Convective Boundary Condition Research Articles

Effect of inclined Lorentzian force on radiated nanoflow Williamson model under asymmetric energy source/sink: Keller box method

An asymmetric energy source/sink can be designed to efficiently convert ambient energy into usable forms; this could have applications in micro-/nanoscale power generation, i.e., energy harvesting. The asymmetric energy source/sink and inclined Lorentzian force could be used to control the flow of fluids within these devices. This study numerically investigates the model of a Williamson nanofluid influenced by an angled magnetic force and an asymmetric energy input/output on a stretching surface with a convective wall boundary condition. The partial differential equations connected to the momentum, energy, and concentration equations are transformed into nonlinear ordinary differential equations (ODEs) by applying relevant similar variables. The obtained ODEs are handled by the Thomas algorithm and a finite difference in the Keller box method. A thorough examination of a change in velocity, temperature, and concentration is done for all the relevant parameters. A higher buoyancy ratio parameter lowers the streamline density. As far as the numerical method is concerned, the Keller box method gives the highest convergence value when compared to other methods, so we use this method to investigate the sleeping behavior of the Williamson nanofluid. The energy source decreases the non-Newtonian passing surface friction. The concentration gradient increases for an increasing value of the chemical reaction parameter. A decreased diffusion rate is seen for increasing Brownian number, while the opposite behavior is noticed for the thermophoretic parameter. The wall friction coefficient increases for augmenting We but decreases for the angled Lorentzian force. Except for radiation, energy transfer is high in all other flows, affecting parameters such as A, B, Nb, Nt, and Pr. By controlling the magnetic field, MHD heat exchangers can manipulate heat transfer rates for various industrial applications. In fusion reactors, strong magnetic fields confine hot plasma, and understanding the interaction between the field and heat sources is crucial for efficient energy generation.

Insight into the peristaltic motion through a tapered channel with Newton’s cooling subject to viscous dissipation, Lorentz force, and velocity slip

Peristalsis has gained significant attention due to its numerous applications in the medical field, engineering, and manufacturing industries. Therefore, the current work intends to look into the effects of variable liquid properties on the magnetohydrodynamics of peristaltic flow exhibited by viscous fluid through a tapered channel. The viscosity of the liquid differs over the thickness of the channel, and temperature-dependent thermal conductivity is considered. The constitutive relation for energy is formulated with the addition of viscous dissipation and heat generation/absorption. The assumption of velocity slip along with the convective boundary condition energizes the thermal system as well as the flow phenomena. The mathematical formulation is established on the grounds of low Reynolds number and long wavelength approximations. Perturbation solution were obtained for the resulting non-linear differential equations of momentum and energy for small values of variable viscosity and variable thermal conductivity. The effects of various relevant parameters on flow properties were investigated through graphical analysis. The results show that the maximum velocity does not occur in the middle of the tapered channel, but moves toward the upper wall with the increase in the variable viscosity difference between the walls. The application of viscosity is essential in many engineering and industrial processes.

Analytical analysis and heat transfer of CuO and MgO engine oil base nanofluid with the influence of dynamic viscosity, magnetic field, and convective boundary conditions

AbstractThis research work investigates the semi‐numerical analysis and heat transfer of MHD 2D, Copper Oxide, and Magnesium oxide engine oil base nanofluid with the consider effect of dynamic viscosity and convective boundary conditions (BCs). The convective BCs and the effect of dynamic viscosity on an extensible surface are considered by the flow system. We converted a set of PDEs into NODEs by applying the appropriate transformations. Using the HAM, we solve this dimensionless coupled equation one for temperature and other for velocity. The impact of various parameters for both temperature and velocity are demonstrated, such as the slip parameter, magnetic parameter (MP), Eckert number (EN), PN, and dynamic viscosity. In response to changes in developing factors, the flow features, such as temperature profiles (TPs) and velocity profiles (VPs), are analyzed and simulated using a physical description. The results of this study add to our knowledge of how engine oil‐based nanofluids promote heat transmission and offer practical advice for thermal management and engineering applications.

Thermal dissipation of two-step combustible tangent hyperbolic fluid with quadratic Boussinesq approximation and convective cooling

This study explores thermal criticality and dissipation involving a two-step reaction in a hyperbolic tangential fluid flow and quadratic Boussinesq approximation to model the complex internal heat transfer mechanisms during combustion. Subject to suitable convective boundary conditions, the transformed energy and momentum equations are numerically solved using Galerkin approximation integration coupled with a weighted residual scheme. The outcomes are disseminated using a variety of graphs to illustrate for parametric sensitivities of the thermal and velocity profiles. Based on the results, it is discovered that increases in the Frank-Kamenetskii parameter, Brinkman number, Weissenberg number, activation energy, activation ratio term, and second step term all aid in the complete combustion of hydrocarbons. Monitoring all terms that stimulate internal heat generation is essential to avoid system blow-ups.

