Keller Box Technique Research Articles

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.

Consequences of thermal conductivity and thermal density on heat and mass transfer in the nanofluid boundary layer flow toward a stretching sheet in the presence of a magnetic field

The term “thermal conductance” is used to describe a material’s ability to transport or conduct heat. Materials with high thermal conductivity are employed as heating elements, while those with poor thermal conductivity are used for insulation purposes. It is known that the thermal conductivity of pure metals decreases as temperature increases. In this study, the primary focus is on the physical assessment of thermal conductivity, entropy, and the improvement rate of thermal density in a magnetic nanofluid. To achieve this, nonlinear partial differential equations are transformed into ordinary differential equations. These equations are further solved using a computational method known as the Keller box technique. Various flow parameters, such as the Eckert number, density parameter, magnetic-force parameter, thermophoretic number, buoyancy number, and Prandtl parameter, are examined for their impact on velocity, temperature distribution, and concentration distribution. For the asymptotic results, the appropriate range of parameters, such as 1.0 ≤ ξ ≤ 5.0, 0.0 ≤ n ≤ 0.9, 0.1 ≤ Ec ≤ 2.0, 0.7 ≤ Pr ≤ 7.0, 0.1 ≤ Nt ≤ 0.5, and 0.1 ≤ Nb ≤ 0.9, is utilized. The key findings of this study are related to the assessment of heat transfer in a magnetic nanofluid considering thermal conductivity, entropy generation, and temperature density. It is observed that the temperature distribution increases as entropy generation increases. From a physical perspective, thermal conductivity acts as a facilitating factor in enhancing heat transfer. The study concludes by emphasizing the consistency achieved through a comparison of the latest findings with previously reported analyses.

Thermal conductivity impact on MHD convective heat transfer over moving wedge with surface heat flux and high magnetic Prandtl number

The present evaluation focused on heat transfer and magnetic flux along the moving non-conducting wedge shape with thermal conductivity and surface heat flux effects. A suitable and well-known similarity transformation for integration is used for the coupled non-linear partial differential equations with stream formulations. The Keller Box technique is utilized to integrate the final non-similar equations numerically. The discretized algebraic equations are displayed graphically and numerically using the MATLAB software. The physical characteristics like temperature, magnetic field, velocity profiles, skin friction, heat transfer and magnetic intensity are investigated with various factors. The influence of relevant characteristics like thermal conductivity ξ, Prandtl number Pr, wedge parameter β, variable viscosity ε, and Biot number Bi is interpreted graphically and numerically. It is noted that velocity graph effects are declined at lower value of Biot number and enhanced value is obtained at the higher value of Biot number. The fluid temperature with highest thermal slip effects is displayed with minimum value of thermal conductivity but minimum value is obtained at large value of thermal conductivity. The maximum heat flux value is obtained at large value of moving parameter.

Mixed convective magneto flow of nanofluid for the Sutterby fluid containing micro-sized selfpropelled microorganisms with chemical reaction: Keller box analysis

The current work aims to scrutinize the bioconvection Sutterby nanofluid flow of the Cattaneo-Christov heat and mass flux over a rotating disk. The effects of thermophoresis and Brownian motion receive considerable consideration. The process of analyzing heat and mass transfer phenomena involves taking into account the impacts of thermal radiation and chemical reactions that are susceptible to convective boundary conditions. Firstly, we reduce the PDEs of the physical model to ODEs through alter transformation and then numerically solved the transformed ODEs using Keller Box technique. An analysis of numerical data follows to ascertain the role of numerous flow variables on the flow profiles. Based on the findings, it is evident that an increase in the fluid variable Δ and the porous variable K leads a decrease in the, radial F'(ζ), axial F'(ζ) and tangential G(ζ) velocities. Furthermore, we find that the growing values of the thermal radiation Rd variable and the thermal Biot number B T greatly aid in raising the fluid’s temperature. Concentration profile shows decreasing behavior for rising values of Schmidt number Sc but upsurge for solutal Biot number B C . The microorganism is decayed with greater Lewis number Lb and Peclet number Pe.

