Convective Boundary Condition Research Articles

Combined viscous dissipation and joule heating effects on chemically radiative MHD micropolar flow with heat source and convective boundary conditions

Combined viscous dissipation and joule heating effects on chemically radiative MHD micropolar flow with heat source and convective boundary conditions

Mixed convection hybrid nanofluid flow past a non-isothermal cone and wedge with radiation and convective boundary condition: Heat transfer optimization

Mixed convection hybrid nanofluid flow past a non-isothermal cone and wedge with radiation and convective boundary condition: Heat transfer optimization

Exploring MHD radiative Maxwell nanofluid flow on an expanding surface for the impact of activation energy associated with velocity slip and convective boundary conditions

Exploring MHD radiative Maxwell nanofluid flow on an expanding surface for the impact of activation energy associated with velocity slip and convective boundary conditions

Mathematical modeling and numerical simulations of convective heat transport in a stagnant flow of water‐based copper, aluminum oxide and MWCNTs nanofluid upon a stretching spinning disk

AbstractThis study investigates the flow and heat transfer (HT) characteristics of a ternary hybrid nanofluid (THNF) composed of Cu, Al2O3, and multi‐walled carbon nanotubes (MWCNTs) over a rotating stretching disk under the influence of a magnetic field. As a result, THNFs hold promise for diverse applications, including HT enhancement, thermal management in electronics, lubrication, and biomedical uses. Thus, this study develops and simulates a mathematical analysis to investigate the flow of a ternary hybrid power‐law nanofluid over a rotatory stretching disk. The impact of the magnetic field and convective boundary conditions is also considered. The leading equations, including the energy, conservation of mass, and momentum, are altered into nonlinear ODEs and are numerically tackled using MAPLE 2022 to investigate the impression of relevant parameters upon dimensionless velocity, the concentration of nanoparticles, temperature, skin friction, mass, and HT rates. Furthermore, a trend is observed where the nondimensional tangential and radial velocities and the surface temperature decrease as the fluid transitions from pseudoplastic to dilatant behavior. This study confirms that THNFs outperform single and binary nanofluids (NFs) in HT, with key quantitative outcomes like the Nusselt number showing an increase of up to 15%. This enhanced performance stems from the synergistic effects of combining Cu, Al2O3, and MWCNT nanoparticles in the fluid. The Nusselt number is enhanced by 10%–15% when using THNFs compared to mono and hybrid NFs, and skin friction is reduced by 8%–12% under a moderate magnetic field.

Mathematical solutions for coupled nonlinear equations based on bioconvection in MHD Casson nanofluid flow

<p>The mathematical formulation of fluid flow problems often results in coupled nonlinear partial differential equations (PDEs); hence, their solutions remain a challenging task for researchers. The present study offers a solution for the flow differential equations describing a bio-inspired flow field of non-Newtonian fluid with gyrotactic microorganisms. A methanol-based nanofluid with ferrous ferric oxide, copper, and silver nanoparticles was considered in a stretching permeable cylinder. The chemical reaction, activation energy, viscous dissipation, and convective boundary conditions were considered. The Casson fluid, a non-Newtonian fluid model, was used as flowing over a cylinder. The fundamental PDEs were established using boundary layer theory in a cylindrical coordinate system for concentration, mass, momentum, and microorganisms' field. These PDEs were then transformed into nonlinear ODEs by applying transforming variables. ODEs were then numerically solved in MATLAB software using the built-in solver bvp4c algorithm. We established an artificial neural network (ANN) model, incorporating Tan-Sig and Purelin transfer functions, to enhance the accuracy of predicting skin friction coefficient (SFC) values along the surface. The networks were trained using the Levenberg–Marquardt method. Quantitative results show that the ferrous ferric oxide nanofluid is superior in increasing Nusselt number, Sherwood number, velocity, and microorganism density number; silver nanofluid is superior in increasing skin friction coefficient, temperature, and concentration. Interestingly, heat transfer rate decreases with the magnetic and curvature parameters and Eckert number, whereas the skin friction coefficient increases with the magnetic parameter and Darcy–Forchheimer number. The present results are validated with the previous existing studies.</p>

