Values Of Prandtl Number Research Articles

Study on the effect of flow velocity and thermal buoyancy on the dynamic behaviour of flow inside a two-hole chamber

This work aims to study the behaviour of the fluid inside a square chamber that has two openings at the top of vertical walls for the entry and exit of the fluid. Also, the chamber is arranged around two hot cylinders located vertically. The fact that the fluid is cold and the walls of the cylinders are hot, a vertical transfer of the fluid is shown due to thermal buoyancy force. The study was accomplished numerically. The pertinent parameters examined are as follows: the number of Reynolds (= 1-40) and the number of Richardson (= 0-1). The value of Prandtl number of the working fluid is (Pr = 1). The values of Nu number for the two cylinders are calculated and expressed in terms of the values of Re and Ri. The results showed that the effect of the fluid on the cylinders differs from the lower cylinder to the upper cylinder. Also, the presence of counter-flows in some cases creates hydrodynamic force in the opposite direction. For example, for Re = 40 increasing the Ri value from 0 to 1 increases Nu by an average of 3.84% for the upper obstacle and 81% for the lower one.

Spectral relaxation computation of electroconductive nanofluid convection flow from a moving surface with radiative flux and magnetic induction

Abstract A theoretical model is developed for steady magnetohydrodynamic viscous flow resulting from a moving semi-infinite flat plate in an electrically conducting nanofluid. Thermal radiation and magnetic induction effects are included in addition to thermal convective boundary conditions. Buongiorno’s two-component nanoscale model is deployed, which features Brownian motion and thermophoresis effects. The governing nonlinear boundary layer equations are converted to nonlinear ordinary differential equations by using suitable similarity transformations. The transformed system of differential equations is solved numerically, employing the spectral relaxation method (SRM) via the MATLAB R2018a software. SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation, and linearization for solving a nonlinear system of equations. Effects of embedded parameters such as sheet velocity parameter$\lambda$, magnetic field parameter$\beta$, Prandtl number$Pr$, magnetic Prandtl number$Prm$, thermal radiation parameter$Rd$, Lewis number$Le$, Brownian motion parameter$Nb$, and thermophoresis parameter$Nt$ on velocity, induced magnetic field, temperature, and nanoparticle concentration profiles are investigated. The skin-friction results, local Nusselt number, and Sherwood number are also discussed for various values of governing physical parameters. To show the convergence rate against iteration, residual error analysis has also been performed. The flow is strongly decelerated, and magnetic induction is suppressed with greater magnetic body force parameter, whereas temperature is elevated due to extra work expended as heat in dragging the magnetic nanofluid. Temperatures are also boosted with increment in nanoscale thermophoresis parameter and radiative parameter, whereas they are reduced with higher wall velocity, Brownian motion, and Prandtl numbers. Both hydrodynamic and magnetic boundary layer thicknesses are reduced with greater reciprocal values of the magnetic Prandtl number Prm. Nanoparticle (concentration) boundary layer thickness is boosted with higher values of thermophoresis and Prandtl number, whereas it is diminished with increasing wall velocity, nanoscale Brownian motion parameter, radiative parameter, and Lewis number. The simulations are relevant to electroconductive nanomaterial processing.

Darcy Forchheimer bioconvection flow of Casson nanofluid due to a rotating and stretching disk together with thermal radiation and entropy generation

Present work is pursued to examine the 3D bioconvection Casson nanofluid flow between two rotating and stretchable disks. The consequences of Darcy Forchheimer flow along with thermal radiation, magnetic field and heat source/sink are analyzed. Effects of thermophoresis and Brownian motion are also considered. Flow related partial differential equations are converted to the ordinary differential equations by using similarity transformations. Shooting technique is applied to solve the prevailing equations with the support of MATLAB Packages. Radial and tangential components of velocity for different values of Casson parameter, magnetic field parameter and porosity parameter are depicted through graphs. Temperature profile on varying the values of Prandtl number is also discussed. Moreover, thermal profile for increasing radiation parameter, thermophoresis parameter and Brownian movement parameter is analyzed. Nanoparticle's concentration effects on micro-organisms with growing Lewis number and Peclet number are studied graphically.