The impact of soret, Dufour, and chemical reaction on MHD nanofluid over a stretching sheet

This paper focuses on the effects of DuFour, heat radiation, and chemical reaction on a two-dimensional natural convective flow of stable electrical magnetohydrodynamics (MHD) nanofluid across a permeable stretched sheet, in addition to the effects of suction.This work investigates the boundary layer flow dynamics of a nanofluid via a stretched sheet in the presence of a magnetic field, accounting for DuFour effects and chemical reactions. The non-linear partial differential equations were transformed into a non-linear ordinary differential equation by using the appropriate similarity transformation. The Keller box technique is used to numerically solve ordinary differential equations. Graphs are used to show variations in temperature, concentration, and velocity to different physical constraints. Raising the thermophoresis parameter (Nt) results in inferior concentration profiles due to a decrease in the Lewis number parameter (Le) and Brownian motion parameter (Nb). The concentration profile is reversible with temperature and decreases as the chemical reaction parameter increases. As we increase the Du levels, the temperature declines. The patterns in the altering rates of heat and mass transfer, as well as the skin-friction coefficient, are also analyzed using numerical data.”

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Numerical simulations of Williamson fluid containing hybrid nanoparticles via Keller box technique

In this investigation, a Williamson hybrid nanoliquid flow over a stretchy surface has been considered. Furthermore, the convective boundary condition is incorporated for the analysis. In view of the practical applications thermal radiation is used to analyze the energy transfer phenomenon. The momentum and energy expressions are solved numerically by employing the KB approach (Keller Box Technique). The energy transfer rate has been discussed in the table. Further, velocity, temperature and Nusselt number impacts against thermal radiations are discussed in detail. This research portrayed that with the growth of suction/injection factor, the energy transmission and skin friction increase. Moreover, the heat transfer rate decreases for both (Al2O3+CuO)/SA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${(Al}_{2}{O}_{3}+CuO)/SA$$\\end{document} and Al2O3/SA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${Al}_{2}{O}_{3}/SA$$\\end{document} the on the growth of Weissenberg parameter. In the same vain heat transfer rate improves for the increment in the convective parameter.

Energy bandgap and thermal characteristics of non-Darcian MHD rotating hybridity nanofluid thin film flow: Nanotechnology application

Abstract The primary purpose of this research is to examine how the presence of thermal features variation affects the velocity and heat transfer rate of nanofluids composed of sodium alginate and molybdenum disulfide [Na-Alg/MoS2]m and sodium alginate and molybdenum disulfide and graphene oxide [Na-Alg/MoS2 + GO]h, respectively, flowing between two rotating, permeable plates. Both centripetal and Coriolis forces, which act on a spinning fluid, are taken into account. The impacts of magnetized force, thermal radiative flux, heat source (sinking), and varied pressure in the Darcy–Forccheimer material are considered. Using the physical vapor deposition method, single and hybridity nanofluid thin films of thickness 150 ± 5 nm may be created. The controlling mathematical equations of the suggested model are solved using the Keller-box technique in MATLAB software. The surface friction coefficient of a hybrid nanofluid is less, and the heat transfer rate is greater than that of a regular nanofluid. The rate of heat transmission is slowed by the rotational parameter. The thermal efficiency of mono nanofluids is as low as 6.16% and as high as 21.88% when compared to those of hybrid nanofluids. In particular, the findings of density functional theory (DFT) calculations reveal that the energy bandgap Δ E g Opt \Delta {E}_{{\rm{g}}}^{{\rm{Opt}}} drops from 1.641 eV for conventional nanofluid to 0.185 eV for hybridity nanofluid. Based on the findings, the addition of graphene oxide nanoparticles to the base nanofluid converts it from a semi-conductor to a hybridity nanofluid as a superconductor.

Exploring magnetic and thermal effects on MHD bio-viscosity flow at the lower stagnation point of a solid sphere using Keller box technique

The study of liquid comprising nanoparticles for energy transmission characteristics has gained prominence due to its diverse real-life applications in different energy systems. Recently, scientists have been endeavoring to introduce a new type of liquid, despite the already proven effectiveness of Nano liquid's thermal efficiency. To meet the demands of various engineering and industrial applications, scientists have developed a new class of liquid called hybrid Nano liquid by dispersing two types of nano-sized particles in a regular liquid. Given the significance of hybrid Nano liquid in this study, we have considered (titanium dioxide, sodium alginate, silver) and (graphite oxide) in an MHD Casson fluid (bio-viscosity blood) near the lower stagnation point of a solid sphere. Additionally, this research addresses thermal radiations and the effects of magnetic fields. For the numerical results of the proposed ODEs, the Keller box method was employed. Engineering quantities obtained from this investigation are discussed in tables. From the observed graphs, it is evident that the velocity of the liquid near the lower stagnation point decreases as the magnetic effects increase.