Accelerating and decelerating flow of radiatively Casson fluid between two permeable disks under convective boundary conditions

Accelerating and decelerating flow of radiatively Casson fluid between two permeable disks under convective boundary conditions

Bi-directional tangent hyperbolic MHD hybrid nanofluid flow over an expanding surface with Darcy dissipation connecting to velocity slip and convective boundary condition

Bi-directional tangent hyperbolic MHD hybrid nanofluid flow over an expanding surface with Darcy dissipation connecting to velocity slip and convective boundary condition

Homotopy Perturbation Method for Analyzing the Effect of Viscous Dissipation on Steady Natural Convection Couette Flow with Convective Boundary Conditions

This research article presents an analytical study of convective flow in a vertical channel with convective boundary conditions. Because of the nonlinear nature of the governing energy and momentum equations, the homotopy perturbation method was employed. The effects of various physical parameters on temperature and velocity profiles are illustrated in Figures 2 to 9, and a comparison table is provided to validate the results. Notably, both temperature and velocity distributions increased with higher viscous dissipation. Furthermore, the velocity profile decreased with an increase in the Biot number, while the temperature profile adjacent to the plate increased as the Biot number grew. Shear stress also exhibited an upward trend with rising viscous dissipation. Finally, an increase in the Grashof number and Biot number is found to elevate the skin friction on both plates. The mean temperature is higher when air is used as the working fluid compared to mercury. To validate this study, the temperature and velocity results were compared with previously published work, showing excellent agreement. This confirms the efficiency of the Homotopy Perturbation Method in solving coupled and nonlinear system of differential equations. Additionally, it was observed that both temperature and velocity increase with a rise in the Prandtl number, attributed to the dominance of momentum diffusivity over thermal diffusivity.

Research on Temperature Field Analysis Method of High-Speed Bearing Chamber–Bearing System

The analysis of the temperature field of a high-speed bearing chamber–bearing system is very complex. We used the temperature field analysis method on a 40,000 rpm bearing chamber–bearing system by simulation, which builds on the finite volume method and introduces a decoupling method that separates fluid dynamics from the thermal analysis of the solid temperature field. Firstly, according to bearing operating conditions, the characteristics of the oil–air two-phase distribution in the bearing chamber are determined using the Volume of Fluid (VOF) method. The convective heat transfer boundary conditions derived from this analysis serve as the thermal boundary conditions for the subsequent thermal analysis. Secondly, considering the heat generation of the bearings and the thermal boundary conditions, a temperature field analysis model is formulated. The calculated results are found to be in close agreement with the actual test data, with an error of less than 10% under three operational conditions. Thirdly, the presented method to evaluate the temperature field of the bearing chamber–bearing system has not been studied in other published literature. Additionally, compared with the thermal fluid–structure interaction method, the method described in this paper can save 90.75% of calculation time, which significantly improves efficiency. Therefore, the above method is reliable for evaluating the temperature field of the bearing chamber–bearing system.

A mathematical model for the interaction of anisotropic turbulence with porous surfaces

Leading-edge noise is a complex phenomenon that occurs when a turbulent fluid encounters a solid object, and is a notable concern in various engineering applications. This study enhances a mathematical leading-edge noise model (Hales et al., J. Fluid Mech., vol. 970, 2023, A29) for anisotropic flow and porous boundaries. The model has two key components. First, we adjust the velocity spectrum to account for the possibility of anisotropy in the flow. This paper rigorously introduces a third dimension for the turbulence spectrum that preserves the turbulence kinetic energy and mathematical definitions for integral length scales. Second, we adapt the fully analytical acoustic transfer function to account for different boundaries by implementing convective impedance boundary conditions when formulating the gust-diffraction problem. This problem is then solved using the Wiener–Hopf technique. We discuss important aspects of this method, including the factorisation of a non-trivial scalar kernel function and the application of suitable edge conditions for the problem. Each modification is inspired by experimental leading-edge noise data using a series of different porous leading edges and anisotropic turbulence generated by a cylinder upstream of the edge. Experimental data demonstrate the interplay between anisotropy and leading-edge modifications while achieving the characteristic mid-frequency noise reduction expected from porous leading edges. Our model is adapted to best fit the trends of the data via a tailored impedance function, leading to good agreement with all datasets across an extended frequency range. This tailored function is used to successfully validate the model against other datasets from a different set of experiments.

