Narrow Results

The impact of nanoliquid in the evolution of various industries and electronic devices is very remarkable. Motivated by these uses, this exploration describes the second law analysis in the Maxwell two-phase nanoliquid subject to the Lorentz force due to axisymmetric heated convective rotating flow with microorganisms and slip conditions. Thermal radiation, thermal variable conductivity, and chemical reaction are examined in the heat and concentration equation. The mass equation has been accounted for through the chemical reaction. Additionally, the physical properties of the entropy rate are considered. The constitution equations have been transformed into dimensionless form through the suitable transformation. The reduced system of equations has been solved analytically by the homotopy analysis method (HAM). The physical variables on Bejan number, entropy minimization, microorganism, concentration, velocity, and temperature distributions have been presented in graphical form. Computational results of moment coefficient, heat, mass, and motile density versus other factors are examined. The Maxwell fluid and slip variable display a reduction in radial velocity. An increase in the stretching parameter. The thermal layer is enlarged against the larger values of variable thermal conductivity, thermal radiation, and Biot number. Entropy generation and Bejan number are escalated due to the augment in the temperature difference variable, Brikamann number, and magnetic field.

The application of fluid flow through a rotating disk in a solar thermal power plant can help in increasing energy production, reduce costs, and improve the overall efficiency of the system. The concentrated solar power (CSP) technology can help in assisting solar energy for sustainable power generation. This work explores the heat transfer assessment of magnetized tangent hyperbolic fluid flowing over a porous rotating disk under the effects of thermal radiation, convective heating, Ohmic heating and viscous dissipation. The solution of transformed ODEs is obtained by the Legendre wavelet collocation method (LWCM). To visualize the impact of acting variables, the results are portrayed by graphs and tables. From the outcomes, it is noted that the rate of heat transfer is enhanced up to 84.79% with an increase in radiation parameter. Moreover, the radial velocity enhances as the rotation parameter is accelerated. The dual behavior in temperature outlines is obtained due to escalated values of the porosity parameter. For the validation of the present results, a tabular comparison is shown with earlier work.

Magnetohydrodynamic flow of nanofluids and heat transfer between two horizontal plates in a rotating system have been examined numerically. In order to do this, the group method of data handling (GMDH)-type neural networks is used to calculate Nusselt number formulation. Results indicate that GMDH-type NN in comparison with fourth-order Runge–Kutta integration scheme provides an effective means of efficiently recognizing the patterns in data and accurately predicting a performance. Single-phase model is used in this study. Similar solution is used in order to obtain ordinary differential equation. The effects of nanoparticle volume fraction, magnetic parameter, wall injection/suction parameter and Reynolds number on Nusselt number are studied by sensitivity analyses. The results show that Nusselt number is an increasing function of Reynolds number and volume fraction of nanoparticles but it is a decreasing function of magnetic parameter. Also, it can be found that wall injection/suction parameter has no significant effect on rate of heat transfer.

This communication is to analyze the Marangoni convection MHD flow of nanofluid. Marangoni convection is very useful physical phenomena in presence of microgravity conditions which is generated by gradient of surface tension at interface. We have also studied the swimming of migratory gyrotactic microorganisms in nanofluid. Flow is due to rotation of disk. Heat and mass transfer equations are examined in detail in the presence of heat source sink and Joule heating. Nonlinear mixed convection effect is inserted in momentum equation. Appropriate transformations are applied to find system of equation. HAM technique is used for convergence of equations. Radial and axial velocities, concentration, temperature, motile microorganism profile, Nusselt number and Sherwood number are sketched against important parameters. Marangoni ratio parameter and Marangoni number are increasing functions of axial and radial velocities. Temperature rises for Marangoni number and heat source sink parameter. Activation energy and chemical reaction rate parameter have opposite impact on concentration profile. Motile density profile decays via Peclet number and Schmidt number. Magnitude of Nusselt number enhances via Marangoni ratio parameter.

