sluice gate

The present study is aimed to assess discharge characteristics of skew side sluice gate. It is determined to develop equations for elementary discharge coefficient, Ce when a side sluice gate is placed at an angle with the main channel. Also, the present study is undertaken to develop generalized equations for elementary discharge coefficient of skew side sluice gate both for free and submerged flow conditions. Solving governing flow equations and further numerical integration by using fourth order Runge–Kutta method are used to find computed discharge. Error between observed and computed discharge is found and it is minimized to obtain optimum set of constants to develop Ce. Equations for Ce when the side sluice gate is placed at various angles are developed both for free and submerged flow conditions. Also, generalized equations for elementary discharge coefficient are developed. Further, Kling-Gupta Efficiency, KGE and validation of generalized equations for elementary discharge coefficient both for free and submerged flow conditions have indicated that there is an agreement between observed and computed discharges and thus shown accuracy. The findings of the present study are useful to study further on flow characteristics of skew side sluice gate which has vital practical significance.

Physically consistent immersed boundary method: A framework for predicting hydrodynamic forces on particles with coarse meshes

In the present paper, a fluid-particle coupling method is directly derived from the Navier-Stokes equations (NSE) by applying the concept of volume-filtering, yielding a physically consistent methodology to incorporate solid wall boundary conditions in the volume-filtered flow solution, thereby allowing to solve the governing flow equations on non-body conforming meshes. The resulting methodology possesses similarities with a continuous forcing immersed boundary method (IBM) and is, therefore, termed physically consistent IBM (PC-IBM). Based on the recent findings of Hausmann et al. [1], the closures arising in the volume-filtered NSE are closed by suitable models or even expressed analytically. The PC-IBM is fully compatible with the large eddy simulation framework, as the volume-filtered NSE converge to the filtered NSE away from solid boundaries. The potential of the PC-IBM is demonstrated by means of different particle-laden flow applications, including a dense packing of fixed particles and periodic settling of 500 particles. The new methodology turns out to be capable of accurately predicting the fluid forces on particles with relatively coarse mesh resolutions. For the flow around isolated spheres, a spatial resolution of six fluid mesh cells per diameter is sufficient to predict the drag force with less than 10% deviation from highly resolved simulation for the investigated particle Reynolds numbers ranging from 10 to 250.

دراسة عددية لتعزيز انتقال الحرارة للتدفق المضطرب في ال نابيب المدملة

The importance of heat transfer enhancement has gained greater significance in many engineering applications, and a great amount of effort has been devoted to the use different techniques to improve the thermal performance of flowing fluids in pipes. Dimpled tubes were used for this purpose in this study. In this investigation, the heat transfer-flow characteristics of turbulent flow in dimpled tubes subjected to uniform heat flux are numerically investigated. The rate of heat transfer, friction factor, and performance evaluation criterion were determined for various designs of dimpled tubes and compared with smooth tubes. The considered cases are conducted in the Reynolds number range of 3000 to 12,000. The ANSYS Fluent R19 is used for this purpose. The Reynolds-averaged Navier-Stokes equations(RANS) are used to model the governing flow equations. The realizable k-ε turbulence model is used with enhanced wall conditionsto simulate turbulent flow adjacent to the inner wall surface. The results revealed that the rate of heat exchange in dimpled tubes higher than that of smooth ones. but with additional pressure loss. Moreover, the heat transfer performance of the staggered arrangement is higher than the inline arrangement by 17 %. Also, the performance evaluation criteria (PEC) increases with the increasing in dimples diameter, and decreases with increasing in relative pitch spacing, the maximum enhancement reaches 31% for d = 5 mm, and relative pitch spacing S/D = 2 at Re = 4000.

Entropy generation and Cattaneo–Christov heat flux analysis of binary and ternary hybrid Maxwell nanofluid flows with slip and convective conditions