Computational study of magnetized and dual stratified effects on Non-Darcy Casson nanofluid flow: An activation energy analysis

The current research looks into magnetohydrodynamics Casson nanofluid flow and suction/injection implications for a nonlinearly stretched interface. To improve heat transport, joules of heat, radiation impacts and thermal stratification are used. A Darcy-Forchheimer porous media is used to conduct fluid flow. Chemical reactions involving energies of activation and solutal stratum are additionally considered. The Keller-box technique is used to solve the resulting non-linear set of ordinary differential equations. The impacts of a number of variables are examined employing diagrams of quantity, velocity, and heat. Increased assessments of porousness, Darcy-Forchheimer, and Casson fluid characteristics result in a decrease in velocity trends. For improved measurements of Lewis number and solutal fractionated factors, the intensity pattern reduces. The skin friction factor increases with increasing Casson parameter estimate. In the instance of the porous and nonlinear stretching parameters, the Nusselt number rises. For increasing levels of the Lewis number and Brownian motion factors, the Sherwood number drops. Furthermore, Nusselt number ratios are estimated with Prandtl numbers with regard to current information available, which shows remarkable consistency. For varied incorporated parameters, streamlines, heatlines, and masslines additionally displayed.

Entropy generation in water conveying nanoparticles flow over a vertically moving rotating surface: Keller box analysis

PurposeThe purpose of this study is to investigate the entropy generation in different nanofluids flow over a vertically moving rotating disk. Unlike the classical Karman flow, water-based nanofluids have various suspended nanoparticles, namely, Cu, Ag, Al2O3 and TiO2, and the disk is also moving vertically with time-dependent velocity.Design/methodology/approachThe Keller box technique numerically solves the governing equations after reduction by suitable similarity transformations. The shear stress and heat transport features, along with flow and temperature fields, are numerically computed for different concentrations of the nanoparticles.FindingsThis study is done comparatively in between different nanofluids and for the cases of vertical movement of the disk. It is found that heat transfer characteristics rely not only on considered nanofluid but also on disk movement. Moreover, the upward movement of the disk diminishes the heat-transfer characteristics of the fluid for considered nanoparticles. In addition, for the same group of nanoparticles, an entropy generation study is also performed, and an increasing trend is found for all nanoparticles, with alumina nanoparticles dominating the others.Originality/valueThis research is a novel work on a vertically moving rotating surface for the water-conveying nanoparticle fluid flow with entropy generation analysis. The results were found to be in good agreement in the case of pure fluid.

Analysis of slip condition in MHD nanofluid flow over stretching sheet in presence of viscous dissipation: Keller box simulations

In present paper the mathematical study of Slip conditions on electrically conducting nanofluid over a vertically stretching sheet is presented with effects of viscous dissipation, thermal radiation and Soret and Dufor. The state of flow has been explained mathematically with help of partial differential equations. Model equations are made convenient for calculation by suitable transformations. With the help of Kellerbox technique unknown functions are approximated in flow situation. The influence of medium porosity, magnetic field strength, thermal radiation, Soret and Dufour effects, Buoyancy forces, viscous dissipation wall slip parameter, and heat source are investigated in detail. Effects of emerging parameters on velocity, concentration, temperature and profiles are investigated. In relation to the parameters involved, we can observe the rates of momentum, heat, and mass transfer near the stretching surface. It can be concluded from the study that velocity slip parameter accelerates with fluid motion, temperature of nanoparticles is enhanced due to rise in Eckert number and Biot number, while the Soret effect enhances the nanoparticles concentration close to the stretching sheet. Also, under common assumptions, the analytical approximations for the solution of the current model that were produced by using the Keller box approach were shown to be in very excellent agreement with certain early publications.

Significance of thermal density and viscous dissipation on heat and mass transfer of chemically reactive nanofluid flow along stretching sheet under magnetic field

The main focus of the current research is to evaluate heat and mass transfer across stretchable sheet under applied magnetic field. The chemical reaction and variable density is essential for thermal behavior of nanofluid. The present study presents a careful inspection of chemical reaction, thermal density, viscous dissipation and thermophoresis on heat and mass transfer of magneto and chemically reactive nanofluid across the stretching sheet. The physical attitude of entropy and chemical reaction improvement rate in magneto nanofluid is the primary focus of the present research. By applying the proper transformation, nonlinear partial differential expressions are introduced to the structure of the ordinary differential framework. The flow equations are simplified into nonlinear differential equations, and these equations are then computationally resolved via an efficient computational technique known as Keller box technique. The governing flow factors like Eckert number, reaction rate, density parameter, magnetic-force parameter, thermophoretic number, buoyancy number and Prandtl number on velocity, temperature distribution and concentration distribution are evaluated prominently. It is noticed that prominent enhancement in temperature of fluid is assessed for maximum Prandtl number. It is found that the reasonable change in concentration distribution is evaluated for each Prandtl number with entropy generation. It is examined that the dimensionless Nusselt coefficient is decreased for maximum Brownian motion. It is seen that the dimensionless mass transfer is increased for maximum Brownian motion in the presence of buoyancy and magnetic forces.