This study describes the Casson (a non-Newtonian fluid) nanofluid bioconvection flow across a spinning disc in the presence of gyrotactic microorganisms, many slips and thermal radiation. Also, the flow is considered as a reversible flow. The esterification process is taken into account. Using the proper variables, a system of extremely nonlinear PDEs is converted into a system of ODEs. To arrive to the solution of such equations, a numerical approach is used. Using the bvp4c approach, nonlinear flow equations can be numerically solved. Investigated are the effects of different numbers on the thermal field, volumetric concentration of nanoparticles and microbiological field. The key characteristics of the parameters in relation to the profiles of the velocity, temperature, concentration and microorganisms are graphically assessed with appropriate physical effects. A graphical explanation is provided for the wall shear stress, local Nusselt number, local Sherwood number and local motile density number. Rate of motile density number shows a prominent difference between reversible and irreversible flows for Brownian motion and Peclet number. The results of the theoretical simulations have dynamic applications in the fields of biotechnology and thermal engineering.

In this paper, the thermal analysis is performed on the three-dimensional flow of viscous nanofluid over a rotating disk. The disk rotation is assumed as of the form $(v\sim r^m)$ where $(m\ge 1)$, thus, there are different azimuthal velocities of the disk at different radii, and it increases with the increase in $m$. Also, the effect of nanoparticles on the thermal conductivity of fluid is investigated by thermophoresis and Brownian motion features. For the governing problem, suitable similarity transformations are employed that convert the produced partial differential equations to ordinary differential equations. The flow field and energy transport are presented graphically and discussed in detail for the torsional exponent $m$, $N_t$ and $N_b$, respectively. It is noted that the temperature and concentration profile rise for the thermophoresis parameter while the opposite trend showed for Brownian motion. Moreover, the power-law index parameter $m$ declines the flow field temperature and concentration profiles.

Some of the fundamental properties of the nanofluids affect not only the transport phenomenon but also enhance the the heat transfer characteristics. The advancement in Rotatory machine technology can also be attributed mainly to a lot of research work that had been done on rotating disk flows with addition of nanoparticles in the base fluid. Taking cue of these developments, we examined the nanofluid (Cu+H₂O) flow over a rotating disk moving upward/ downward with viscous dissipation by reducing the governing Navier–Stokes equations into ordinary differential equations using appropriate transformations and then numerically evaluated them by the BVP Mid-rich scheme in Maple software. The study of velocity and thermal profiles is carried out and examined graphically. The results show that the upward movement of the disk escalates the radial and azimuthal velocity profiles along with the thermal gradient. In contrast, the addition of nanoparticles decreases the heat transfer rate at a constant disk movement.

In this research work, we investigate an unsteady flow over a rotating disk. We assign symbols to the selected dependent and independent quantities. Then all physical systems are modeled to mathematical form by applying physical laws for an ionized liquid flow over a rotating disk with nanoparticles from the set of Poisson Nernst–Planck model, Energy equation and Navier–Stokes equations. The set of partial differential equations along with the boundary conditions are transformed to a set of coupled ordinary differential equations for an electro-viscous flow of nanofluid over a rotating disk by using similarity transformations. The unknown physical quantities are investigated through Parametric Continuation Method (PCM). For physical purpose, physical quantities like flow behavior thermal properties, thermal variation, the distribution of ions in the fluid region, skin friction, are analyzed through graphical and tabulated results. As exact solutions are not possible for nonlinear ordinary differential equations (ODEs) system, therefore, such quantities are subjected to numerical calculation following Parametric Continuation Method (PCM) and validated the result through BVP4c package in Matlab.