Levenberg-Marquardt Design for Analysis of Maxwell Fluid Flow on Ternary Hybrid Nanoparticles Passing over a Riga Plate Under Convective Boundary Conditions

This study provides an examination of the effects of the Maxwell fluid on ternary hybrid nanoparticles passing through a Riga plate under convective boundary conditions using neural network backpropagation. Water is combined with the ternary nanoparticles Al2O3,GrapheneandCNT as the base fluid. Heat sources and sinks as well as thermal radiation are taken into account in the heat transfer study. Partial differential equations can be transformed into a form without any dimensions by applying a similarity transformation. The Finite element method is then employed to resolve this altered equation. The problem's highly nonlinear equations are numerically resolved by utilizing techniques from the Artificial Neural Network method. The Artificial Neural Network method solution technique is used to solve these ordinary differential equations and create the Neural Network Backpropagation reference dataset. The plots illustrating the solution and error analysis for varying different parameters are analyzed in MATLAB using this reference dataset. Regression analysis, error histogram, and mean squared error data are used to assess neural network backpropagation performance. The techniques for testing, validating, and training are applied to the model solution. The impacts of fluid flow and thermal field were examined through important factors. It is found that velocity field shows an opposite pattern for Maxwell fluid variable, it is an increasing function of the modified Hartmann number and the temperature distribution is more influenced by the Biot number and thermal radiation.

Reynolds-averaged Navier–Stokes assisted direct numerical simulation of low Reynolds number flow over airfoils

The simulation of insect flight, like that of dragonflies operating at low Reynolds numbers, has numerical challenges due to the complex morphological structure. The corrugated airfoils trap vortices, and in these recirculation zones, turbulence models may be inadequate to resolve the near-wall flow features well. Hence, accurately capturing the laminar–turbulence transition and identifying the point of separation and reattachment requires resorting to direct numerical simulations (DNS) over a large domain, that is computationally expensive. We propose conducting DNS over a truncated subdomain constrained by Reynolds-averaged Navier–Stokes (RANS) solution to reduce the computational domain size and costs. A precomputed RANS simulation over a large domain is used to prescribe a velocity boundary condition (BC) at the truncated domain of the DNS; a convective BC is imposed as outflow. We validate the proposed RANS-assisted DNS (DNSR) by simulating subdomains of varying sizes and comparing the mean and fluctuating velocity fields, and aerodynamic characteristics with the DNS with free-slip BC. This technique reduces domain size and computational cost significantly (by at least half). A criterion for the ideal subdomain size is determined by satisfying the condition at the location where the non-dimensional mixing length is approximately 60. We validated our criterion by simulating flow over the NACA (National Advisory Committee for Aeronautics) 0012 airfoil at angles of attack α≤12°, corroborating with established literature. Finally, we study a three-dimensional corrugated airfoil with our approach, to capture the transition from two- to three-dimensional structures in the wake as the angle of attack increases.

Dual Solutions of Two-Dimensional Hybrid Nanofluid Flow and Heat Transfer Past a Porous Medium Permeable Shrinking Sheet with Influence of Heat GenerationAbsorption and Convective Boundary Condition

In this study, the dual solutions of two-dimensional hybrid nanofluid flow and heat transfer past a porous medium permeable shrinking sheet with influence of heat generation/absorption and convective boundary condition were examined using the bvp4c solver with the MATLAB computational framework. The utilization of two-dimensional hybrid nanofluid flow and heat transfer in the presence of a porous medium permeable shrinking sheet, considering the effects of heat generation/absorption and convective boundary conditions, has wide-ranging applications in industries such as cooling systems, aerospace, chemical engineering, biomedical applications, energy systems, microfluidics, automotive thermal management, industrial drying, and nuclear reactor cooling, etc. These applications employ the improved thermal characteristics of hybrid nanofluids and the efficient heat control offered by porous media and convective boundary conditions. The governing partial differential equations (PDEs) are transformed into a collection of higher-order ordinary differential equations (ODEs) together with their corresponding boundary conditions. These equations are subsequently shown both numerically and graphically. The main objective of this inquiry is to examine the relationship between the solid volume fraction of copper and the permeability parameter of the porous medium, specifically focusing on the values of f''(0) and - (0) according to the suction effect. The current research has also integrated the temperature and velocity profile of a hybrid nanofluid flow, which corresponds to the influence of porous medium permeability, heat generation/absorption, and convective boundary condition. Dual solutions are acquired by certain combinations of parameters. Non unique solutions are obtained when the critical point reaches , for suction effects. Increasing the intensity of heat generation absorption and convective boundary condition leads to a more pronounced temperature profile and thicker boundary layer.

