Convective Boundary Condition Research Articles

Effects of Brownian and thermophoresis on the nanofluid flow with zero nanoparticle mass flux and convective conditions through non-linearly expanding Riga plate

The present flow phenomena characterize the behavior of the Brownian motion and thermophoresis considering the Buongiorno model nanofluid through a non-linearly expanding Riga plate. The conjunction of thermal radiation with zero nanoparticle mass flux and convective boundary conditions enriches the thermal properties of the nanofluid. With the recent need in various industrial applications, the biomedical sector, for the design and development of the production process of various equipment, the role of nanofluid is vital. Further, the suitable variables leading to transformation rules are useful to get rid of the dimensional form of the governing equations. Traditional numerical technique with the help of shooting-based Runge–Kutta fourth-order technique is adopted for the solution of a transformed set of equations. The physical behavior of the characterizing components is presented and described briefly. Further, the important outcomes are the use of Hartmann number that overshoots the velocity profile, whereas the heat transfer retards significantly and enhanced thermophoresis attenuates the heat transfer rate.

Design of novel thermal management system for Li-ion battery module using metal matrix based passive cooling method

Reliable, efficient and safe energy storage is important for electric vehicles and renewable energy storage of power grid. Lithium-ion battery is preferred as energy storage device due to its higher energy density, low self-discharge and longer cycle life. Lithium-ion cells generate heat during high discharge rates and harsh ambient temperature operation, which raises cell temperature and impacts its performance. Therefore, an efficient thermal management system (TMS) is necessary to alleviate thermal issues during charge/discharge process. A combination of phase change material (PCM) with high conductive plate metal matrix is proposed to eliminate the limitation on the heat transfer characteristics of air-cooled systems. To analyze the thermal and electrochemical behavior of a Lithium-ion cell, a detailed CFD simulation with empirical NTGK electro-chemical model is used. The model is first validated with available experimental data and the analysis is then extended to predict thermal response of individual cell of 3s3p module under natural convection boundary conditions. Poor heat transfer capability associated with natural convection at elevated temperature and discharge rate causes the cell maximum temperature (Tmax) and uniformity (ΔT) to be higher than acceptable values of 45 °C and 3 °C respectively. A thermal management system based on passive cooling using PCM is proposed and analyzed using CFD model by first validating the PCM melting behavior under uniform heating. The model is then extended to analyze the impact of PCM on cell temperature rise at different discharge rates of 8 A - 25 A (≈1C - 3.2C) and various operating temperatures of 25°C to 35°C. Low thermal conductivity of PCM limits heat dissipation which leads to higher temperature gradient. A novel TMS based on plate metal matrix structure enclosing PCM is proposed to enhance heat conduction across PCM and increase heat dissipation to maintain battery module under safe operating temperature limits. This approach has brought down the module maximum temperature to 44.1 °C and temperature difference to 1.6 °C during operation at 25 A (3.2C) and 35 °C. Hence, PCM with high latent heat and low thermal conductivity could be used with high conductivity plate metal matrix to improve cell performance by keeping the cell temperature at required range.

Magnetic Field Impacts on Nanofluid Flow Towards a Stretching Sheet Embedded in a Porous Medium with Considerations of Variable Viscosity and Convective Boundary Conditions

Magnetic Field Impacts on Nanofluid Flow Towards a Stretching Sheet Embedded in a Porous Medium with Considerations of Variable Viscosity and Convective Boundary Conditions

Double stratification impacts on MHD flow of micropolar nanofluid over a stretching surface inserted in porous medium

A comprehensive analysis of double stratification impacts on the MHD flow of a nanofluid produced by a porous stretching sheet has been conducted by using a numerical approach. The convective boundary conditions (CBCs) and Newtonian heating (NH) cases have been particularly considered in this problem. The governing equations defined in partial differential equations (PDEs) form are converted into ordinary differential equations (ODEs) by using appropriate transformations to meet the requirement of the used numerical method which is bvp4c in the MATLAB software package. Moreover, the numerical findings of the ODEs are displayed via graphical and tabular forms. The impacts of different flow parameters used in particular problem are discussed for the profiles of the velocity, temperature and concentration of micropolar nanofluid along the values of coefficient of skin-friction [Formula: see text], Nusselt number [Formula: see text], the Sherwood number [Formula: see text] and in relation with the variation parameters in general, CBC and NH are calculated to get a clear insight into the flow situation. Some of the findings show that the skin friction increases by increase in magnetic, permeability and material parameters in all cases but the skin friction is reduced by increasing the thermophoresis parameter for CBC and NH cases, respectively. Microrotation profile decreases when material parameter increases, whereas microrotation profiles enhance with increase of the magnetic field and porosity of porous medium.