On doubly stratified bioconvective transport of Jeffrey nanofluid with gyrotactic motile microorganisms

Nanofluids have already proven great potential in the thermal amplification of several manufacturing industries and have been widely employed in energy technologies in recent times. Therefore, the current framework investigates the characteristics of the Jeffrey nanofluid flow with the influence of activation energy and motile microorganisms over a sheet is considered. The influence of the magnetic field is another important physical parameter in the flow analysis and has been regarded in this review. The remarkable properties of nanofluid are demonstrated by thermophoresis and Brownian motion characteristics. Thermophoresis has relevance in mass transport processes in many higher temperature gradient operating systems. An appropriate similarities transformation is utilized make convenient to partial differential equation into ordinary differential equations. The well-known shooting tactic is utilized to estimate numerical outcomes of obtained ordinary system of flow. The governing dimensionless equations are integrated subject to the aid of the bvp4c scheme in the built-in software of MATLAB to find out the solution. The procedure assumed employing MATLAB. The characteristics of physical parameters against the velocity of fluid, temperature, concentration, and motile microorganisms are elaborated through graphs and tables. The dynamic physical declaration of attained results reveals that buoyancy ratio parameter and bioconvection Rayleigh number plays a vibrant role in the declining flow of Jeffery nanofluid while contrasting nature is analyzed for mixed convection parameter. The increasing behavior of temperature is observed for larger variations of heat sink/source parameters and thermophoresis parameter while it shows conflicting nature for increasing values of Prandtl number. The concentration of nanoparticle is reduced with the advanced values of Prandtl number, Lewis number and Brownian motion, perceived from the results. The mounting valuation of the Peclet number and Bioconvection Lewis number caused a reduction in motile microorganism concentration. The envisaged hypotheses could be beneficial for modifications to extrusion systems, bio-mimetic systems, efficient energy generation, bio-molecules and improved production systems.

Non-similar forced convection analysis of Oldroyd-B fluid flow over an exponentially stretching surface

In the study of boundary layer regions, it is in practice to dimensionalize the governing system and grouping variables together into dimensionless quantities in order to curtail the total number of variables. In similar flow phenomenon the physical parameters do not vary along the streamwise direction. However in non-similar flows the physical quantities change in the streamwise direction. In non-similar flows we are forced to non-dimensionalize the governing equations through non-similarity transformations. The forced flow of Oldroyd-B fluid is initiated as a result of stretching of a surface at an exponential rate. Flows over stretching surfaces are important because of their applications in extrusion processes. The forthright purpose of this study is to consider the non-similar aspects of forced convection from flat heated surface subjected to external viscoelastic fluid flow, described by the freely growing boundary layers enclosed by a region that involves without velocity and temperature gradients. The governing system of nonlinear partial differential equations (PDE’s) is transformed into dimensionless form by proposing new non-similar transformations. The dimensionless partial differential system is solved by using local non-similarity via bvp4c. Thermal transport analysis is conducted for distinct values of dimensionless numbers. It is revealed that heat shifting process expanded by the increase in the numerical values of Prandtl number and relaxation time. The dimensionless convective heat transfer coefficient results revealed that it is declining by expanding relaxation time constant [Formula: see text] and a boost is observed by enlarging the Pr and retardation time constant [Formula: see text]. A comparison of Nusselt number is presented.

Effect of Non-linear Radiation on MHD Mixed Convection Flow of a Micropolar fluid Over an Unsteady Stretching Sheet

The current analysis explores the results of non-linear radiation on an unsteady stretching mixed Micropolar fluid. Issue modelling leads to a framework of PDE, reworked by transformations into non-linear ODEs. The Homotopy analysis methodology is applied to resolve the matter. The diagrams address the impact of the Magnetic parameter, unsteadiness parameter, Eckert number, Micropolar parameters, buoyancy parameters, Radiation parameter, Temperature ratio and Schmidt number on velocity, temperature, and concentration gradients. Amount of Nusselt number will increase in massive Prandtl number values, within the case of the high values of the unsteadiness parameter skin friction, wall couple stress and Sherwood decrease.

