Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non‐Fourier heat flux model

Nonlinear, steady‐state, viscous flow, and heat transfer between two stretchable rotating disks spinning at dissimilar velocities are studied with a non‐Fourier heat flux model. A nondeformable porous medium is intercalated between the disks and the Darcy model is used to simulate matrix impedance. The conservation equations are formulated in a cylindrical coordinate system and via the von Karman transformations are rendered into a system of coupled, nonlinear ordinary differential equations. The emerging boundary value problem is controlled by number of dimensionless parameters, that is, Prandtl number, upper disk stretching, lower disk stretching, permeability, non‐Fourier thermal relaxation, and relative rotation rate parameters. A perturbation solution is developed and the impact of selected parameters on radial and tangential velocity components, temperature, pressure, lower disk radial, and tangential skin friction components and surface heat transfer rate are visualized graphically. Validation of solutions with the homotopy analysis method is included. Extensive interpretation of the results is presented which are relevant to rotating disk bioreactors in chemical engineering.     

Heat Transfer and Fluid Flow over a Single Disk in a Fluid Rotating as a Rigid Body

Laminar heat transfer problem is analyzed for a disk rotating with the angular speed ωin a co-rotating fluid (with the angular speed Ω). The fluid is swirled in accordance with a forced-vortex law, it rotates as a solid body at β= Ω/ω= const. Radial variation of the disk's surface temperature follows a power law. An exact numerical solution of the problem is obtained basing on the self-similar profiles of the local temperature of fluid, its static pressure and velocity components. Numerical computations were done at the Prandtl numbers Pr = 1(?)0.71. It is shown that with increasing βboth radial and tangential components of shear stresses decrease, and to zero value at β= 1. Nusselt number is practically constant at β= 0(?) 0.3 (and even has a point of a maximum in this region); Nu decrease noticeably for larger βvalues.     

Heat transfer analysis of CNTs-water nanofluid flow between nonparallel plates: Approximate solutions

Approximate solutions are given to investigate the problem of heat transfer and flow of a nanofluid between two nonparallel plates. Two different types of carbon nanotube (CNT) nanoparticles, namely functionalized single-walled carbon nanotubes and functionalized multi-walled carbon nanotubes are considered with water as the base fluid. The chemical functionalization is attributed to the attachment of the covalent bond of functional groups onto carbon nanotubes. Using the appropriate similarity variables, the model partial differential equations are transformed into ordinary differential equations and tackled analytically via the homotopy perturbation method. Comparison of the obtained results is carried out with those obtained by the previously published in the literature as well as the Runge–Kutta–Fehlberg method and an excellent agreement is achieved. The effects of various emerging parameters on nanofluid velocity, temperature, skin friction coefficient, and Nusselt number are illustrated graphically and comprehensively discussed.     

Simulation of heat transfer and hydrodynamics over a free rotating disk using an improved radial velocity profile

INTRODUCTIONIn many casess hydrodynamics and heat tlansfer inrotating-disk systems may be successfully simulatedusing integral methods. Restrictions imposed by theboundary layer approach are well-known. However,advanced integral methods employing justified modelassumptions in each specific case are quite competitive in comparison with modern CFD-paCkages. Commonly accepted advantages of the integral methodsare relative simple and high speed in calculations.Integral methods in the case o…     

MHD nonlinear natural convection flow of a micropolar nanofluid past a nonisothermal rotating disk

The aim of this analysis is to examine the steady, laminar boundary layer flow of a micropolar nanofluid owing to a rotating disk in the presence of a magnetic field and thermal and solutal nonlinear convection and nonisothermal parameters. The governing joined partial differential equations are converted into nonlinear ordinary differential equations by means of available transformations. The equations are calculated using the method bvp4c from Matlab software. The convergence test has been maintained; for the number of spots greater than the appropriate mesh number of points, the precision is not influenced, but the set time is boosted. Moreover, various quantities of the main parameters on skin friction coefficients, wall couple stress coefficients, Nusselt number, Sherwood number, velocities, temperature, and concentration of nanofluid are analyzed by means of tables and graphs. The results indicate that the presence of the nonisothermal parameter boosts the radial skin friction, temperature, and Sherwood number but causes decaying concentration distributions, the azimuthal skin friction coefficient, and Nusselt number that indicate the diffusion of momentum occurs more around the surface of the rotating disk.     

Three‐dimensional boundary layer flow over a rotating disk with power‐law stretching in a nanofluid containing gyrotactic microorganisms

The nanofluid model containing microorganisms over a rotating disk with power‐law stretching is constructed in this paper. The combined effects of nanoparticles and microorganisms in nanofluid are investigated by solving the governing equations numerically. The numerical solutions of the skin friction coefficient and local Nusselt number are in agreement with the corresponding previously published results. The quantities of physical interest are graphically presented and discussed in detail. It is found that the power‐law stretching index has produced profound influence on the flow as well as the heat and mass transfer.     

Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well-known scheme, namely the shooting method along with the Runge-Kutta-Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non-Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.     

Numerical analysis on the heat and mass transfer MHD flow characteristics of nanofluid on an inclined spinning disk with heat absorption and chemical reaction

This work examines the heat transfer properties of magnetohydrodynamic nanofluid flow. Through a similarity conversion, the leading structure of partial differential equations is changed to that of ordinary differential equations. A rigorous mathematical bvp4c methodology is used to generate numerical results. The purpose of this study is to characterize the different temperature, concentration, and velocity limitations on a nanofluid with a magnetic effect that is spinning. The findings for rotating nanofluid flow and heat transfer characteristics of nanoparticles are shown using graphs and tables. The influence of physical factors such as heat transfer rates and skin friction coefficients is studied. When the magnetic parameter M is raised, the velocity of the nanoliquid decreases. A rise in thermal radiation (Rd) causes the temperature graphs to grow substantially, although the concentration profiles exhibit the opposite tendency. The effect of the convective heat transfer factor Bi on temperature is shown to increase as Bi increases, but the concentration distribution decreases as Biot increases.     

Steady flow and heat transfer of the power-law fluid over a rotating disk

This paper deals with the steady flow and heat transfer of a viscous incompressible power-law fluid over a rotating infinite disk. Assumed the thermal conductivity follows the same function as the viscosity, the governing equations in the boundary layer are transformed into a set of ordinary differential equations by generalized Karman similarity transformation. The corresponding nonlinear two-point boundary value problem was solved by multi-shooting method. Numerical results indicated that the parameters of power-law index and Prandtl number have significant effects on velocity and temperature fields. The thickness of the boundary layer decays with power-law index. The peak of the radial velocity changes slightly with power- law index. The values near the boundary are affected dramatically by the thickness of the boundary layer. With the increasing of the Prandtl number the heat conducts more strongly.     

An Exact Solution for Heat Transfer of a Jet Co-Axially Impinging on a Rotating Disk and Its Comparisons with Stagnation Point Experiments

IntroductionJet impingement is a widely used high-efficiencytechnique fOr cooling rotating disks, which are end-wallsurfaces of gas turbine rotors, comPuter disk drives etc.Fluid f'low, heat trallsfer and geometric arrangement inthe case of a single round jet impinging co-axially in anorthogonal mode on a rotatng disk are characterized byFig. l.Many peculiarihes of fluid fIow and heat transfer ofreal impinging jets under comPlicated conditions(different system geometry, impinging flow proper…     

Effect of SWCNTs and MWCNTs Maxwell MHD nanofluid flow between two stretchable rotating disks under convective boundary conditions

The aim of the current analysis is to investigate heat and mass transfer characteristics of single and multi‐walled water‐based carbon nanotubes Maxwell nanofluid flow between continuously rotating stretchable disks under the sway of chemical reaction and radiation. Boundary conditions of the convective type of temperature are employed at both lower and upper rotating disks in the preparation. Similarity variables are employed to transform the governing partial differential equations into the nonlinear ordinary differential equations. The computational finite element method is applied to solve this nonlinear system of equations along with boundary conditions. The sway of different admissible parameters on the profiles of concentration, temperature, and velocity are inspected and revealed through graphs. Furthermore, the numerical solutions for rates of temperature, concentration, and rates of velocity are depicted in tabular form. It is revealed that temperature sketches deteriorate with augmented values of Deborah number at both upper and lower disks of single‐walled carbon nanotubes and multi‐walled carbon nanotubes with water‐based Maxwell nanofluids.     

Influence of an inclined stretching cylinder over MHD mixed convective nanofluid flow due to chemical reaction and viscous dissipation

This paper analyzed the steady two‐dimensional magnetohydrodynamic mixed convective viscous nanofluid and heat transfer toward an inclined stretching cylinder with chemical reaction and uniform magnetic field. The governing partial differential equation in a cylindrical form is reduced to a set of nonlinear ordinary differential equations by using appropriate similarity transformation and solved numerically by spectral quasilinearization methods (SQLMs). A new approach of this method is employed to derive numerical expressions for velocity, temperature, and concentration profile. The convergence and accuracy of our numerical scheme are observed. The SQLM is employed to find out the convergent series solution. There is an increase in the temperature profiles due to the increase in the thermophoresis parameter. The increase in effective Eckert number results in the increase of the temperature profile.     