Significance of Temperature-Dependent Density on Dissipative and Reactive Flows of Nanofluid along Magnetically Driven Sheet and Applications in Machining and Lubrications

Nanofluid lubrication and machining are challenging and significant tasks in manufacturing industries that are used to control the removal of a material from a surface by using a cutting tool. The introduction of a nanofluid to the cutting zone provides cooling, lubricating, and chip-cleaning benefits that improve machining productivity. A nanofluid is a cutting fluid that is able to remove excessive friction and heat generation. Chemical reactions and temperature-dependent density are essential in the thermal behavior of a nanofluid. The present study presents a careful inspection of the chemical reactions, temperature-dependent density, viscous dissipation, and thermophoresis during the heat and mass transfer of a nanofluid along a magnetically driven sheet. The physical attitude of viscous dissipation and the chemical reaction improvement rate in magneto-nanofluid flow is the primary focus of the present research. By applying the proper transformation, nonlinear partial differential expressions are introduced to the structure of the ordinary differential framework. The flow equations are simplified into nonlinear differential equations, and these equations are then computationally resolved via an efficient computational technique known as the Keller box technique. Flow factors like the Eckert number, reaction rate, density parameter, magnetic force parameter, thermophoretic number, buoyancy number, and Prandtl parameter governing the velocity, temperature distribution, and concentration distribution are evaluated prominently via tables and graphs. The novelty of the current study is in computing a heat transfer assessment of the magneto-nanofluid flow with chemical reactions and temperature-dependent density to remove excessive friction and heating in cutting zones. Nanofluids play significant roles in minimum quantity lubrication (MQL), enhanced oil recovery (EOR), drilling, brake oil, engine oil, water-miscible cutting fluids, cryogenic cutting fluids, controlled friction between tools and chips and tools and work, and conventional flood cooling during machining processes.

Sensitivity analysis of non-isothermal mixed convective heat and mass transfer in nanofluid flow over a horizontal circular cylinder with Brownian motion

In the current study, the sensitivity analysis for the combined convection boundary layer flow over a horizontal circular cylinder embedded in a nanofluid has been made. The governing partial differential equations are transformed into a dimensionless form by utilizing a suitable similarity transformation. The Keller-box technique is utilize to get a numerical solution. The numerical outcomes of the Sherwood number, skin friction coefficients, and Nusselt number have been shown graphically. Lewis number ( 5 ≤ Le ≤ 10 ) , Brownian motion parameter ( 0.1 ≤ N b ≤ 0.3 ) , thermophoresis motion parameter ( 0.1 ≤ N t ≤ 0.3 ) are the important physical parameter for the current research work. Sensitivity analysis is carried out after applying the RSM to develop a correlation between dependent variables and significant physical parameters after designing the best-fitting model. Numerical results show that the skin friction coefficient is more prominent at the center of the cylinder and skin friction is highly sensitive with Lewis number, Nusselt number is highly sensitive with the Brownian motion parameter.

Thermal decomposition of hybrid nanofluid confined by radiated curved stagnated surface capturing partial slip effects

Thermal aspects of hybrid nanofluid are more special owing to enhanced thermal performances. Such improved thermal characteristics makes the hybrid nanomaterials productive with applications of solar systems, heating of engineering devices, cooling phenomenon, energy production etc. Following to such attentive applications in mind, this continuation aims to reflects the comparative thermal efficiencies of hybrid nanofluid model with nonlinear radiative phenomenon due to curved surface. Two famous types of nanoparticles namely alumina oxide (Al2O3) and copper (Cu) are taken as hybrid nanoparticles. The oblique stagnated flow due to curved radiative surface is accounted for the curved configuration. The flow pattern is inspected with implementation of velocity and thermal slip conditions at the boundary. Non-linear partial differential equations are transmuted into non-linear ordinary differential equations through the use of similarity transformations. The Keller-Box technique, which is a well-known method, is utilized to obtain the numerical results. Furthermore, the impact of slip parameters, velocity ratio parameters, Prandtl number, non-uniform heat source and sink parameters, radiation parameter, stream lines, heat transportation rate along with skin-friction on thermal and velocity distributions are examined and depicted via graphs and tables. It is observed that temperature profile enhanced due to velocity ratio parameter and curvature constant. The improvement in heat transfer is more impressive for nonlinear radiative phenomenon as compared to linear thermal radiation consideration. Furthermore, a control of heat transfer pattern is observed due to interaction of thermal slip effects.