Nonsimilar boundary layer flow of Cross fluid induced by a heated stretched sheet

AbstractThis paper deals with the nonisothermal boundary layer flow of Cross fluid due to a stretching sheet. Unlike previous studies on boundary layer flow of Cross fluid, a nonsimilar formulation is adopted to transform the boundary layer equations into nondimensional form. The problem is characterized by three dimensionless parameters, namely, the Deborah number, the Prandtl number, and dimensionless distance along the sheet. The transformed equations are simulated by a numerical scheme with the help of MAPLE software. The velocity and temperature profiles inside the boundary layer are calculated and shown graphically. The skin friction coefficient and Nusselt number at various axial stations are also tabulated for several values of Deborah number and Prandtl number.

Computational optimization for the deposition of bioconvection thin Oldroyd-B nanofluid with entropy generation

The behavior of an Oldroyd-B nanoliquid film sprayed on a stretching cylinder is investigated. The system also contains gyrotactic microorganisms with heat and mass transfer flow. Similarity transformations are used to make the governing equations non-dimensional ordinary differential equations and subsequently are solved through an efficient and powerful analytic technique namely homotopy analysis method (HAM). The roles of all dimensionless profiles and spray rate have been investigated. Velocity decreases with the magnetic field strength and Oldroyd-B nanofluid parameter. Temperature is increased with increasing the Brownian motion parameter while it is decreased with the increasing values of Prandtl and Reynolds numbers. Nanoparticle’s concentration is enhanced with the higher values of Reynolds number and activation energy parameter. Gyrotactic microorganism density increases with bioconvection Rayleigh number while it decreases with Peclet number. The film size naturally increases with the spray rate in a nonlinear way. A close agreement is achieved by comparing the present results with the published results.

Non-isothermal flow of Sisko fluid in a stenotic tube induced via pulsatile pressure gradient and periodic body acceleration

A theoretical study for pulsatile unsteady blood flow and heat transfer effects via tapered stenotic artery is presented. This study is based upon a non-Newtonian Sisko-fluid model. The order of magnitude analysis is executed for the derivation of momentum and energy equations for the mild constriction model. The coordinate transformation is utilized to transform the computational domain. A finite difference scheme is utilized for the solution of modeled non-linear partial differential equations. The computed results are exhibited in form of graphs for velocity, wall shear stress (WSS), resistive impendence, flow rate, and temperature for appropriate ranges of important physical parameters governing the flow, including the Sisko fluid material parameter power-law index stenosis height the amplitude of body acceleration shape parameter Prandtl number and Brinkman number This investigation deduces that the flow rate and blood velocity rise with the escalation in the amplitude of body acceleration and shape parameter whereas both decrease by varying material parameter, power-law index, and stenosis height. The wall shear stress (WSS) rises with increasing the power-law index, material parameter, and stenosis height, whereas it decreases with the escalation in the amplitude of body acceleration and shape parameter. The resistive impedance increases with the increase of the size of stenosis and power-law index. The temperature field appears to dominate for smaller values of Prandtl number and larger values of Brinkman number.