The model presented in this paper deals with the investigation of the unsteady laminar flow past a stretchable disk. The nanofluids Al₂O₃/H₂O and Cu/H₂O are considered for the analysis where the thermal characteristics and flow behavior of these nanofluids are compared. In addition, the system is subjected to the suction force that has significant impacts on velocity of the nanofluid flow. Further, the nanoparticle solid volume fraction is another important parameter that is discussed which has a prominent role on both profiles of the nanofluid. Furthermore, the investigated mathematical model is framed using PDEs that are transformed to ODEs using suitable transformations. The system of equations obtained in this regard is solved by employing the RKF-45 numerical method where the results are obtained in the form of graphs. Various nanofluids flow parameters arise in the study and the impact of all these parameters has been analyzed and interpreted. Some of the major outcomes are that the higher values of nanoparticle solid volume fraction enhance the temperature while it decreases velocity of the flow. The comparison of flow of the two nanofluids concluded that alumina–water nanofluid has a better velocity while the copper–water nanofluid has a better thermal conductivity.

The hydromagnetic flow of magnetite–water nanofluid due to a rotating stretchable disk has been numerically assessed. The nanofluid flow has been modeled utilizing the adapted Buongiorno model that considers the volume fraction-dependent effective nanofluid properties and the major slip mechanisms. In addition, experimentally gleaned functions of effective dynamic viscosity and effective thermal conductivity are deployed. The modeled equations are transformed into a first-order ODEs scheme employing Von Kármán’s similarity conversions and then resolved via the Runge–Kutta algorithm through the shooting technique. The impact of pertinent terms over the physical quantities, nanoliquid temperature and nanoliquid concentration is explained with the support of graphs. Results show that rising volume fraction of magnetite nanoparticles (NPs) and magnetic field term enhance the drag force. Mass transport rate is demoted with augmenting values of magnetic field parameter whereas is promoted with increase in Schmidt number. Further, it is detected that the changes in stretching strength parameter are directly proportional to Nusselt number and inversely proportional to the thermal field. The findings of this numerical analysis have applications in spin coating, rotating disk reactors, storage devices for computers, food processing, and rotating heat exchangers.

The present investigation computes the heat transport phenomenon of the magnetohydrodynamic (MHD) flow of CuO-Ag/H₂O hybrid nanofluid over a spinning disc. The authors are confident that there is very less analysis covering the fluid flow containing silver and copper oxide nanoparticles over a rotating disk. Therefore, the authors are interested to consider the water-based nanoliquid flow over a spinning disk. Furthermore, the velocity slip and thermal convective conditions are taken into consideration. The formulation of the problem is made in the form of PDEs and is then converted into the nonlinear ODEs by employing suitable similarity transformations. The homotopic analysis approach is applied for the semi-analytical solution of these resulting equations. The convergence of homotopic approach has also revealed with the help of figure. The performance of the hybrid nanofluid flow velocities and temperature has been shown in a graphical form against distinct flow parameters. Also, the numerical results of skin friction coefficient and Nusselt number have been calculated in a tabular form. The outcomes of the current problem show that the increase in the skin friction of the water-based copper oxide nanofluid is greater than the water-based silver nanofluid at 4% of the nanoparticle volume fraction. Also, the skin friction of the hybrid nanofluid is increased by 8% compared to the silver nanofluid at 4% of the nanoparticle volume fraction. Furthermore, the heat transfer rate of the water-based copper oxide nanofluid is greater than the water-based silver nanofluid at 4% of the nanoparticle volume fraction. Also, the heat transfer rate of the hybrid nanofluid is 52% greater than that of silver nanofluid at 4% of the nanoparticle volume fraction. It is found that the Nusselt number of the hybrid nanofluid is highly affected by the embedded parameters as compared to nanofluids.