Chemical Reaction and Thermal Radiation Effects on MHD Casson and Maxwell Nanofluid Flow over a Porous Stretching Surface

The focus of this article is on two-dimensional magnetohydrodynamic Casson and Maxwell nanofluid flows on a porous stretched surface, considering the effects of chemical reactions and thermal radiation. For this problem, convective boundary conditions are assumed. By using similarity transformations, the governing partial differential equations of the issue were converted into ordinary differential equations with the help of the similarity transformation, which were then theoretically solved using the Runge-Kutta Fehlberg method and the shooting approach. Plots are used to show how relevant characteristics, such as heat radiation, porosity, and magnetic parameter, have an impact. It is seen that the velocity profiles decrease as the magnetic field increases. Furthermore, the local Sherwood number and the local Nusselt number decrease as the velocity slip parameter rises. The results of this study were compared with the previously published works under some restrictions, and they are found in excellent agreement.

Implementation of homotopy analysis method for entropy-optimized two-phase nanofluid flow in a bioconvective non-Newtonian model with thermal radiation

The analytical and numerical simulation for the two-phase magneto-hydrodynamics flow in entropy-optimized nanofluid past a stretching sheet with extended Darcy-Forchheimer porous medium and microorganisms is explored. The key focus is to analyze the combined influences of viscous dissipation, chemical reaction, mass suction velocity, and convective boundary conditions. These effects play a pivotal role in the manufacturing process that involves coatings as well as the processing of polymer in addition to enhancing the cooling efficacy in chemical reactors and biomedical equipment. The irreversibility aspects of thermal transfer are also explored by the Bejan number. The ongoing investigation is conducted by both the numerical (using the Mathematica ND solve command) and analytical approach (employing the homotopy analysis method (HAM)). Therefore, the key results include the augmented entropy generation with the escalating values of radiation, Brinkman number, magnetic field, and non-Newtonian parameter. On the other hand, the Bejan number shows a similar elevated pattern for the same dimensionless factors. Furthermore, the escalating rate of mass transmission is observed with Schmidt number, Prandtl number, and thermophoresis, whereas the boosting rate of motile transmission is noted with Peclet number, Schmidt number, and bio-convection Lewis number. Also, the magnitude of the rate of thermal transport near the surface exhibits an ascending pattern with the posited Brownian motion, thermophoresis, and radiation.

Artificial neural network model for convectively heated Casson fluid with the appliance of solar energy

This study is to illustrate the thermometric exchange of Casson fluid’s double diffusive nonlinear radiative heat flux over vertical plate associated with convective boundary conditions, incorporating artificial intelligence (AI)-based neural network computation technique. The AI analysis provides enhanced and optimized results with predictive modeling. The analysis utilizes a dataset generated through Mathematica environment and then embedded the filtered matrix dataset in MATLAB employs AI analysis using the Neural Auto Regressive Exogenous (NARX) method for optimized solutions. Levenberg–Marquard algorithm is used to train neural network. The model’s importance and applications span nuclear reactors, aerodynamics, hydrodynamics, transportation and radiating processes of energy transfer. The physical problem is governed by PDEs that is transformed into a set of ODEs by using similarity transformation. The flow is analyzed against the variation in significant influencing parameter like Prandtl number (Pr), velocity ratio ([Formula: see text]), convective coefficient ([Formula: see text]), Rayleigh number (Ra), buoyancy ratio parameter ([Formula: see text]), radiation parameter ([Formula: see text]) and Casson fluid parameter ([Formula: see text]). Findings of this paper are significant for various industrial, engineering and research-based activities.