Hybrid nanomaterials significantly enhance thermal systems through improved thermal conductivity, efficient energy storage, and customized thermomechanical properties. Due to their superior thermophysical characteristics, binary/ternary hybrid nanofluids are crucial in fields such as industry, biomedicine, transportation, and pharmaceuticals. This study examines the hydromagnetic flows and heat transfer properties of binary (CuO+Fe3O4/sodium alginate) and ternary (CuO+Fe3O4+MoS2/sodium alginate) hybrid Maxwell nanofluids over a radially stretching rotating disk. The governing flow equations incorporate Cattaneo–Christov heat flux, mixed convection, velocity and thermal slips, nonlinear radiation, viscous dissipation, and Joule heating in a Darcy–Forchheimer porous medium. These axisymmetric partial differential equations are transformed into ordinary differential equations using similarity variables, and the spectral quasilinearization method (SQLM) is applied for numerical solutions. Results reveal the effects of relevant parameters on velocity, temperature, skin friction, and heat transfer rates. Novelty lies in the comparative analysis of flow behaviors and entropy production rates between binary and ternary hybrid Maxwell nanofluids. When the heat source is included, the Nusselt number increases by 12.9% for ternary nanofluids and 16.07% for binary nanofluids as the thermal relaxation number increases from 0.5 to 1.5. Furthermore, the ternary hybrid nanofluid shows greater resistance to Lorentz and porous medium forces and exhibits a higher temperature distribution and better thermal management capabilities compared to the binary hybrid nanofluid.

Nano particle distribution in blood via electroosmotic peristaltic flow in a non-uniform wavy membrane base capillaries

ObjectiveThe primary purpose of this article is to undertake a mathematical investigation into the electro osmotically thermally driven transport of solute particles, which are typically on a micro to nano-meter scale, suspended in blood. The study is conducted within a non-uniform porous channel for a Williamson fluid. The main objective of this research is to explore the interactions and consequences of solute particles and nanoparticles in the Esophagus, particularly regarding their potential applications in drug delivery and biomedical engineering, especially in the context of electroosmotic non-Newtonian fluids. SignificanceThis research also has significant implications for microscale physiological phenomena. In this investigation, blood serves as the base fluid, and a nanofluid is created by introducing Nickel and Cobalt nanoparticles into the blood. Both nanoparticles have critical medical applications, especially in drug delivery and cancer treatment. To delve deeper into the study of nanomedicine delivery, Nickel and Cobalt nanoparticles are introduced into the blood alongside other smaller solute particles. MethodologyThe mathematical modeling is conducted in a rectangular coordinate system, and the governing flow equations are linearized using approximations that consider low Reynolds numbers and large wavelengths. The numerical solution is computed for a coupled set of nonlinear equations that describe the profiles of fluid-particle velocity, temperature, and fluid-particle composition. The study explores the influence of various key parameters and presents these effects through graphical representations. FindingsIt is observed that an increase in the suspension concentration and the Williamson fluid parameter leads to higher fluid velocity, while the temperature distribution exhibits the opposite trend. The introduction of nanoparticles into the fluid decelerates the flow and raises the temperature.

A Comparative study of flow and C[sbnd]C heat flux over a magnetic field under the influence of nanomaterial and carbon nanotubes

The aim of this study is to investigate convective heat transfer on a flat surface in the presence of magneto-hydro-dynamic (MHD) flow. The analysis considers the Darcy-Forchheimer porosity medium in the flow. The study focuses on analyzing the heat transfer rate, incorporating joule heating and convective-conductive heat flux effects. The influence of varying fluid properties on the flow behavior is examined. The governing flow equations are initially expressed as partial differential equations (PDEs) and then transformed into ordinary differential equations (ODEs) using appropriate similarity transformations. The numerical method RKF-45 is employed to solve these ODEs. The results highlight the impact of different parameters in the model. It is observed that a higher Darcy parameter leads to a decrease in fluid velocity. Additionally, the performance of carbon nanotubes is superior compared to MoS2 nanoparticles in this study.

Mixed Convection Flow of a Casson Fluid Past a Thin Needle

Mixed Convection Flow of a Casson Fluid Past a Thin Needle

Exploring double-diffusive nanofluid flow in divergent/convergent nondarcy porous space: A machine learning numerical approach with zero mass flux

In this study, authors address the problem of analyzing the Jeffrey–Hamel nanofluid flow within a nonparallel channel under the influence of a thermally balanced non-Darcy permeable medium. Our objective is to explore the behavior of the nanofluid, employing the Buongiorno nanofluid model, and considering factors such as zero mass flux conditions, variable rheological fluid properties, and the presence of temperature jump phenomena through ANN-PSO-NNA. To tackle this intricate issue, propose a novel approach using Artificial Neural Networks (ANN) integrated with particle swarm optimization (PSO) hybrid with neural network algorithm (NNA). This combined technique is referred to as ANN-PSO-NNA. The governing flow equations based on the Jeffrey–Hamel analysis are first transformed into dimensionless forms. To establish the efficacy of our approach compare it with the widely used NDSolve method. Furthermore, the study presents the absolute error analysis for four distinct cases offering a quantitative assessment of the accuracy of ANN-PSO-NNA. The absolute error between the NDsolve and the proposed ANN-PSO-NNA is given for four different cases, ranging from 1.95E-06 to 1.18E-08. The biases and weights obtained through proposed method range from −10 to 10. This enables us to gauge the performance of the ANN-PSO-NNA minimum values of the fitness function 2.37E-08, 2.30E-08, 3.92E-08, and 1.22E-08 from multiple independent runs, which are showcased to be convergent, underscoring the robustness of the ANN-PSO-NNA approach. Employing graphical representations, explores the influence of various parameters on the velocity and temperature profiles. Our integrated approach offers a comprehensive understanding of the underlying dynamics, paving the way for optimized designs and enhanced efficiency across these diverse engineering applications.