Reiner–Rivlin nanofluid flow due to rotating disk has significance in manufacturing of computer disks, pumping of liquid metals, spin coating, centrifugal machinery, turbo-machinery, crystal growth and rotational viscometer. In light of such real and relevant industrial applications, this study deals with the numerical investigation of unsteady rotationally symmetric flow of Reiner–Rivlin nanofluid over a stretchable rotating disk. The purpose of this investigation is to explore heat transfer characteristics of Reiner–Rivlin nanofluid subject to radial stretched surface implementable in several thermal systems. For facilitation of heat transport in complex thermal systems, mathematical models, such as Cattaneo–Christov, Buongiorno and nonlinear thermal radiation models, are assumed to be introduced. Runge–Kutta–Fehlberg technique along with shooting method is used for numerical computation of the transformed equations. It is captivating that radial and circumferential velocities decelerate with rise in Reiner–Rivlin and stretching strength parameters, respectively. Amplified thermal relaxation and Reiner–Rivlin parameters led to diminution of wall temperature gradient. Nanoparticle concentration profiles exhibit opposite behavior in response to escalation of activation energy and reaction rate parameters.

Owing to the growing interest of bioconvection flow of nanomaterials, many investigations on this topic have been performed, especially in this decade. The bioconvection flow of nanofluid includes some novel significance in era of biotechnology and bio-engineering like bio-fuels, microbial enhanced oil recovery, enzymes, pharmaceutical applications, petroleum engineering, etc. The current analysis aims to explore the various thermal properties of Sutterby nanofluid over rotating and stretchable disks with external consequences of variable thermal conductivity, heat absorption/generation consequences, activation energy and thermal radiation. The considered flow problem is changed into dimensionless form with convenient variables. The numerical structure for the obtained non-dimensional equations is numerically accessed with built-in shooting technique. The consequences of various physical parameters are observed for enhancement of velocity, temperature, concentration and motile microorganism. It is noted that both axial and tangential velocity components decrease with Reynolds number and buoyancy ratio parameter. The nanofluid concentration improves with activation energy and concentration Biot number. Moreover, an improved microorganisms profile is noticed with microorganism Biot number and bioconvection Rayleigh number.

This study investigates the convective heat transfer characteristics in the vicinity of a stagnation point for the flow of Maxwell nanofluid over a porous rotating disk. The analysis takes into account the complex inert-active effects arising from nonlinear thermal radiation, activation energy, and the presence of a Darcy–Forchheimer medium. Through numerical simulations, the enhancement of heat transfer due to the addition of nanoparticles is explored, considering their impact on heat transport. The rotational and porous characteristics of the disk, coupled with nonlinear thermal radiation and activation energy effects, are crucial factors in shaping the overall heat transfer behavior. The study aims to provide valuable insights into the complicated interactions of these phenomena, contributing to the understanding of advanced heat transfer processes and their potential applications in various engineering systems. Using suitable variables to convert the system of leading equations to dimensionless form has then been evaluated by employing the bvp4c approach. It has been revealed that Radial flow has retarded with an upsurge in Deborah number, inertial factor, and porous factor while has upsurge with growth in rotational factor. Angular velocity has declined with higher values of Deborah number, and porous factor and has upsurged with escalation in inertial and rotational factors. Azimuthal flow has weakened with an upsurge in porous factor and has augmented with growth in Deborah number, inertial factor, and rotational factor. Thermal profiles have augmented with an upsurge in rotational, porous, inertial, thermophoresis, Brownian, and radiation factors, and Deborah number has declined with growth in the Prandtl number. Concentration distribution has declined with an upsurge in Schmidt number, Brownian motion factor, rotation factor, and porous factor, while has grown with the escalation in chemically reactive, thermophoresis, inertial factors, and Deborah number.

Modern micro- and nanotechnologies have achieved tremendous advancements in the development of nano-electronic devices in modern eras. These technologies are increasingly using advanced fluid media to improve performance. One of the emerging trends is the concurrent utilization of nanofluids and biological micro-organisms. In this study, we are inspired by bio-nanofluid rotating disk microorganisms used in medical engineering. This analysis examines the behavior of the Sutterby nanoliquid when subjected to convective heating conditions on a rotating stretched disk, taking into account the presence of mixed convective flow. Nanofluids, which consist of transparent liquids containing evenly dispersed tiny particles, show potential for improving heat transmission in a wide range of applications. The investigation, utilizing the Sutterby model, which represents a non-Newtonian fluid, covers a range of phenomena including mixed convective flow, convective heating, chemical reaction, and bioconvection. The controlling nonlinear differential system is addressed using suitable similarity transformations. The computer program MATLAB uses the Keller box approach to solve transformed ordinary differential equations (ODEs). Analyzed data have been acquired for important physical characteristics. The effects of these parameters are elucidated and analyzed quantitatively and visually across various profiles. Increasing the magnetic and material parameters leads to a decrease in axial, radial, and tangential speeds. Variations in the Biot number, thermophoresis, and thermal radiation directly affect the temperature increase in the fluid. The study’s findings could be used in oceanography, melting, moving organic fluids, and the process of cooling.

