Keller Box Scheme Research Articles

Nanoscale heat transport analysis of magnetized trihybrid nanofluid over wedge artery: Keller Box and Finite element scheme combination

Nanoscale heat transport analysis of magnetized trihybrid nanofluid over wedge artery: Keller Box and Finite element scheme combination

Evaluation of thermal and concentration slip effects on heat and mass transmission of nanofluid over a moving wedge surface using Keller box scheme

The current research is based on the impact of thermal and solutal slip in the boundary layer nanofluid flow through a moving accelerating wedge. The present investigation is considered with the influence of Brownian motion and thermophoresis. Thermal insulation, geothermal engineering, crude oil extraction, and heat exchangers are very important applications of nanofluid movement over a wedge surface with thermal and concentration slip. The suggested mathematical analysis is expressed in terms of partial differential equations (PDEs). These PDEs are transformed into ordinary differential equations via similarity transformation. The Keller Box technique is used to integrate the resultant non-similar equations. The set of discretized and first order differential equations is formed with the help of central difference and the Newton–Raphson technique. The graphical and numerical results are extracted with the help of MATLAB. The numerical results with the influence of the Prandtl factor (Pr), constant moving factor (λ), thermal slip factor (S2), and concentration slip parameter (S2) are interpreted visually and numerically. Graphical representations of velocity, thermal, and mass concentration profiles are analyzed in depth. The solution for skin friction coefficient, heat transport rate, and mass transport rate is calculated. The moving velocity function increases as Pr increases. The rate of slip temperature and slip concentration rate is enhanced for a lower Prandtl factor. The maximum slip behavior in temperature function and fluid concentration slip is deduced for each value of thermal-slip and concentration-slip factors. For high Prandtl and Brownian motion factors, the rate of Nusselt number is enhanced significantly.

Thermal stability and slip effects in micropolar nanofluid flow over a shrinking surface: A numerical study via Keller box scheme with block-elimination method

Thermal stability and slip effects in micropolar nanofluid flow over a shrinking surface: A numerical study via Keller box scheme with block-elimination method

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.

Magnetohydrodynamic Nanofluid Flows Passing through a Smart Fabric under the Influence of Magnetic Field and Radiative Flux

The study of MHD have been widely on topics with complex problems. Just as this topic involves inductive polymers or smart fabrics for engineering in machinery or protective equipment. The smart fabrics can be involved in MHD studies become a useful material. The smart fabric is a sheet of inductive polymer that can be an influence in the MHD analysis as well as a parameter that can be considered. In this study, the MHD of nanofluid namely Iron-(III)-oxide flows past in smart fabrics under influence of magnetic field and radiative flux is studied by constructing a mathematical model and then the model solved numerically using the Keller-Box scheme. The effect of Mixed Convection and stretching parameter is considered on the model. Numerical simulations were carried out to examine the effect of the parameters, are obtained the profile of velocity and temperature increase when the magnetic and stretching parameters increases, the velocity profile and temperature decreases when the Prandtl number are increases, the profiles of velocity are decreases and temperature increases when porosity variable and volume fraction parameter’s value increases, and the profile of temperature increase when the mixed convection’s value and the radiation parameter increases.

A Novel Approximation Approach for the Analytical Solution of the Flow of Micropolar Fluid Through a Permeable Channel

An attempt is made in this study to investigate the problem of micropolar fluid flow in a porous medium theoretically. Employing the Berman’s similarity solution, the model equations governing the flow is transformed into a set of nonlinear ordinary differential equation and solved using Temimi-Ansari method. Expressions for the velocity and micro-rotation profiles are obtained under the impressions of diverse parameters affecting the flow problem. Using symbolic computation software Mathematica, the nondimensional equations are solved numerically using the Keller Box scheme. Comparison between the analytical solution obtained by TAM and the numerical result are compared with results in literature to observe rapid convergence. Findings from the study showed in the presence of

Coupled heat and mass transfer mathematical study for lubricated non-Newtonian nanomaterial conveying oblique stagnation point flow: A comparison of viscous and viscoelastic nanofluid model