Study of heat transfer in MHD viscoelastic fluid of second grade over a stretching porous sheet with electromagnetic effects and nonuniform source/sink

This work is devoted to the study of non-Newtonian fluid of second grade. This model assumes that the flow and heat transfer in MHD viscoelastic fluid is subject to convective boundary conditions in the presence of electromagnetic field and nonuniform source/sink. The flow is considered over a porous sheet. The governing partial differential equations are converted as ordinary differential equations using suitable similarity transformations. The resulting coupled of nonlinear differential equations are successfully solved by means of Optimal Homotopy Asymptotic Method (OHAM). The effects of different physical parameters such as: the second-grade viscoelastic parameter, thermal radiation parameter or Eckert number are analyzed. Several closed form analytical approximate solutions for dimensionless stream function and temperature are presented for some particular cases. Our procedure is based upon an original construction of the solutions using a moderate number of the convergence-control parameters. These parameters lead to very high precision, comparing our approximate solutions with numerical solutions. Let us note that every nonlinear differential equation is reduced to two linear differential equations. The values of the convergence-control parameters are determined using rigorous mathematical procedures. OHAM is an iterative approach which rapidly converges after only one approximation, is effective, explicit, simple and easy to apply. These remarks are in fact the true power of our procedure to solving nonlinear problems without the presence of small or large parameters in the governing equations or boundary/initial conditions.

Investigation of the effects of various nanoparticle morphologies on mass and heat transport in SiO2-H2O unsteady magnetohydrodynamic nanofluid flow through a stretched cylinder

This article investigates the effects of the various silicon dioxide ( Si O 2 ) nanoparticles immersed in water ( H 2 O ) base fluid on velocity and heat transport over an unsteady stretching cylinder under the influence of magnetohydrodynamics ( MHD ), velocity slip, and convective boundary conditions. The physical model is initially developed in the form of partial differential equations (PDEs) by using the conservation principle. Employing suitable transformations, the set of PDEs has been transformed into a system of Ordinary differential equations (ODEs). The nonlinear equations in the proposed model are optimally and dynamically assessed. To produce numerical solutions for nonlinear systems, MATLAB's BVP4C solver technique is used. Furthermore, the numerical technique is validated by calculating residual error. The recent investigation’s novel results include: the nanoparticles SiO 2 of play an important role in enhancing the thermal conductivity of the traditional base fluid H 2 O . The shape of the nanoparticles also plays a remarkable role in heat transfer enhancement. Increases in viscus dissipation, convective boundary conditions, and MHD parameters play a remarkable role in increasing the temperature of the nanofluid. Furthermore, platelet-shaped Si O 2 nanoparticles are reported to have the highest flow rate, highest temperature, and highest value of Nusselt numbers.

Convective heating and mass transfer in Buongiorno model of nanofluid using spectral collocation method of shifted Chebyshev polynomial

In this article, the investigation is made to shed a light on the influence of convective boundary conditions on the boundary layer flow over a linearly stretching flat surface. The equations (partial differential equations) describing the model are transformed into system of nonlinear ordinary differential equations using similarity transformations. Equations contain various non-dimensional flow characterizing numbers viz. Prandtl number Pr, Lewis number Le, Biot number Bi, Brownian motion parameter Nb and thermophoresis parameter Nt. The influence of these parameters on thermal boundary layer, concentration distribution and temperature are analyzed in detail, by solving the equations using novel Shifted Chebyshev collocation method. The computed results, reduced Nusselt number, reduced Sherwood number, surface temperature and concentration profiles as functions of dimensionless numbers are validated by comparing the predicted results with available earlier findings (using other methods). To assert the convergence and stability of the scheme used (for much larger, but moderate, parameters values), predicted results are presented in various tabular forms. For presenting finer details of the computed values some results are also given graphically. The innovative semi-numerical scheme is robust and efficient compared with other conventional methods, used in previous studies and enables the analysis of the complex problem adequately.