During the dissolution of stainless steel in a highly concentrated iron(III) chloride (3.5 M) solution, patterns in the micrometer range can be observed on the surface of the rotating disk. These patterns are formed by convection vortices in the direction of hydrodynamic flow. At fast rotational speeds (2000–6000 rpm), the etched patterns are spiral in shape. By digitizing the observed patterns, the mathematical equation for the spirals can be determined and a description obtained for their invariant logarithmic shape, with an aspect ratio of for the radial and tangential velocity. A comparison with classical hydrodynamic equations for the rotating disk electrode and the analysis of previous investigations of patterns formed on slowly rotating disk electrodes provides an explanation for chemically induced invariant hydrodynamic pattern formation.

Forced vibration of a rotating disk subjected to a stationary transverse load is studied in this paper. Time and frequency responses are obtained and effects of the rotating speed on the natural frequencies are evaluated. Finite element method (FEM) is employed as the solution technique and natural frequencies are obtained for different speeds. Forced vibration is then considered and disk responses are determined using the Galerkin method. The solution is determined in two different coordinate systems. In the first one, the disk is assumed to be rotating in an inertial coordinate system, while in the second coordinate system, a rotating peripheral force is applied on a stationary disk. The objective here in this paper is to compare the two modeling scenarios and is to find limiting range of the rotational speed for employing the stationary coordinate system.

This paper is concerned with the axisymmetric free vibration analysis of a rotating annular plate with variable thickness by using the Ritz method. The rotating plate has a constant angular speed and subjected to a tensile centrifugal body force. The annular plate is fixed at the inner edge and free at the outer edge. Exact stresses, strains, and radial displacement of the rotating annular plate are obtained via plane elasticity. Presented herein are the natural frequencies and modes shapes for the rotating, nonuniform annular plate with various angular speeds and different ratios of the inner radius to the outer radius.

The free vibration and buckling of a rotating annular plate with constant angular speed free at the inner edge and fixed at the outer edge subjected to a compressive centrifugal body force are analyzed using the Ritz method. Exact stress components and radial displacement of the rotating annular plate are obtained via the plane elasticity. Convergence studies in the frequencies and the critical buckling angular speed are made up to four significant figures. The natural frequencies and the corresponding mode shapes and the critical buckling angular speeds are presented for the rotating annular plates with various angular speeds and ratios of the inner radius to the outer radius.

This paper presents elastic solutions of a disk made of functionally graded material (FGM) with variable thickness subjected to rotating load. The material properties are represented by combination of two sigmoid FGM (S-FGM) namely aluminum–ceramic–aluminum and the disk's different thickness profiles are assumed to be represented by power law distributions. Hollow disks are considered and the solutions for the displacements and stresses are given under appropriate boundary conditions. The effects of the material grading index n and the geometry of the disk on the displacements and stresses are investigated. The results are compared with the known results in the literature on metal–ceramic–metal FGMs. Also the solutions are compared S-FGM versus FGM and non FGM and variable thickness versus uniform thickness. It is found that a sigmoid functionally graded disk with concave thickness profile has smaller displacements and stresses compared with concave or linear thickness profile. It is also observed that an S-FGM rotating functionally graded disk with metal–ceramic–metal combination can be more efficient than the one with ceramic–metal or metal–ceramic.