Electrically conducting mixed convective nanofluid flow past a nonlinearly slender Riga plate subjected to viscous dissipation and activation energy

This paper reports the mass and energy transmission characteristics of an electrically conducting mixed convective nanofluid flow past a stretching Riga plate. An additional effect of viscous dissipation, Arrhenius activation energy and heat source is also studied. The energy and mass transmissions are evaluated by a zero-mass flux of nanoparticle and convective boundary conditions. Buongiorno’s relations are proposed for the Brownian motion and thermophoretic diffusion. The similarity substitutions are employed to derive the non-dimensional set of modeled equations. The obtained set of equations is numerically processed via parametric continuation method (PCM). Several flow factors affecting the velocity, energy, and mass distributions are graphically discussed. It has been perceived that the fluid velocity field declines with the influence of velocity power index (m), while improves with the upshot of modified Hartmann number (Q). The effect of Schmidt number and chemical reaction diminishes the concentration profile [Formula: see text]. Furthermore, the energy curve enhances with the effect of thermophoresis factor, Biot and Eckert number.

Saturated Porous Ferroconvection in a Ferrofluid Layer with Viscosity as a Function of Magnetic Field: Focus on Convective Boundary Condition

The present work aims to examine the influence of magnetic field dependent (MFD) viscosity on the onset of ferroconvection (FC) in a horizontal porous layer saturated with a quiescent ferrofluid (FF) and subjected to a uniform vertical magnetic field. It is assumed that the porous boundaries at the bottom and top are rigid-paramagnetic. The thermal conditions consist of a constant heat flux at the lower surface and a convective boundary condition at the upper surface, encompassing fixed temperature and uniform heat flux cases. The application of the Galerkin technique to the resulting eigenvalue problem reveals that the stability region expands as the porous parameter, Biot number, MFD viscosity parameter and magnetic susceptibility increase in magnitude. Conversely, the stability region contracts as the magnetic number and non-linearity of magnetization increase. Furthermore, it is noted that under uniform heat flux boundary conditions, the criterion for the initiation of ferroconvection remains unaffected by the non-linearity of fluid magnetization.

Buoyancy driven bioconvective Casson nanofluid flow over a vertical stretching cylinder in Darcy–Forchheimer permeable medium with Arrhenius activation energy and chemical reaction

A mathematical framework is conceived to analyze the flow of Darcy–Forchheimer Casson nanofluid around a vertically stretchable cylinder, taking into account the convective boundary conditions. The heat and mass transport phenomena are visualized in the existence of activation energy and gyrotactic microorganisms with buoyancy effects. Additionally, an external magnetic field is applied to the flow problem. This particular model finds applications in biomedical engineering, the oil and gas industry, heat exchangers and thermal systems, environmental engineering, and renewable energy. By employing suitable transformations to transform partial differential equations into ordinary ones, the MATLAB function bvp4c package is utilized to numerically solve the equations. The findings presented through graphs illustrate the influence of various parameters on velocity, heat and mass transfer, and the density of gyrotactic microorganisms. The analysis revealed that fluid momentum decreases with increasing porosity numbers, while higher activation energy values enhance concentration. Moreover, an increase in the Peclet number reduces the microorganism’s distribution. Tables compute the motile microorganism’s density, Nusselt number, and Sherwood number. A substantial rise in activation energy prominently increases concentration, accompanied by a decrease in the Sherwood number. The density of microorganisms rises with higher values of the curvature parameter, Prandtl number, and Brownian motion parameter, but decreases with an increasing Hartman number. Noteworthy concordance is noted when juxtaposing the findings of this investigation with those of earlier scholarly research.

Effects of Darcy and Viscous Dissipation on Natural Convection Flow in a Vertical Tube Partially Filled with Porous Material under Convective Boundary Condition

In this paper, a study is presented considering the effects of Darcy and Viscous dissipation in a steady natural convection incompressible fluid through a vertical composite tube partially filled with a porous material. The fluid motion in the vertical composite tube is caused by a temperature gradient due to heat applied to the wall of the tube. The Brinkman Darcy extended model was used to stimulate the fluid flow under the working fluids of water and air. The Homotopy pertubation method was used to solve the temperature and velocity equations in both the clear and porous fluids. An increase in the Brinkman number increases the temperature and velocity profiles of both working fluids. An increase in the thickness of the porous material can be used to increase the velocity of the fluid in the composite vertical tube. An increase in the internal conductive resistance leads to a decrease in the buoyancy force and, as a result, the fluid thickness, which leads to a decrease in the velocity of the fluid.