MHD dissipative Powell-Eyring fluid flow due to a stretching sheet with convective boundary conditions and slip velocity

The novelty and motivation of this research can be emphasized by examining how the heat transfer mechanism of a non-Newtonian Powell-Eyring fluid, which flows because of a stretched sheet, is affected by factors like viscous dissipation, the slip velocity phenomenon, and Joule heating. In addition, the investigation delves into the heat transfer behavior of the fluid flow when it comes into contact with a convectively heated stretched surface that is influenced by varying fluid properties. This analysis also takes into account the influence of changing fluid characteristics and the presence of magnetic field. The numerical solutions of modelled equations that governing the problem are detected using the shooting technique. Also, in order to confirm the validity of the present investigation, a proper comparison with certain published works as a particular case of the present model is presented, and a perfect agreement is noted. With the use of diagrams and tables, the flow problem’s effective parameters are thoroughly discussed. Likewise, through a tabular representation, the values of the local Nusselt number and the skin-friction coefficient are computed and analyzed. Many significant conclusions can be drawn from numerical results. Most importantly, the local Nusselt number rises monotonically with both the surface convection parameter and the slip velocity parameter, but the local skin-friction coefficient has the opposite trend. The results indicate that the nanofluid temperature is enhanced by factors such as the surface convection parameter, magnetic field, and viscous dissipation. On the other hand, the slip velocity phenomenon leads to the opposite effect.

Oscillatory and transient role of heat transfer and magnetic flux around magnetic-driven stretching cylinder under convective boundary conditions

The magnetic outcomes are frequently implemented for assessing fluid specifications around stretching magnetized surfaces and energy producing technology of thermodynamics. Magnetohydrodynamic reactors and magneto-hydrodynamic generators are two primary methods for producing magnetic flux through ionized fluids along a warmed and magnetized stretched surface. The desired outcomes of the current work are to investigate magnetic flux and heat transmission in the presence of convective boundary conditions using an electrically-conducting fluid over a stretchable cylinder. Most of the parameters are considered in the discussion with intensity and variance due to time dependent methodology. The suggested fluctuating dynamic computational framework is formulated for associated forms of coupled model under boundary variables. The appropriate non-dimensional variables are used to transform the complicated mathematical expression into a non-dimensional representation. To make the non-dimensional representation easier to work for efficient statistical calculations, it is reduced further. Later, for a variety of variables, significant computations are performed via the implicit finite difference methodology. The main finding of current communication is to explore the prominent slip effect in temperatures for every Biot number around all positions. From a physical standpoint, the phenomenon was predictable since surface heat flux is employed as sporting source to increase heat transmission in electric-conducting fluids. For every possible angle, the field of magnetism increases with minimal intensity of surface heat flux. Since, magnetizing functions referred to as an insulating layer that diminishes high temperatures across surfaces and fluids.

Effect of Arrhenius activation energy on two-phase nanofluid flow and heat transport inside a circular segment with convective boundary conditions: Optimization and sensitivity analysis

This paper analyzes the heat transport phenomena of two-phase nanofluid within a permeable circular segment with an interaction of Arrhenius activation energy and, examines the interaction of convective boundary conditions affecting the flow characteristics. The pre-exponential factor of the Arrhenius equation deals with the collision between molecules, and it has significant applications for getting the rate of a chemical reaction and is used to estimate material properties with changes in temperature and energy. To a greater extent, the external uniform heat source encourages thermal properties on account of the behavior of Brownian and thermophoresis parameters. The transformation of the standard nondimensional form of the governing equations is obtained for the assumption of appropriate similarity variables and stream function. The set of these transformed equations is tackled numerically with the shooting technique. The characteristics of physical parameters on the flow phenomena are presented graphically and the validation with earlier research displays a strong correlation for the specific case. The special attraction of the present investigation is the regression analysis for the simulated results of heat and solutal transfer rates using Response Surface Methodology considering various characterizing parameters like heat source, thermal radiation, curvature, activation energy, thermal and solutal Biot numbers within certain range.

Three-dimensional MHD Casson Nanofluid Flow Over a Moving Surface in the Presence of Heat Generation and Convective Boundary Conditions

Three-dimensional MHD Casson Nanofluid Flow Over a Moving Surface in the Presence of Heat Generation and Convective Boundary Conditions

Modeling and simulation of the input–output behavior of a geothermal energy storage

This paper investigates mathematical modeling and numerical methods for simulations of the input–output behavior of a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. There, a given volume under or aside of a building is filled with soil and insulated to the surrounding ground. The thermal energy is stored by raising the temperature of the soil inside the storage. It is charged and discharged via pipe heat exchangers filled with a moving fluid. Simulations of geothermal energy storages aim to determine how much energy can be stored in or taken from the storage within a given period of time. The latter depends on the dynamics of the spatial temperature distribution in the storage, which is governed by a linear heat equation with convection and appropriate boundary and interface conditions. We consider semidiscretization and full discretization of that PDE using finite difference schemes and study associated stability problems. Finally, we present numerical results.