Pulsatile flow and peristaltic motion interaction of Walter’s B liquid

This work focuses on the interaction of peristaltic with the induced periodic flow of Walters B liquid in a channel with porous space. The model takes into account the impact of Hall current. In order to solve the governing flow equations, the amplitude ratio (wave amplitude/channel width) is used as a parameter in the perturbation technique. The impact related to various parameters on the velocity distribution, stress at the walls and streamline patterns have been examined using graphical representation. Our analysis indicates that with a rise of the Hall current parameter, the velocity of the fluid enhances whereas by rising the Hartmann number, we observed a fall in the velocity. Further, the size of the trapping bolus grows with the rise of the Hall parameter and Reynolds number. The size of the bolus, on the other hand, decreases as the viscoelastic parameter rises. To validate the model, the analytical solution derived has been compared with that of Afifi and Gad (Acta Mechanica 149, 229–237 (2001)), and the outcomes show remarkable agreement.

Keller box numerical analysis of power-law rotating disk for nanofluid flow with chemical reaction

The present study concentrates on the numerical treatment of the flow of the 3D boundary layer on a nanofluid above a rotating disk. The chemical reaction and generation or absorption of heat has been incorporated. According to published literature nanofluids play a key role in the improvement of thermal conductivity. More significantly, nanofluids are utilized in medical field, engineering and in industry. In addition, this attempt will be helpful for the researcher to analyze energy and mass transport rates for nanofluids. Further, in this study, Brownian motion and thermophoretic impacts are taken into account. The governing flow equations are converted to ODEs (ordinary differential equations) via suitable similarity transformations. The numerical outcomes are recovered with the utilization of well know technique KBM (Keller box method). The velocity and energy transport rates are discussed graphically for power law index, thermophorsis, and Brownian motion. Graphs present the temperature and concentration distribution increase for the upturn of thermophoretic impacts. While, temperature and concentration distribution show decreasing behavior for Brownian movement factor. In addition, increment in power index factor diminishes the temperature distribution and concentration of the liquid.

Numerical analysis of turbulent flow and heat transfer enhancement using V-shaped grooves mounted on the rotary kiln’s outer walls

Rotary kilns have been widely employed in various industrial uses, especially the cement production. This article deals with enhancing the thermal performance of a rotary kiln duct with V-shaped grooves mounted on the outer wall. Four V-shaped grooves with different depths h/D ranging from 0.1 to 0.4 were designed. The Reynolds Averaged Navier–Stokes equations (RANS) of two-dimensional steady-state flow are used to model the governing flow equations by using the finite volume approach (FVM) in FLUENT. k-ε standard, k-ε Realizable, k-ω SST and k-ε RNG turbulence models of the RANS approach and the k -ω SST model has been adopted to validate CFD results. In this study, the numerical results have revealed that the increase in groove depth decrease the temperature of the rotary kiln’s outer wall than the smooth walls and gives the largest Nu number, especially for the groove with h/D =0.3 and 0.4 depths.

Numerical simulation for radiative hybrid nanofluid (TiO2+Fe3O4∕H2O) flow due to a non-uniform stretching sheet with variable permeability

Variable permeability plays a crucial role in various manufacturing and technical applications such as fixed-bed catalytic reactors, heat exchangers, and dying, among others. The primary focus of this paper is to investigate the impacts of variable permeability on hybrid nanofluid (HNF) flow due to nonlinear sheet stretching with thermal heat flux. The HNF is made up of a mixer of [Formula: see text] and [Formula: see text] nanoparticles and water serving as the base fluid. Using efficient similarity transformations, the flow-governing equations are converted into a set of ordinary differential equations, and the resulting system is computationally solved by using the MATLAB program (bvp4c). The impact of various physical variables on the fluid velocity and heat transfer characteristics is analyzed via graphs. It is found that as the permeability parameter rises, the velocity of the HNF diminishes while the temperature amplifies. The drag force coefficient declines with an intensification of the volume fraction of the [Formula: see text] nanoparticles. The HNF [Formula: see text] exhibits 0.45–0.75% increase in heat transfer rate when compared to a nanofluid [Formula: see text] for different values of heat source parameter. The current investigation is compared to the existing literature, revealing a good level of agreement.