Magnetohydrodynamic stagnation point flow of Williamson hybrid nanofluid via stretching sheet in a porous medium with heat source and chemical reaction

The stagnation point flow of non-Newtonian fluids has several engineering and industrial applications. In this article, we considered the investigation of the magnetohydrodynamic stagnation point flow of Williamson hybrid nanofluid with chemical reaction and energy generation effects over a porous extending sheet. Similarly, the characteristics of radiation and convective boundary conditions are also taken. Presumptions of boundary layer movement of Williamson hybrid nanofluid facilitate the simplification of the essential mathematical equations for the conservation of mass, energy, momentum and concentration. By introducing the similarity variables, the controlling partial differential equations have been transformed into dimensionless ordinary differential equations. Then, the most effective homotopy analysis method is used to approximate the solutions of reduced ordinary differential equations. Graphical calculations are carried out for hybrid nanofluid [Formula: see text] and nanofluid [Formula: see text]. To investigate the impacts of leading parameters, graphs for the quantities are generated. At the boundary, the local skin friction factor, the Sherwood number and the Nusselt number are also determined. According to the outcomes, it is discovered that when the porosity parameter increases the velocity profile of the hybrid nanofluid [Formula: see text] climbs above that of the nanofluid [Formula: see text]. An increase in thermal radiation parameter and Biot number causes a greater thickness of the thermal boundary layer, which in turn raises the temperature of the hybrid nanofluid. Furthermore, the increased chemical reaction decreases the concentration in both [Formula: see text] hybrid nano liquid and [Formula: see text] mono nanofluid cases.

Entropy generation analysis of a micropolar fluid in a corrugated channel with convective and slip conditions

This study focuses on examining the entropy generation in a corrugated channel, considering convective boundary conditions and slip flow, with a micropolar fluid. The governing equations for the micropolar fluid flow, including linear and angular momentum equations, as well as the energy equation, are solved using the perturbation technique. The effects of corrugations, slipping flow, and convective boundary conditions on the entropy generation and the flow behavior are analyzed. The results show that the entropy generation enhanced with the corrugation amplitude, while it reduced for the slip flow. Moreover, entropy generation is affected by the convective boundary conditions, and it is an increasing function with the convective heat transfer coefficient. Additionally, the study demonstrates that micropolar fluid exhibits distinct flow characteristics in comparison to classical Newtonian fluids. These findings have practical implications for the design and optimization of microfluidic devices, as well as for gaining insights into the behavior of micropolar fluids in various engineering applications.

Iterative numerical method for nonlinear moving boundary problem with a convective boundary condition

Iterative numerical method for nonlinear moving boundary problem with a convective boundary condition

The influence of Marangoni convection in engine oil base nanofluid with the impact of variable viscosity and viscous dissipation on infinite disk

AbstractIn this research work, we will investigate the influence of MC (Marangoni convection) in engine oil as base fluid with viscous dissipation and the influence of variable viscosity on an infinite disk. The flow system takes into account MC with influence of variable viscosity, convective boundary conditions, and viscous dissipation. Furthermore, for the sake of the present research paper, the graphical results of the temperature and velocity profiles are presented. To convert a collection of PDEs to NODEs, we applied appropriate transformations. We utilize the Homotopy analysis method to solve this set of equations. The effects of temperature and velocities on numerical perceptions involving Casson, magnetic, Schmidt number, thermophoresis, and Brownian motion input factors are shown. A physical description is used to simulate and evaluate the structures of flow features such as velocity and temperature profiles in response to changes in developing factors. It is hoped that this issue would contribute positively to improving the heat transformation ratio in order to satisfy the demands of the industrial and engineering sectors.