Rotating micropolar hybrid nanofluid: Exothermic/endothermic effects and waste discharge on exponential sheet

This research offers a comprehensive investigation into the steady‐state, three‐dimensional flow of an incompressible hybrid nanofluid over a bi‐directionally stretching exponential sheet. A central aspect of the study is the behavior of rotating micropolar fluids within a Darcy‐Forchheimer porous medium, enhanced by the inclusion of electromagnetic forces. The effects of embedding nanoparticles and in a water‐based fluid are explored to reveal their influence on fluid motion and heat transfer. The thermal dynamics are scrutinized, with particular emphasis on the roles of heat absorption and viscous dissipation. Moreover, this study incorporates both endothermic and exothermic reactions in radiative flows, alongside the impact of Soret and Dufour diffusion effects. The discharge of wastewater is a critical issue in environmental management and industrial applications, underscoring the need for rigorous regulation to prevent water pollution and ensure adherence to environmental standards. This research addresses the non‐Newtonian flow resulting from wastewater discharge, incorporating Arrhenius activation energy in the analysis. Furthermore, the behavior of microorganisms within the flow is studied under velocity slip conditions and a range of convective boundary conditions. Through the application of similarity transformations, the governing differential equations are derived and solved numerically using MATLAB's bvp4c solver, with results depicted through detailed graphical analysis to illustrate the fluid's complex behavior. The heat transfer rate gets reduced by 1.96% with the enhancement in the Eckert number.

Analytical Investigation on Flow Reversal in a Fully Developed Steady Mixed Convection Flow With Boundary Condition of the Third Kind

ABSTRACTThis work presents exact solutions to analyze the effect of the Biot number on mixed convection flow in a vertical channel with asymmetric heating and flow reversal. The equations governing flow formation and temperature distributions are offered with convective boundary conditions. Closed‐form solutions for temperature, velocity, and skin friction are found and simulated graphically.

Finite element solutions of Jeffery fluid considering Xue-and Yamada-Ota model on circular cylinder with a thermal jump

The current investigation is based on FEM (finite element approach) simulations of Jeffery fluid in heat transfer analysis on a circular cylinder subjected to convective boundary conditions. The mathematical model of the X- and YO-model is formulated to investigate the impacts of thermal efficiency. Kerosine oil is assumed to be a base fluid along with nanofluid silicon dioxide and titanium dioxide. Heat transfer occurs through the effects of heat source and quadratic thermal radiation. The objective of the current model is to determine the comparative thermal performance between Xue- and Yamada-Ota models utilized in solar energy, biomedicines electronic processes, etc. It is demonstrated that such a developing model has not yet been studied using finite element methodology. Yamada-Ota hybrid nano-fluid model has maximum thermal production as compared to thermal production for Xue-hybrid nano-fluid. Skin friction coefficients increase when mixed convection and radiation numbers are enhanced.

Numerical study of an electrically conducting nanofluid flow past a vertical stretching Riga plate

The heat and mass transfer through electrically conducting and mixed convective nanofluid flow across an elongating Riga plate is studied. Riga plate is an electromagnetic sheet, in which electrodes are assembled alternatively. The arrangement of Riga plate produces electromagnetic behavior in the fluid flow. In the current analysis, the influence of Arrhenius activation energy, viscous dissipation and heat source/sink over the surface of Riga sheet is considered. The heat and mass transfer are examined by convective boundary conditions and nanoparticles (NPs) zero-mass flux. The Brownian motion and thermophoretic diffusion of fluid molecules are applied via Buongiorno's approach. Von Karman's similarity approach is implemented to reset the modeled equations into the dimensionless form of ordinary differential equations (ODEs). The system of ordinary differential equations is solved numerically via PCM (parametric continuation method). The fluid velocity, temperature field, and concentration gradients are analyzed by varying various flow parameters and graphically portrayed. The numerical results are validated by comparing them with the published studies. It can be resolved form the results that the flow rate decilnes with the effect of power index m, whereas enhances with the consequence of Hartmann number. The significance of thermophoresis term augments the temperature curve of the fluid.