Contribution of joule heating and viscous dissipation on three dimensional flow of Casson model comprising temperature dependent conductance utilizing shooting method

This report examines the flow of non-Newtonian fluids down a bilateral surface under the influence of a magneto-hydrodynamic effect that is applied in many fields seen in the applied sciences and has received the attention of researchers because of its vast usage. It is assumed that the movement of particles generated fluid due to the movement of walls in the light of horizontal and vertical directions. Thermal study is carried out by employing the contribution of Joule heating, viscous dissipation and radiation. The phenomena of variable thermal conductivity and mass diffusion coefficient are also used in the modeling of the law of conservation of energy transport and species. The contribution of Brownian thermocouple and diffusion is captured by using the Buongrino model. The impact of various impact parameters was sketched. The involvement of the various parameters is measured in terms of dimensional stress, heat rate and mass. The limitation case of the current investigation is compared with the case of the published publications and an excellent arrangement is noted. The rate of transfer of thermal energy at wall of hot surface has gained using large values of Prandtl number because of large values of Prandtl number results reduction in thermal boundary layer while ratio between momentum and thermal boundary layers called Prandtl number. Hence, reduction in thermal boundary layer (TBL) results maximum production in rate of transfer of thermal energy.

Direct numerical simulation of thermal channel flow for medium–high Prandtl numbers up to [formula omitted

A new set of DNS of a thermal channel flow have been conducted for friction Reynolds and Prandtl numbers up to 2000 and 10, respectively, reaching the Prandtl number of water, 7, for new Reynolds numbers, never simulated before. The Mixed Boundary Condition has been used as the thermal boundary condition. A new scaling of the thickness of the conductive sublayer is presented for medium–high Prandtl number values. The maximum of the intensity of the thermal field does not increase with the Reynolds number for the highest Prandtl numbers. This entails a good scaling near the wall of the viscous diffusion and the dissipation terms in the budgets of the temperature variance. The Nusselt number shows a power function behaviour with respect to the Prandtl number in a certain range of the friction Péclet number. Finally, the turbulent Prandtl number presents an increase near the wall for highest Prandtl numbers due to the reduction of the thermal eddy diffusivity. The statistics of all simulations can be downloaded from the web page of our group: http://personales.upv.es/serhocal/.

Scale of plume clustering in large-Prandtl-number convection.

Clustering of plumes in turbulent Rayleigh-Bénard convection has been numerically observed in low-Prandtl-number fluids. In this framework, turbulent plumes undergo a phase-separation process leading to large-scale clusters and circulations, sometimes called plume superstructures and reminiscent of solar granulation and supergranulation. On the other hand, the possible presence of large-scale plume aggregates has not been explored in the case of large values of the Prandtl number, Pr, relevant to geological settings such as convection in planetary interiors. Here we address this problem and numerically explore the behavior of plume ensembles in turbulent convection at very high Prandtl number values, including the case Pr→∞. The results indicate the presence of plume clustering, albeit at smaller scale, also for large Pr number fluids, suggesting interesting consequences for mantle convection processes.

Instability of natural convection in a vertical fluid layer with net horizontal throughflow

The implication of a uniform horizontal throughflow on the linear stability of buoyancy-driven convection in a vertical fluid layer is studied. The vertical boundaries of the fluid layer are rigid-permeable and holding at uniform but different temperatures. The instability to small-amplitude perturbations is tested by parameterizing the basic stationary flow through the Peclet number and the Prandtl number (representative of liquid mercury, air, water and oil). A modal analysis is performed, and the stability eigenvalue problem is solved numerically using the Chebyshev collocation method. The neutral stability curves are presented, and the critical values of the wave number, wave speed as well as the Grashof number are computed for different prescribed values of the governing parameters. The effect of horizontal throughflow on the stability of fluid flow is found to be dependent on the values of Prandtl number, and their intricacies have been discussed in detail. The results for the case of no throughflow are also highlighted as a particular case from the present study.