Thermal Analysis of a Casson Boundary Layer Flow over a Penetrable Stretching Porous Wedge

This work aims to analyze the Casson thermal boundary layer flow over an expanding wedge in a porous medium with convective boundary conditions and ohmic heating. Moreover, the effects of porosity and viscous dissipation are studied in detail and included in the analysis. The importance of this study is due to its applications in biomedical engineering where the analysis of behavior of non-Newtonian blood flow in arteries and veins is desired. Within the context of blood flow, it is also applicable to many other fields, for instance, radiative therapy, MHD generators, soil machines, melt-spinning, and insulation processes. The modeled problem is a set of PDEs, which is nondimensionalized to derive a nonlinear boundary value problem (BVP). The obtained BVP is solved using the shooting technique, endowed with the order four Runge-Kutta and Newton methods. The impact of different parameters on the momentum and temperature fields is investigated along with two important parameters of physical significance, i.e., the Nusselt number and the surface drag force. Results are validated, and an excellent agreement is seen for the parameters of interest using MATLAB built-in function bvp4c. A significant finding is that by increasing the Casson liquid parameter, the velocity decreases as the wedge expands quicker than the free stream velocity at R=2. However, the velocity increases for the case when R=0.1. A decrease in the Darcy number increases the temperature profile. Furthermore, the convective parameter accelerated the heat transmission rate, and a rise in the Prandtl number thickens the thermal boundary layer. The findings of this investigation contribute to problems in fluid dynamics and heat transfer that involve studying the behavior of a non-Newtonian fluid with Casson rheological properties near a solid porous wedge surface.

Irreversibility estimation of MHD thermosolutal convection of Powell–Eyring fluid flow through an inclined microchannel

ABSTRACT Due to the impressive utility of the mass transport phenomena on microscales for various miniaturised devices, the theoretical and experimental studies in microchannel flows to analyse heat and mass transport find enormous interest in researchers. Investigations in microchannel flows have gigantic applications in biochips, drug delivery, and cooling of microchips. This article examines the combined heat and mass transport of Powell–Eyring fluid through a permeable inclined microchannel considering magnetism, thermo-diffusion, and Navier's slip effects under convective boundary conditions. To solve the nonlinear system numerically MATLAB bvp4c solver is employed. This analysis reveals that the entropy generation due to thermosolutal irreversibility is enhanced strictly with the thermo-diffusion effect and solutal Biot number. The Bejan number profile shows a dominating character of Reynold's number close to the upper channel wall and deteriorates with the immense solutal Grashoff number. Also, it achieves maximum and minimum values for the supreme thermal Biot number and Eckert number, respectively in the middle of the channel. The outcome of the study may provide significant insight into controlling flows through microchannels as well as manipulating microfluidic and biomedical devices for minimising energy loss and designing an efficient model for better thermal performance and transmission of chemical species.

MHD radiative Gr-Ag-TiO2/H2O ternary hybrid nanofluid flow upon a permeable movable wedge with irreversibility analysis

ABSTRACT The mass-based ternary hybrid nanofluid model is applied for the magnetohydrodynamic (MHD) flow over a moving wedge with wall permeability, thermal radiation, and convective boundary condition. The masses of the nanoparticles and the base fluid are considered instead of the volumetric concentration of the first, the second, and the third nanoparticles. In the base fluid of water, three types of nanoparticles such as titania, silver, and graphene have been embedded. A similarity method is used to reduce variables and also to turn prominent equations of ternary hybrid nanofluid flow into a simplified form. The shooting technique with the Runge-Kutta-Felhberg method has been used to numerically solve the converted boundary layer equations. The largest Nusselt number is related to the ternary hybrid nanofluid, in which a heat transfer enhancement of 6.55% has been obtained in comparison with regular fluid. The Nusselt number for five shapes of the third nanoparticles is obtained (when both the first and second nanoparticles are spherical), and when the third nanoparticle has the shape of the disk, the most heat transfer has occurred. The highest entropy generation is related to the stagnation point case (m = 1) and the lowest belongs t the downhill case (m = –0.0825).

Thermal Boundary Layer over a Vertical Plate in Porous Medium with a Convective Surface Boundary Condition

Thermal Boundary Layer over a Vertical Plate in Porous Medium with a Convective Surface Boundary Condition

Thermal Spreading/Constriction From an Isothermal Source Into a Multilayer Orthotropic Semi-Infinite Flux Tube

Abstract Thermal spreading and constriction have been widely studied due to relevance in heat transfer across interfaces with imperfect contact and problems such as microelectronics thermal management. Much of the past work in this field addresses an isoflux source, with relatively lesser work on the isothermal source problem, which is of much relevance to heat transfer across rough interfaces. This work presents an analytical solution for thermal spreading/constriction resistance that governs heat flow from an isothermal source into a multilayer orthotropic semi-infinite flux tube. The mixed boundary condition due to the isothermal source is accounted for by writing a convective boundary condition with an appropriately chosen spatially-varying Biot number. A series solution for the temperature field is derived, along with a set of linear algebraic equations for the series coefficients. An expression for the nondimensional thermal spreading resistance is derived for Cartesian and cylindrical problems. It is shown that, depending on the values of various nondimensional parameters, heat transfer in either the thin film or the flux tube may dominate and govern the overall thermal spreading resistance. Results for a single-layered isotropic flux tube are derived as a special case of the general result, for which, good agreement with past work is demonstrated. An easy-to-use polynomial fit for this special case is presented. This work contributes a novel technique for solving mixed boundary problems involving an isothermal source, and may also help solve practical problems related to interfacial heat transfre and thermal management.