Unsteady Compressed Williamson Fluid Flow Behavior under the Influence of a Fixed Magnetic Field (Numerical Study)

A numerical investigation is conducted into a two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with fixed thermal conductivity and external squeezing accompanied by viscous dissipation effect. Based on the flow geometry under consideration, the current flow model was created. The momentum equation takes into consideration the magnetic field when describing the impact of Lorentz forces on flow behavior. The energy equation takes varying thermal conductivity into account while calculating heat transmission. The extremely complex nonlinear, unstable governing flow equations for the now under investigation are coupled in nature. Due to the inability of analytical or direct methods, the Runge-Kutta scheme (RK-4) via similarity transformations approach is used to tackle the physical problem under consideration. The physical behavior of various control factors on the flow phenomena is described using graphs and tables. For increasing values of the Weissenberg parameter and the permeable velocity parameter, the temperature boundary layer thickens. As the permeable velocity parameter and squeezed flow index increased, the velocity profile shrank. The velocity profile grows as the magnetic number rises. Squeezed flow magnifying increases the Nusselt number's magnitude. Furthermore, the extremely complex nonlinear complex equations that arise in fluid flow issues are quickly solved by RK-4. The current findings in this article closely align with the findings that have been reported in the literature.

Heat transfer analysis of MHD oscillatory SWCNT/MWCNT‐H2O hybrid nanofluid flow in a channel

AbstractRegulating the thermal conductivity of the fluid in various heat exchange systems plays an important role. In this regard, the carbon nanotubes (CNTs), with their higher thermal conductivity, can enhance the heat transfer potential. The main objective of the present study is to explore the impact of suction and injection on the oscillatory flow of CNT‐based hybrid nanofluid through a channel under the influence of the magnetic field for analysing heat transfer perspectives. While developing a mathematical model of the problem, we also considered other relevant elements, such as thermal radiation for optically thin fluids and porous mediums. The behaviour of a water‐SWCNT + MWCNT hybrid nanofluid is studied concerning the volume fraction of CNTs. The governing flow equations have been solved to obtain the correct solutions for the distribution of velocities and temperatures. Graphs and tables are used to assess the impact of relevant parameters on the flow and derived quantities. Adding CNTs to a fluid reduces its temperature and velocity, making it ideal for cooling systems. However, plates exhibit a maximum heat transfer of 35.35% and 25.35%, respectively, for and . The magnetic and constant pressure parameters greatly diminish the fluid's velocity, while the thermal buoyancy forces strengthen the flow. The effectiveness of the current study is confirmed by comparing its results to those from previous investigations.

Irreversibility and spectral analysis for nanofluid with melting and higher order slip effects

This work is intended to examine the impacts of first and second-order velocity slips, viscous dissipation, and melting on mixed convective flow of nickel zinc ferrite + SAE 20W-40 motor oil based nanofluid along a stretching or shrinking sheet for the first time. The multigrade 20W-40 motor oil is categorized by Society of Automotive Engineers (SAE). An irreversibility analysis has also been performed using the second law of thermodynamics. The resulting non-dimensional flow-governing equations are modified into ODEs (Ordinary Differential Equations) and then the numerical estimates are provided by adopting the spectral local linearization method. Next, the efficiency of the above-mentioned spectral procedure is verified through the maximum error norms. Finally, the influence of important parameters included in this evaluation on the flow profiles and physical quantities is systematically represented. Based on the findings, the melting effect enhances the heat transference rate by 24.6% and reduces entropy by 38.4%. The use of higher-order velocity slips and viscous dissipation effects results in a lower friction factor. In the presence and absence of ferrite particles, the streamline visualization is clarified. This type of simulation is extremely useful for the readers in considering the rates of cooling or heating at electromagnetic interfaces, industrial devices, orthopedic joint replacements, aircraft turbines, bone plate surgeries, and so on.