Lambert W function for effect of gas compression on premixed flames with ignition temperature approximation

The assumption that the gradient of temperature at the burned-side edge of a premixed flame front is zero has been usually imposed in investigating the adiabatic profile of flames for quasi-isobaric flow or in the zero-Mach-number limit. However, the non-monotonic behaviour of temperature is also observed for flames, or deflagrations, in the process of deflagration-to-detonation transition inside tubes or in the context of laser ablation or thermonuclear explosions in the universe. This non-adiabatic profile of a flame front is mainly due to the effect of gas compression, which is different from the conductive or volumetric heat loss. To clarify this point, we derive the non-zero condition of temperature gradient by considering the additional region, or the compression zone, behind a freely propagating flame front. The method of singular perturbations, or matched asymptotic expansions, is employed to calculate the inner and outer solutions of the compression zone of thickness with the squared Mach number assumed to be small, . The inner solutions are expressed by use of Lambert W function, and the pressure and dissipation terms in the heat-conduction equation play an important role to capture the non-adiabaticity of a flame front for non-zero values of Mach number. The strong ignition temperature approximation is imposed to obtain exact solutions in the outer region, composed of the reaction and preheat zones. The adiabatic value of ignition temperature is determined. The non-adiabatic feature is categorised into two cases. One case shows the non-monotonic behaviour of temperature. The other case presents the monotonic profile of temperature, but its maximum value is beyond the adiabatic value. The boundary, which determines whether the compressibility effect increases or decreases the flame temperature, is given with respect to the values of ignition temperature, heat release and Prandtl number.

Significance of Hall effect on heat and mass transport of titanium alloy‐water‐based nanofluid flow past a vertical surface with IMF effect

AbstractIn this mathematical presentation, we examined the significance of Hall current on MHD buoyancy‐driven boundary layer flow of a Ti6Al4V‐H2O based nanofluid past a vertical surface implanted in a uniform permeable region. The vertical surface is considered to be magnetized and induced magnetic field (IMF) impacts are also considered. The nondimensional flow model is solved with the assistance of the two‐term perturbation scheme. Various results are obtained by numerical computation for different significant parameters. These results are presented and analyzed in graphical and tabular form. In the boundary layer domain, the transpiration velocity across the surface tends to diminish the main flow, IMF along the main flow, fluid temperature, and concentration. It is remarkably noted that IMF along the main flow grows for incrementing values of volume fraction coefficient of nanofluid. In the magnetic boundary layer domain, the main flow and IMF along the main flow grow with Hall current. Furthermore, it is seen that for the progressing values of magnetic Prandtl number, the main flow reduces while normal flow and IMF along the main flow is induced in the boundary layer domain.

Impact of mixed convection on flow dynamics and heat transfer through an isotropic porous triangular array of periodic heated/cooled cylinders

AbstractThe effect of aiding and opposing buoyancy (−1 ≤ Ri ≤ 1) on flow and heat transfer across cylinders specifically arranged in an equilateral triangular array in a heat exchanger has not previously been studied. Periodic boundary condition in the transverse direction is imposed where porosity of the array ranges from 0.7 to 0.99. The influence of buoyancy and Prandtl number (1 and 50) on the flow structure and its effect on the overall heat transfer is thoroughly elucidated in the present work. The impact of aiding/opposing buoyancy on the thermal performance of the array is predominant at higher porosities. The average drag of the array of cylinders increases with an increase in the aiding buoyancy and decreases with an increase in opposing buoyancy with respect to forced convection. The porosity of the triangular array has an inverse relation with the average drag coefficient, barring few exceptions which are explained in detail in the present work. The heat exchange is assertively higher at opposing‐buoyancy cases for all values of porosity and Prandtl number. The present results are in agreement with the available experimental/numerical studies.

Global stability analysis of the natural convection between two horizontal concentric cylinders

In this investigation, the 2D flow between two horizontally positioned concentric cylinders (gravity perpendicular to the axis of the cylinders), where the inner cylinder is kept at constant temperature Ti higher than the outer border temperature To, is analyzed. Buoyancy forces initiate the movement of the fluid and the generated flow is studied in a fixed geometry for values of Prandtl numbers (Pr) between 0.01 and 1, and Rayleigh numbers (Ra) between 102 and 5·106. To solve the problem, a Chebyshev-Fourier spectral code is developed in polar coordinates (r,θ) respectively, and a complete map of steady-state solutions is obtained where regions with multiple solutions are identified. Later, a global stability study of the obtained stationary solutions is carried out, providing a transition curve to unstable areas as a function of the control parameters of the problem (Pr,Ra). Finally, to check the stability results, temporal evolution simulations are accomplished for several cases where dual solutions are presented, finding intermediate almost stationary solutions, and demonstrating that there exist typically single oscillating plume or double oscillating plume solutions (depending on the parameter space), where some of them have higher heat transfer coefficients, which may be interesting alternatives to improve heat exchange systems by means of passive control techniques.