Non-similar approach on the MHD Carreau nanofluid flow with quadratic radiation and Soret-Dufour effects

The present study aims to investigate the influence of magnetohydrodynamic (MHD) Carreau nanofluid flow past a stretching cylinder with quadratic Rosseland heat radiation. This paper examines the consequences of the Soret-Dufour effects when considering the influence of thermophoresis and Brownian effects. The convective and diffusive boundary conditions have been implemented. The modeled mathematical system of non-linear partial differential equations (PDEs) is transformed into a dimensionless representation using a non-similar approach. The ensuing set of dimensionless equations are solved numerically with local non-similarity method (LNM) aided by the finite difference algorithm. The findings of the study unveil that the presence of the Dufour and Soret effect declines the heat transfer and mass transfer rates, respectively. It is also noted that flow profiles are more profound in the case of stretching cylinder configuration. Per unit increase in the hydrodynamic slip parameter augments the drag coefficient by 35.87% and 33.40% for cylinder and sheet configurations, respectively. The present study has potential applications in biomedicine, such as targeted drug delivery, hyperthermia, theranostics and cardiovascular treatments.

A thermal case study of three dimensional MHD rotating flow comprising of multi-wall carbon nanotubes (MWCNTs) for sustainable energy systems

The carbon nanotubes (CNTs) possess unique properties due to their structural mechanism. The CNTs comprise of exceptional electrical, mechanical and thermal attributes. This paper aims to interpret the correlation of carbon nanotube nanoparticles with motile microorganisms in a rotating magnetohydrodynamic flow with respect to slip as well as convective boundary conditions. Multi-wall carbon nanotubes (MWCNTs) are incorporated as nanoparticles whereas water (H2O) as host fluid. The dimension free appearance of governing differential equations is caused by the similarity transformation. Afterward, the combination of order reduction and finite differences is used to determine the approximate solution of the problem. The consequences of problem parameters for temperature, velocity, Nusselt number and skin friction are deliberated through tables and graphs. The code efficiency is assessed by equating the results, under limiting cases, with the previous ones and found to be in an exceptional agreement. The temperature seems to be elevating with the influence of Biot number. On the other hand, a decreasing trend in the velocity profile is noticed when we increase the parametric values of rotation as well as slip parameter. The Peclet number is one of the factor that reduces the microbe's density distribution within the boundary layer regions.

Entropy optimization in mixed convective boundary layer flow of CNTs Casson nanoliquid through a vertical cylinder moving with nonlinear velocity

This article inspects entropy generation and mixed convection boundary layer flow of carbon nanotubes (CNTs) Casson nanoliquid via semi-infinite vertical cylinder which moves with nonlinear velocity in Darcy-Forchheimer porous medium. Appropriate similarity variables have been employed to convert the original partial differential equations into ordinary differential equations that have been solved using overlapping grid spectral quasilinearisation method (SQLM). Comparison of accuracy, convergence and stability between the two methods is made. Rate of entropy generated, flow fields and engineering quantities are discussed for different embedding parameters. It is revealed that single-wall CNTs are more efficacious to improve heat transport features than multi-wall CNTs. The fluid flow and thermal dispersion processes improve with consideration of curved surface, CNTs, non-Newtonian fluid and injection of the fluid. The curvature surface and suction of the fluid contribute towards growth of skin friction factor and rate of thermal transference. Entropy generated expands by accounting for viscous nature of the fluid, strong nonlinearity, suction, non-Newtonian fluid, convective boundary condition and CNTs. The study finds applications in various processes, which are massively impacted by heat transport enhancement and high porosity. Boundary layer flow and heat transfer analysis through cylinders are relevant to various metallurgical and engineering solicitations.

Computational analysis of radiative nanofluid flow past an inclined cylinder with slip effects using the Yamada–Ota model

The notion of the paper is to analyse the flow attributes of a carbon nanotube-based hybrid nanofluid over an inclined cylinder. This study accounts for the impacts of mixed convection, thermal radiation, suction/blowing, and slip boundary conditions. The solution of the governing equations is obtained using the "bvp4c solver", and presented through graphs and tables. The obtained results are validated by comparing them with published work. The study reports that increasing the temperature slip parameter led to a reduction in both velocity and temperature distributions. The presence of an electric parameter contributed to an increase in nanofluid flow, while the temperature of the nanofluid exhibited a decrease. Moreover, increasing the Hartmann number from 0.2 to 1.1 results in a 1.39% increase in the heat transfer rate within the hybrid nanofluid model. However, the pure fluid model demonstrates a more substantial enhancement, with a significant 3.8% rise in the heat transfer rate.