Abstract The lubrication phenomenon plays a novel role in the chemical industries, manufacturing processes, extrusion systems, thermal engineering, petroleum industries, soil sciences, etc. Owing to such motivated applications, the aim of the current work is to predict the assessment of heat and mass transfer analysis for non-Newtonian nanomaterial impinging over a lubricated surface. The flow is subject to the oblique stagnation point framework. The lubricated phenomenon is observed due to viscoelastic nanofluid. The impacts of chemical reaction are also endorsed. The fundamental conservation laws are utilized to model the flow problem and similarity transformation are used to transform the governing system of partial differential equations into ordinary differential equations. A thin layer of power law lubricant is used to enhance the lubrication features. The numerical object assessment regarding the simulation process is captured by implementing the Keller Box scheme. The physical characterization endorsing the thermal fluctuation with flow parameters is inspected.

An efficient numerical scheme for solving the melting transportation of energy with time dependent Carreau nanofluid

The current work is categorized into the following formatBackground: Heat transfer controlling through therapy and blood flow has clinical importance in different levels of the human body. Biological faculties utilize blood in which iron oxide nanoparticles are incorporated for contrast agents and in the biomedical fields as they possess key and intrinsic characteristics, like low toxicity, capability of blood carrying nanoparticles, surface engineering and colloidal stability. This paper has a unique approach for analysis of blood flow containing nanoparticles with mathematical model of Carreau nanofluid. Furthermore, heat transport analysis has been provided by using the melting heat conditions and free convection.Carreau nanofluid for blood flow gives a set of partial differential equations (PDEs), which are handled by using the Keller Box scheme to obtain the numerical performances of the results. The obtained results are compared with Bvp4c, which is MATLAB built in program and found smooth agreement. The graphical plots and statistical tables have been provided for various dimensionless parameters to get the numerical simulations of the problem against velocity, temperature, and heat transfer Nusselt number. From the obtained results, the velocity and temperature of the fluid diminishes by the virtue of an amplification in unsteady parameter A. A positive variation in melting parameter M in the case of Prandtl number Pr and unsteady parameter A magnifies the heat transfer Nusselt number. This article shows the novelty in the sense that the effect of Tiwari and Das model accompanied with melting heat transfer phenomenon in the case of unsteady Carreau fluid has not investigated before in the available literature related to the Carreau fluid.

A computational description of time-dependent transport of a water-based nanofluid with hybrid nanocomposite Cu–Al2O3 over a parabolic surface by Keller-box scheme: A modified Buongiorno model

This paper discusses the high heat transfer demand from application prospects. Hybrid nanofluid is a well-known liquid with higher heat transfer capabilities. Here, the time-dependent flow of hybrid nanocomposite, by hybridizing the metal (Cu) and metallic oxide (Al2O3) and inserting them into water-based nanofluid, is examined. The flow takes place over the upper half of a parabolic surface. The modified Buongiorno model is used to express the physical phenomenon in mathematical equations form. The governing system of partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs) by applying certain transformations. Computation of the final equations has been done by a numerical scheme, known as the Keller-box method. The significance of dimensionless flow causing physical parameters is shown through graphs and tables. The findings reveal that among the hybrid nanofluids with two types of nanoparticles varying from 0% to 5%, a nanofluid having 5% of both nanoparticles is the one with the maximum surface drag force and heat transport rate, which are 41.8% and 22.7% higher to water, respectively. A higher amount of Al2O3 than Cu results in a suitable hybrid combination for application purposes to produce higher cooling rate with less surface drag. Also, the thickness of the surface, unsteadiness, nanoparticles suspension and power index of wall temperature enhance the heat transfer rate. Thin parabolic surfaces experience less drag and have larger boundary layer thicknesses (momentum, thermal and concentration) as compared to thicker parabolic surfaces. Also, the addition of copper slows down the hybrid fluid flow field, but alumina magnifies the mobility of hybrid fluid.