A study on the characteristics of carbon nanofluid for heat transfer enhancement of heat pipe

For the purposes of enhancing the heat-transfer utility of the heat pipe in a solar collector, the present work attempted to improve nanoparticle dispersion stability by means of a chemical reformation process wherein nanofluid is formulated with hydroxyl radicals combined with oxidized multi-walled CNTs (MWCNTs). Experiments entailing measurements of thermal conductivity and viscosity in distilled water as functions of temperature were carried out to determine the best nanoparticle mixture ratio. The thermal conductivity increased with the increasing volumetric ratio of the oxidized MWCNTs and with increasing temperature. The viscosity also increased, slowly, until its concentration reached 0.01%, and then steeply increased, and was lower at high temperature.     

On MHD and slip flow over a rotating porous disk with variable properties

The steady laminar magnetohydrodynamics (MHD) flow of a viscous Newtonian and electrically conducting fluid over a rotating disk with slip boundary condition is investigated taken into account the variable fluid properties (density, (ρ), viscosity, (μ) and thermal conductivity, (κ)). These fluid properties are taken to be dependent on temperature. The governing equations, which are partial and coupled, are transformed to ordinary ones by utilizing the similarity variables introduced by von Karman and the resulting equation system is solved numerically by using a shooting method. The resulting velocity and temperature distributions are shown graphically for different value of parameters entering into the problem. The numerical values of the radial and tangential skin-friction coefficients and the rate of heat transfer coefficient are shown in tabular form.     

Impact of activation energy and gyrotactic microorganisms on flow of Casson hybrid nanofluid over a rotating moving disk

Many models of various non-Newtonian fluid flows for different geometries are available for analyzing the mass and heat transfer. Nevertheless, for researchers, it is challenging to choose the most suitable model for a specific geometry. Here, we have adopted a modified Buongiorno model to explore the impact of activation energy on the Casson hybrid nanofluid flow over an upward/downward-moving rotating disk filled with the gyrotactic microorganisms. Moreover, the external magnetic field can establish the magnetic effect, which normalizes the features of heat, mass transfer, and fluid flow. Here, we used silver and copper as nanoparticles suspended in human blood as the carrier fluid. The modeled partial differential equations are converted to ordinary differential equations by opting suitable similarity variables. The numerical solutions of these reduced equations are attained by means of Runge–Kutta–Fehlberg fourth-fifth-order method by adopting a shooting scheme. An investigation of the attained outcomes reveals that the flow field is affected appreciably by the activation energy, bioconvection, and magnetic effect. Peclet and concentration difference numbers diminish the microorganism's profile. A rise in values of the Brownian motion parameter leads to an increase in the rate of heat transfer.     

Numerical study of mixed convective heat transfer in a lid‐driven enclosure with rotating cylinders

A numerical simulation is performed to characterize the mixed convective transport in a three‐dimensional square lid‐driven enclosure with two rotating cylinders. The top wall is moving in the positive x‐direction, and the bottom wall is at a higher fixed temperature compared with all other isothermal walls. Both cylinders are rotating in its own plane about their centroidal axis. On the basis of rotation of both cylinders in clockwise or counter‐clockwise directions, four rotational models are studied. Various controlling parameters considered in the present study are Grashof number (10 ³ < Gr < 10 ⁵), rotating speed of the cylinder (5 < ω < 50), and the Reynolds number based on top wall movement is fixed to 100. The effect of cylinder rotation on the heat transfer of bottom wall is reported with the help of streamlines, contour plots of z‐component of vorticity, averaged and local Nusselt number, ratios of secondary flow and drag coefficient. It is observed that the heat transfer at the bottom wall is substantially dependent on the rotational model and rotational speed of the cylinder.     

Mathematical modeling and study of MHD flow of Williamson nanofluid over a nonlinear stretching plate with activation energy

This study investigates the Williamson nanofluid flow through a nonlinear stretching plate. It aims to analze the global influence of Williamson parameter (λ) rather than local, which is researched for a linear stretching case in the literature. In addition, the features of activation energy are also taken into account in the current review. The developed model with the consequent similarity transformation has still not been perceived. The transformed partial differential equations are solved analytically. The consequences of embedded parameters on the velocity, temperature, and concentration profiles are displayed through figures. Also, the consequences of embedded parameters on skin friction, heat transfer, and mass transfer are demonstrated through tables.     

高位进气转静系旋转盘流动与换热的数值模拟

采用扩展混合长度湍流模型和S IM PLE算法,用共轭数值计算的方法模拟航空发动机涡轮盘冷却系统的高位进气、径向出流转静系旋转盘腔模型的流场和温度场,分析了其盘面平均努塞尔数N uav随旋转雷诺数R eω和流量系数Cw的变化。结果表明,随着转速和冷气流量的提高换热得以增强,但在本次计算范围内提高转速对换热的增强幅度小于提高冷气流量对换热的增强幅度。