Analytical study of MHD mixed convection flow for Maxwell nanofluid with variable thermal conductivity and Soret and Dufour effects

The key purpose of this article is to discuss the magnetohydrodynamic mixed convection flow for a Maxwell nanofluid past a stretching and permeable sheet. Variable thermal conductivity and Dufour and Soret effects are also taken into consideration. The modeled equations are transformed into a set of non-linear ordinary differential equations by employing similar transformable variables. The renovated system of equations is interpreted by Homotopy Analysis Method (HAM). The results determined by HAM have been compared with numerical solutions, and a good agreement has been noticed in both solutions. The main outcomes of this investigation are that velocity slows down with augmentation in Maxwell and magnetic parameters, temperature increases with radiation and thermophoretic parameters and reduces with growing values of Prandtl number and Brownian motion parameters, and furthermore, the motile micro-organism is a dropping function of Peclect and bio-convection Lewis numbers and bio-convection concentration difference parameters.

The Generalized Lévêque Equation and its application to flat tubes without and with passive inserts

Searching for an analogy concept between heat transfer and pressure drop is anything but new, nevertheless it is still the subject of researches as it enables the prediction of heat transfer from pressure drop data, which helps reducing experimental effort for heat transfer measurements. The Generalized Lévêque Equation (GLE) is a widely-used analogy concept, which allows the prediction of heat transfer from pressure drop data, if hydrodynamic boundary layer is developed or still developing. This analogy concept has been successfully applied to flow situations with practical relevance like chevron-type plate heat exchangers, packed beds and in tube bundles, where the boundary layers are forced to reform continuously. In this contribution, the GLE is applied to flat tube flow without and with passive inserts, investigating the impact of passive inserts, which force the boundary layers to reform continuously, on the application of the GLE.This paper presents results of an experimental investigation on pressure drop and heat transfer in flat tubes without and with passive inserts, covering a wide range of Prandtl number (8 < Pr < 60) and Reynolds number values (40 < Re < 3500). These parameter ranges and the passive inserts represent the typical conditions and design used for the liquid side of single-phase flat tube heat exchangers used in the automotive industry. 238 experimental data points for heat transfer coefficients are compared to heat transfer coefficients calculated from pressure drop data with the GLE.The results show that the GLE is not applicable to flat tubes without passive inserts, yet becomes applicable with passive inserts, which are forcing a re-formation of boundary layers in the whole range of investigated Reynolds and Prandtl numbers.

Darcy-Forchheimer flow of dusty tangent hyperbolic fluid over a stretching sheet with Cattaneo-Christov heat flux

The current investigation explores the impact of Darcy-Forchheimer flow and Cattaneo-Christov heat transfer of dusty tangent hyperbolic fluid over a stretching sheet. The problem of the model is represented by highly nonlinear partial differential equations which are deduced by using suitable approximations (boundary layer). The governing equations prevalent in the current problem escorted with boundary conditions are transformed into nonlinear coupled ordinary differential equations using proper similarity variables. These equations are further resolved numerically using Runge–Kutta-Fehlberg-45 method. The impacts of various parameters on velocity and temperature profiles have been depicted through graphs and the salient features have been discussed in detail. Furthermore, the numerical values of skin friction coefficient and local Nusselt number are also presented in the form of graphs and tables. It is observed that, the higher values of Prandtl number () reduce the temperature profile for both fluid and dust phases. In addition, the larger values of radiation parameter produce additional heat to operating fluid that shows associate enhancement within the temperature profile.