Thermal examination of chemical interaction and thermophoretic diffusion of Williamson fluid flow across Riga Plate surface with nonlinearity radiation flux

The purpose of this research is to investigate the thermophoretic diffusion and chemical reaction on steady magnetized Williamson fluid flow, heat, and mass transfer along a Riga surface in the presence of variable thermal properties. By imposing the appropriate similarity technique, the system of higher-order formulas has been transformed from partial order into ordinary order. An efficient numerical technique named the classical Keller box scheme has been incorporated to solve these dimensionless coupled non-linear ordinary differential equations. The obtained results are visualized graphically with physical justification. In addition to that, we validated the obtained outcomes by comparing them to earlier literature, and we identified an excellent match, supporting the reliability of the present method. We discovered from our analysis that acceleration in the values of Williamson fluid and viscosity leads to enhancement in both velocity plots. Also, the material and stretching parameters have a major role in the fluid flow control process.

Some Studies on Three Dimensional Turbulent Boundary Layer Flows

This paper describes some studies on flow separation and on the extended Cebeci-Smith turbulence and transition models, carried out using a three-dimensional turbulent boundary layer code developed at the Vikram Sarabhai Space Center (VSSC), Thiruvananthapuram, India. This code uses an orthogonal curvilinear surface fitted co-ordinate system. The governing equations are solved, by an implicit space marching numerical method called the Keller Box Scheme with suitable modifications for reverse crossflows. Initial data on two intersecting planes for starting the solution procedure, are obtained by solving the appropriate limiting form of the governing equations. Three transition models available in the Literature are studied. A few sample results are presented and compared with experimental measurements.

Comparison of Adomian Decomposition Method with Differential Transformation Method for Unsteady MHD Flow and Heat Transfer Over a Stretching/Shrinking Permeable Sheet with Ohmic Heating

In this paper, two semi-analytical techniques were implemented to solve a two-dimensional unsteady MHD fluid flow and heat transfer through a stretching/shrinking permeable sheet with ohmic heating and viscous dissipation. The governing flow equations in PDE form were reduced to ordinary differential equations using appropriate similarity transformation. We obtained approximate expressions for the velocity and temperature profiles. Comparative results obtained employing Adomian decomposition method and differential transformation method were benchmarked against a numerical solution using Keller box scheme. Our findings revealed that the approximate analytical solution obtained using DTM is more dependable with fast convergence, highly accurate with minimal calculations and computationally convenient. However, the requirement of Adomian polynomials to tackle the nonlinear terms in ADM makes its execution sometimes cumbersome and difficult.

An efficient heat transfer analysis of MHD flow of hybrid nanofluid between two vertically rotating plates using Keller box scheme

Nowadays, the majority of pharmaceuticals are created as hybrid nanofluids, and blood is used as a base fluid for testing to determine how the various components of the blood interact chemically. The thermal efficiency of the base liquids is also improved by the hybrid nanofluids. Moreover, the impacts of thermal radiation are also considered. Blood is used as base fluid. To investigate the characteristics of phenomena, we research two different forms of fluid flow, one of which is a hybrid nanofluid and the other of which is a nanofluid flow. The governing set of PDEs is transformed into a set of ODEs with the help of suitable similarity transformations. Nonlinear ODEs are numerically solved with the help of well reputed Keller box technique. Graphical and numerical results versus different physical and engineering parameters are computed by the computational software Matlab. The temperature profile is improved by increasing values of the heat source-sink parameter because the parameter causes the fluid to produce more heat. The volume fraction parameter reduces the fluid's velocity. The velocity profile measured against the suction parameter shows the same form. This study may control various aspects of the microcirculatory system, including the drug delivery process.

Thermal case examination of inconstant heat source (sink) on viscous radiative Sutterby nanofluid flowing via a penetrable rotative cone