Illustration of homogeneous–heterogeneous reactions on the MHD boundary layer flow through stretching curved surface with convective boundary condition and heat source

Illustration of homogeneous–heterogeneous reactions on the MHD boundary layer flow through stretching curved surface with convective boundary condition and heat source

Illustration of Convective Boundary Conditions on the Darcy–Forchheimer Flow of Nanofluid with the Impact of Chemical Reaction

The application of convective heat transport holds great significance in physiological studies, particularly in preventing the overheating of birds and mammals living in warm climates. This process involves the transfer of heated blood from the body’s core to the nearest blood vessels, effectively dissipating the excess heat into the environment. As a result, analyzing convective boundary conditions becomes crucial for understanding heat and solutal profiles in the flow of a two-phase nanofluid model (Darcy–Forchheimer), which also takes into account heat sources and chemical reactions. This model encompasses the combined effects of Brownian and thermophoresis phenomena on flow behavior. The development of a three-dimensional model leads to a set of nonlinear ODEs, which can be tackled using appropriate similarity variables and traditional numerical techniques, i.e., the Runge–Kutta fourth-order combined with shooting technique is adopted to obtain the solutions. To ensure the model’s accuracy, physical parameters are carefully chosen within their appropriate ranges to reflect real-world behavior. This approach helps to capture the physical essence of the system under study. It is observed that the streamlines for the proposed stream function shows the flow pattern of the fluid particles within the domain for the variation of the kinematic viscosity and stream values, and enhanced Brownian motion controls the fluid concentration.

The Role of Quadratic-Linearly Radiating Heat Source with Carreau Nanofluid and Exponential Space-Dependent Past a Cone and a Wedge: A Medical Engineering Application and Renewable Energy

A mathematical analysis for a steady, incompressible, laminar Carreau nanofluid flow over a porous cone and wedge is considered. The novelty of this research work is to scrutinize an exponential space-dependent Cattaneo–Christov heat flux and quadratic Rosseland approximation effects. Two-phase nanofluid model, i.e., Brownian motion, and thermophoretic effects are included. This study also employs non-linear thermal radiation and convective surface boundary conditions to investigate heat transport phenomena. The Carreau nanofluid boundary layer equations are derived using the standard boundary layer approximations. By applying the similarity transformations, the managing set of partial differential equations (PDEs) becomes a system of connected non-linear ordinary differential equations (ODEs). The resultant non-linear ODEs are solved numerically utilizing the numerical method, particularly the bvp4c function in MATLAB. The significances of the fluid motion are visualized by sketching several Carreau nanofluid flow’s relevant parameters using graphic outputs. The effects of a wide range of thermophysical variables on liquid properties including velocity, temperature, concentration, skin-friction, Nusselt number, and Sherwood number are investigated and discussed. This study’s findings are compared to previously announced results within a limited range, where strong validation was seen. The results demonstrate that the opposite mechanism is observed with repercussion of Weissenberg number (We) on velocity profile and concentration, the enhancement of We increases the momentum boundary layer while it reduces the concentration boundary layer. The outcomes could be applied to the cooling of equipment, electronics, and various industrial units.

Non‐similar heat transfer analysis of magnetized flow of Ag‐Mgo/water hybrid nanofluid flow through darcy porous medium

AbstractThis study aims to examine the magnetized flow of Ag–MgO/water hybrid nanofluid over an extending sheet implanted in Darcy porous medium. Thermal radiations, Joule and viscous dissipations are incorporated into energy equation to account for heat transfer. The convective heat flux boundary condition is imposed at sheet surface. Using non‐similar conversions, governing equations are converted to a system of dimensionless partial differential equations (PDEs). These equations are transformed into ordinary ones by using local non‐similar method. MATLAB's bvp4c function is used to numerically simulate the ordinary differential equations (ODEs). The velocity and thermal profiles for positive variation of essential parameters are illustrated graphically. It was concluded that the velocity profile increases for the rising Darcy number. On the other hand, the temperature profile increased for the positive variation of magnetic number, volume fraction, radiation parameter, Eckert number and Biot number while decreasing for all other parameters. The skin friction coefficient and heat transfer rates are thoroughly investigated and findings are reported through tables. It was found that the magnitude of skin friction coefficient rises with an increase in volume fraction, suction and magnetic parameters while the heat transfer is enhanced by increases in Darcy number, suction parameter, radiation parameter, and Biot number. As per the author's knowledge, no work has previously been published on the current model using the local non‐similarity method. This work may provide insight to researchers interested in thermal systems and solar energy harvesting.