Bioconvection in a Porous Medium Saturated with a Casson Nanofluid

The bio-convective heat transfer of an incompressible, viscous, electrically conducting Casson nanofluid past a wedge has been analyzed. Furthermore, using a similarity variable, the governing flow equations are transformed to non-linear coupled differential equations corresponding to a two-point boundary value problem, which is solved numerically. A comparison of the solution technique is carried out with previous work and the results are found to be in good agreement. Numerical results for the coefficient of skin friction, Nusselt number, Sherwood number, micro-organism flux as well as the velocity, temperature, nanoparticles and micro-organisms concentration profiles are presented for different physical parameters. The analysis of the obtained results shows that the field of flow is significantly influenced by these parameters.

Examining the role of activation energy and convective boundary conditions in nanofluid behavior of Couette-Poiseuille flow

Abstract This work investigates the behavior of a nanofluid in a horizontal channel under advection boundary conditions within the domain of magnetohydrodynamic radiative Couette-Poiseuille flow. We utilize the Haar wavelet collocation method (HWCM) to investigate the effects of energy activation. This research relies on the mathematical model introduced by Buongiorno, which effectively captures the flow dynamics and incorporates the influence of chemical processes. To streamline the governing flow equations, we employ boundary layer approximations. The HWCM is employed to numerically solve the non-linear coupled partial differential equations that regulate momentum, heat transport, and mass transfer processes. We examine the impact of several dimensionless convergence parameters on the velocity, temperature, and concentration profiles and give visual representations of these results. It is crucial to highlight that the activation energy of the specific chemical reaction is directly linked to the concentration of nanoparticles. The effect of Brownian motion on nanoparticle concentration varies from that of the thermophoresis parameter.

On Machine-Learning-Aided Two-Scale Solution for Turbulent Fluid Flows

Scale-resolving solutions for computational fluid dynamics problems have usually been challenging due to their request for computing resources. A two-scale framework was proposed for more efficient solutions to couple a local fine-mesh solution with a global coarse-mesh solution. The methodology was successfully implemented and demonstrated for a canonical turbulent channel flow and for a tripped turbulent boundary layer. The solution mapping from the local fine-mesh to the global coarse-mesh region is realized by modifying the flow-governing equations in the under-resolved coarse-mesh region through adding extra forcing source terms generated from the space–time-averaged fine-mesh solutions. However, the high-gradient transitional region presents additional challenges when applying the Chebyshev spectral method for mapping the source terms; thus the high-gradient frontal region has not been fully resolved in the streamwise direction. In the present work, the propagation of the source terms is facilitated by machine learning tools (multilayer perceptron-based neural network) so as to implement the method in flowfields with high gradients or drastic changes in the mean velocity. The neural-network-based propagation model is shown to be capable of accurately estimating the source terms in the near-wall coarse-mesh region. The mean flow there thus can be nicely reproduced by the source-term propagation. The machine-learning tools thus provide potential as the more advanced source-term propagation method for the two-scale framework to be implemented in more complicated flowfields.

Thermal analysis of AA7075-AA7072/methanol via Williamson hybrid nanofluid model past thin needle: Effects of Lorentz force and irregular heat rise/fall

Hybrid nanofluids have received remarkable attention due their promising thermal performance compared to conventional nanofluids. The use of hybrid nanofluids is widely found in the pumping power, solar collector, electronic components, coolants in nano devices, and engine applications etc. Such types of applications grabbed the attentionof researchers and scientistswith the aim to understand in depththe problems involving the hybrid nanofluids. Therefore, the primary objective of the present investigationis to investigatethe thermal performance of hybrid nanofluid consisting of asuspension of aluminum alloys (AA7075-AA7072) in methanol-base fluid. The non-Newtonian Williamson fluid flow model under Lorentz force, and irregular heat rise/fall impact past incessantly moving thinneedleis considered. The governingflow equations are solved by bvp4c solver. Results are computed for governing flow parameters such as magnetic field parameter, needle thickness parameter, Weissenberg number, volume fractions, and irregular heat rise/fall constants. Graphs confirm that augmenting values of magnetic field parameter, needle thickness parameter, and Weissenberg number lead to downfall of velocity field but reverse behavior is noticed for increasing nanoparticles volume fraction. A rise in temperature field has been noticed by increasing the magnitude of magnetic field, irregular heat rise/fallparameter, and nanoparticles volume fraction but a decline in fluid temperature occurswithraising theneedle thickness parameter. Detailed discussion about the observed variation in physical properties under pertinent parameters effects is presented. The proposed model is validated by comparison with previouslypublished results.