To improve heat transfer, this work provides a unique theoretical mathematical model of ternary hybrid nanofluid. In this analysis, the tri-hybrid nanoparticles TiO2, Al2O3, and AA7072 are submerged in ethylene glycol (EG), resulting in the mixture TiO2+Al2O3+AA7072/EG. The tri hybridity nanofluid is considered 3-D flowing via a rotate permeable cone embedded in Darcy-Forchheimer porousness material in the existence of fluctuating temperature generating (sink) and current radiate fluxing. The Keller box scheme (KBS) is exploited to resolve the liquid flowing and temperature equations numerically after converting them to ordinary differential equations employing similarity transformations. The results are graphed, and it is shown that the tri-hybrid nanofluid (THNF) has superior thermal conductance to the hybrid nanofluid (HNF) and that the fluid's velocity and temperature develop as a consequence of enlargement in thermal radiative fluxing and variable thermal conductivity effects. Raising values of De and Fr decline drag friction but drag friction coefficient values are improved as a result of positive variation in M,Re,ς, and λ. It is apparent that the rate of heat transference amplifies owing to magnification in QT, QE and Rd but the heat transfer rate diminishes due to magnification in Re and Fr. Incremental change in volume fraction of nanoparticles φ=0.005to0.03 delivers more heat in the case of tri-HNFs TiO2+Al2O3+AA7072 in contrast to ethylene glycol based TiO2+Al2O3 fluid. The optimal percentage error diminishes for the drag friction phenomenon from 1.4% up to 1.1% by adopting De from 1 to 1.5 and λ=0.5. The percentage error in terms of heat transfer rate is getting smaller from 3.6% to 3.0% because of a positive change in QT by keeping Rd=1.5.

Relative analysis on fluid flow models for graphene oxide suspended blood flow: A Keller-box approach

The biomedical applications and antibacterial properties of graphene oxide (GO) nanoparticles help to treat tumors and improve drug delivery results. The 2-D flow of GO-nanoparticles integrated blood flow through cosine character stenosis artery with radiative heat, heat sink/source, and Cattaneo–Christov temperature flux is assumed. The Darcy–Forchhiemer condition and porosity parameter are imposed in momentum equations. The governing equalities and borderline settings are transformed into ODE using similarity transformation and resolved mathematically using the Keller-box scheme. First, the GO-nanolayer concept has been discussed to inspect heat transmission rate and change in energy and exhibited graphically. A comparison of Maxwell, Sutterby, and Oldroyd-B flow models is made and displayed schematically. It is noticed that the thermal performance is raised due to the GO nanolayer. The energy transmission rate is higher in the Oldroyd-B flow compared to the remaining two flow models. The simulation of this study may help understand the mechanism of blood flows through the stenosis artery. Also, this study can be used for advanced research in biomedical, cancer treatment, etc.

Influence of multi-stratification and multi-slip on the radiative MHD flow of Carreau fluid

In this paper, we scrutinize the impacts of multi-slip with multi-stratification on nanoparticles MHD Carreau fluid flow through a time-dependent stretching sheet with thermal radiation. We obtain the solution upon the application of the Keller-box scheme with an implicit finite-difference scheme. The influence of thermal stratification and concentration stratification is also being measured. The differentce parameters’ influence on the fluid flow is illustrated in diagrams and the quantitative numerical findings are well-argued. For increasing heavier species, fluid index and the reaction rate parameter with Prandtl number [Formula: see text], 10.0 and 15.0 will decrease the concentration of fluid within its boundary limits. Behavior of Weisenberg number on fluid velocity is studied. Moreover, fluid velocity declines as the unsteady parameter rises, while the temperature and concentration significantly decrease. Higher values of solutal and thermal stratification parameters result in decay of velocity and thermal boundary layer thickness while the fluid temperature reflects the opposite behavior.

Retraction Note: A brief comparative examination of tangent hyperbolic hybrid nanofluid through a extending surface: numerical Keller–Box scheme

Retraction Note: A brief comparative examination of tangent hyperbolic hybrid nanofluid through a extending surface: numerical Keller–Box scheme

Heat transfer phenomenon in a retarded boundary layer over a moving continuous cylinder