Non-similar analysis of entropy optimized chemically reactive flow of Williamson fluid with activation energy

Analysis of activation energy for magnetohydrodynamic (MHD) and radiative chemically reactive flow of Williamson material towards a stretching boundary with heat generation in study [1] is revisited. Ohmic heating in energy expression is additionally considered. Different from study [2], the non-similar solutions by Keller-box technique are obtained and analyzed.

Heat transfer analysis of unsteady MHD slip flow of ternary hybrid Casson fluid through nonlinear stretching disk embedded in a porous medium

The original article's purpose is to assess transfer of heat exploration for unsteady magneto hydrodynamic slip flow of ternary hybrid Casson fluid via a nonlinear flexible disk placed within a perforated medium of a magnetic field in the presence. Unsteady nonlinearly stretched disk inside porous material causes flow to occur. In the investigation, convective circumstances on wall temperature are also considered. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriate transformations, and the Keller-box technique is employed for their solution. In forced convection, the variable radiation has no direct impact on fluid velocity, but it is noticed that in the case of aiding flow, fluid velocity rises with an increase in radiation parameter, and the opposite is true in the case of opposing flow. Furthermore, it is experiential that fluid concentration and velocity goes up in creative chemical reactions, and both profiles decrease in detrimental chemical reactions. Moreover, a slightly greater unsteadiness characteristic lowers fluid, concentration, temperatureand velocity. Physical parameters' effects on fluid temperature, concentration, and velocity, as well as on wall shear stress, energy, and mass transfer rates, are studied.

Multiple Slip Effects of Boundary Layer Maxwell-Nanofluid Flow Past a Stretching Sheet: Magnetic Field and Cross Diffusion Effects

The authors are interested in understanding how a magnetic field and cross diffusion influence non-Newtonian Maxwell-Nanofluid boundary layer flow towards a nonlinearly stretched sheet when there are also Thermophoresis and Brownian motion reaction present in the system. Specifically, the purpose of this research is to learn more about the Maxwell and nanofluid properties of a stretched sheet in a normal magnetic field, as well as the reactions of three distinct slip situations (velocity, thermal, and solutal). Partially differential equations with nonlinear coefficients are used to obtain the governing conditions. These conditions are changed into profitable non-direct common differential conditions by utilizing the suitable change factors and change coefficients. To explore the mathematical results of the diminished arrangement of non-direct customary differential conditions, it was created and utilized the Keller box technique, which was produced for mathematical results. The reproduction considers the nanofluid speed, temperature, focus, skin grating coefficients, heat move rate, and mass exchange rate, among different factors. The validity of this strategy is shown through a correlation of the current outcomes with past discoveries in the writing. From this exploration work, the speed profiles are expanding with expanding upsides of Maxwell liquid boundary and diminishes with expanding upsides of Magnetic field and speed slip boundaries. With expanding impacts of Thermophoresis and Brownian movement, the temperature profiles are increment. As the upsides of Dufour number builds, the temperature profiles are additionally increments. A development of the Thermophoresis boundary prompts expanded nano particle volume focus circulation and the opposite impact is seen in the event of Brownian movement impact. The focus profiles are expanding with rising upsides of Soret number boundary.

Dynamics of Ohmic heating and aligned magnetic field on a nanofluid flow between two coaxial cylinders with rotation effect

The flow and thermal transfer of nanoliquid (Water + Fe3O4) between two circular parallel cylinders, one of which is at rest and the other rotating, are examined in this article using an aligned magnetic field and Ohmic heating effects. The improvement of the thermal field caused by the interfacial nanolayer is demonstrated. The resulting set of ordinary nonlinear differential equations is handled by using the Keller–Box technique. Comparable outcomes for base fluid (water) and nanoliquid are obtained and discussed. The impact of the magnetic parameter, Grashof number, Brinkman factor, and radiation components on nondimension velocity and temperature are analyzed and represented graphically. The magnetic parameter and the Brinkman number are found to be proportional to the temperature distribution.