A numerical framework of magneto Williamson hybrid nanofluid over porous sheet; a classical keller box analysis

The current study intends to talk about the unsteady Williamson hybrid nanofluid flow with heat transport across a stretching surface comprising the magnetic hydrodynamic, thermal radiative, suction/injection, and convective boundary condition effects respectively. The study focused on the hybrid Williamson nanofluid, comprising of an EG ethylene glycol (C2H6O2) and two types of nano-solid particles, c zinc oxide and molybdenum disulphide ZnO-MOS2. To accomplish this goal, the modelled expressions are transmitted into dimensionless ODE by making use of several highly established transformations. The aim of the numerical result of the current exploration is studied through Keller Box Analysis (KBA). Tabular data and statistical bar plots are used to compare this strategy. The impact of physical variables such as Magnetic field parameter γ, Williamson fluid variable We, Porous media β, Thermal radiation Rd, Biot number Bi and Prandtl number Pr are analyzed through plots and tables. An augmentation in the strength of the magnetic field and Williamson fluid parameter results in a reduction in velocity. However, a temperature rise is observed for higher values of the Williamson fluid parameter and magnetic parameters. The surface friction drag is diminished by the Forchheimer and Weissenberg values. The rate of mass transfer is strongly positively correlated with both the Schmidt number and chemical reaction. The present study has a remarkable agreement with the results that were previously published, which confirms the application and validation of the Keller-Box scheme.

Pool Fires Within a Large Under-Ventilated Environment: Experimental Analysis and Numerical Simulation Using OpenFOAM

Experimental analyses and numerical simulations are carried out on a test case involving an heptane pool fire within a large under-ventilated environment. During the experiments, the temperature history at several locations within the room is monitored by means of thermocouples, and the fire radiative heat transfer estimated through a plate thermocouple. The experimental layout is then replicated numerically and tested using OpenFOAM CFD code. The study is a preliminary analysis performed for code validation purposes on a full-scale fire scenario. The results of the simulations are compared to the experimental results and critically analysed, finding a reasonable agreement overall. Critical issues in fire modelling are also highlighted. In fact, due to the problem complexity and the limitations of the numerical models available some important aspect that can significantly influence the outcome of the simulations must be calibrated a posteriori, somewhat limiting the general predictive applicability of the fire models. Primarily, these are the heat release rate history, the combustion efficiency, and, to a lesser extent, the convective heat transfer boundary condition at the wall.

Time-dependent Darcy–Forchheimer flow of Casson hybrid nanofluid comprising the CNTs through a Riga plate with nonlinear thermal radiation and viscous dissipation

Abstract Carbon nanotubes (CNTs) are gaining popularity due to their expanding uses in industrial and technical processes, such as geothermal reservoirs, water and air filters, coatings, solar collection, ceramic material reinforcement, electrostatic dissipation, etc. In addition, the CNTs have superior electrical conductivity and biocompatibility. Based on the aforementioned applications, the current work examines the time-dependent and Darcy–Forchheimer flow of water/glycerin-based Casson hybrid nanofluid formed by single-walled CNTs and multi-walled CNTs over a Riga plate under velocity slip. The energy expression is modeled through nonlinear thermal radiation and viscous dissipation impacts. The incorporation of convective boundary condition into the current model improves its realism. By employing suitable variables, the governing models are re-framed into ordinary differential equations. The bvp4c and the homotopy analysis method are used to find the computational results of the re-framed equations and boundary conditions. The novel characteristics of a variety of physical parameters on velocity, temperature, skin friction coefficient (SFC), and local Nusselt number (LNN) are discussed via graphs, charts, and tables. It is found that the fluid velocity decays when enriching the Forchheimer number, unsteady and porosity parameters. The radiation parameter plays an opposite role in convective heating and cooling cases. The modified Hartmann number enhances the surface drag force, and the Forchheimer number declines the SFC. The unsteady parameter develops the heat transfer rate, and the Forchheimer number suppresses the LNN. The simulated flow problem has many applications in engineering sectors, including ceramic manufacture, heating and cooling systems, energy storage units, thermodynamic processes, and other fields.