The phenomena of flow separation on a surface of finite length is analogous to boundary layer flows caused by retarded motion of continuous surfaces, which ultimately seize at some downstream position and increase drag on aerodynamic vehicles. According to the literature, a stationary surface of finite length will generate a boundary layer that is less energetic than one that is developed over a moving continuous surface. This means that a moving continuous surface is preferred to a stationary surface of finite length for the sustainability of the transport phenomena in such a retarded flow, which must eventually meet the flow separation. Therefore, the goal of this study is to conduct a heat transfer analysis in a delayed laminar boundary layer generated by a moving continuous cylinder with a constant radius. Wall temperature of uniform nature is considered in this investigation. In most of the boundary layer flows the self-similarity of the flow does not persist because of choosing the reference velocity of the desired character. Thus, the problem becomes non-similar. In general, the non-similarity of a flow may appear due to various aspects of the problem such as the retarded nature of the reference velocity, the surface temperature, the curvature of the body, etc. Surface transverse curvature imparts favorable consequences on the separating boundary layer and hence on the seizing flow character. The purpose of this investigation is to determine how TVC and the wall velocity power index affect temperature profiles, the local Nusselt number , the thickness of the thermal layer, and the thermal diffusivity of heat in a retarded boundary layer. In addition to this, the influence of Prandtl number and Stanton number has also been investigated. The numerical solution is computed using an implicit finite difference scheme, commonly known as the Keller-Box scheme in MATLAB scientific computing software Investigations reveal that the TVC assists the thermal transport by enhancing the rate of heat transfer and the length of the convectively heat transferring region (starting from the leading edge to the location where the flow gets seized) by increasing the longitudinal region of flow (starting from the leading edge to the location where the flow gets seized) on the surface. The surface wall velocity power index acts to decrease the temperature distribution and reduces the heat transfer rate at the surface. Further, the Prandtl number reduces the thermal boundary layer thickness and the Stanton number but enhances the local Nusselt number.

A renovated Jaffrey-Hamel flow problem and new scaling statistics for heat, mass fluxes with Cattaneo–Christov heat flux model

In dire situations, such as the restricted spatial scale in nanoparticle systems and the analogous analysis of non-Fourier heat conduction and conventional heat conduction, the transmission of heat and momentum will exhibit non-linear and nonlocal behavior. The mechanisms of heat and mass transfer for non-Newtonian fluid flow between two inclined planes (convergent channel) with porous walled are taken into consideration. The Jaffrey-Hamel flow equation is renovated with the contribution of Carreau rheological model. The Cattaneo heat flux is presented to designate the anomalous heat, mass transport of Carreau nanofluid considering the influences of radiation flux, Brownian diffusion, and thermophoresis. Assumption, theories, and conservation law's leads to governing PDEs, which are solved numerically by invoking the Keller-Box scheme. It was concluded that for both conduit, flow reversal occurs only in the divergent domain of the channel but not in the converging where rapid acceleration of flow occurs, and inertial forces dominate the transport process. The flow instability in a porous media incorporate fluid inertia. The renovated model, which incorporates non-Fourier's law of heat conduction, can explain the anomalous thermal conductivity enhancement. The thermal relaxation effects the heat flux significantly, the conduction mechanism switches to oscillatory conduction with narrower temperature.

Modeling and computational framework of radiative hybrid nanofluid configured by a stretching surface subject to entropy generation: Using Keller box scheme

This study examines the characteristics of the velocity, thermal field and entropy profiles for hybrid nanofluid flow passing through a starching sheet with thermal radiation. The carbon nanotube (SWCNT and MWCNT) are used as a nanoparticles with Cattaneo-Christov (CC) heat flux. Ethylene glycol is utilized as a base fluid in this case. To achieve an improved solution, the fluid flow over the geometric properties is designed using highly non-linear PDEs, and the governing equations must be converted into dimensionless non-similar equation systems using the highly efficient well-known Keller-box scheme in computational software MATLAB. The practical feasibility of these solutions is determined by the range of the controlling parameters. The velocity distribution reduces as the magnetic parameter estimate increases, however, the temperature field and entropy production increase as the magnetic parameter fluctuation esclates. As the slip parameter is increased, the velocity field diminish. The thermal field is enhanced for rising the radiation parameter, and the entropy profile is boosted for increasing Brinkman parameter values. The findings of this research might have a significant impact on industries where local cooling and heating via impingement jets are needed in electronic devices, heat sinks, drying technologies, and so on. To the best of the authors' knowledge, this is the first effort to employ a hybrid nanofluid to analyze entropy formation due to magnetohydrodynamics flow over a starching sheet.