Range Of Prandtl Numbers Research Articles

Effects of moving wall on the flow of micropolar fluid inside a right angle triangular cavity

PurposeThe main purpose of this study is to examine the effects of moving wall on the mixed convection flow and heat transfer in a right-angle triangular cavity filled with a micropolar fluid.Design/methodology/approachIt is assumed that the bottom wall is uniformly heated and the right inclined wall is cold, whereas the vertical wall is adiabatic and moving with upward/downward velocity v0/−v0, respectively. The micropolar fluid is considered to satisfy the Boussinesq approximation. The governing equations and boundary conditions are solved using the Galerkin finite element method. The Penalty method is used to eliminate the pressure term from the momentum equations. To accomplish the consistent solution, the value of the penalty parameter is taken 107. The simulations are performed for a wide range of Richardson number, micropolar parameter, Prandtl number and Reynolds number.FindingsThe results are presented in the form of streamlines, isotherms and variations of average Nusselt number and fluid flow rate depending on the Richardson number, Prandtl number, micropolar parameter and direction of the moving wall. The flow field and temperature distribution in the cavity are affected by these parameters. An average Nusselt number into the cavity in both cases increase with increasing Prandtl and Richardson numbers and decreases with increasing micropolar parameter, and it has a maximum value when the lid is moving in the downward direction for all the physical parameters.Research limitations/implicationsThe present investigation is conducted for the steady, two-dimensional mixed convective flow in a right-angle triangular cavity filled with micropolar fluid. An extension of the present study with the effects of cavity inclination, square cavity, rectangular, trapezoidal and wavy cavity will be the interest of future work.Originality/valueThis work studies the effects of moving wall, micropolar parameter, Richardson number, Prandtl number and Reynolds number parameter in a right-angle triangular cavity filled with a micropolar fluid on the fluid flow and heat transfer. This study might be useful to flows of biological fluids in thin vessels, polymeric suspensions, liquid crystals, slurries, colloidal suspensions, exotic lubricants, solar engineering for construction of triangular solar collector, construction of thermal insulation structure and geophysical fluid mechanics, etc.

Linear stability of mixed convection in a differentially heated vertical channel filled with high permeable porous-medium

Linear stability analysis is used to analyze the stability of parallel flow induced by an external pressure gradient and buoyancy force in a differentially heated vertical channel filled with a fluid-saturated high permeable porous medium. The non-Darcy model which gives rise to the volume averaged Navier-Stokes (VANS) equation is used except for some comparative study where Darcy model is also used. The investigation is made for a wide range of Prandtl numbers (Pr) that includes mercury, air, water and heavy oils. The spectral method has been adopted to solve the governing equations of the problem. In the entire considered range of Reynolds number (Re) the linear stability results show that the type of instability for mercury is thermal-shear (i.e., the instability is hydrodynamic in origin, resulting from an unstable velocity distribution, and obtains most of its kinetic energy (KE) through shear source), for water as well as heavy oil it is thermal-buoyant (i.e., most of the KE for this instability is obtained through work done by fluctuating buoyant force), whereas for air it is interactive (i.e., KE for this instability is obtained from both shear as well as buoyant sources). When Re is fixed at 1000, the appearance of point of inflection in the basic flow velocity for a fluid with Pr less than 30 acts as a necessary condition for instability for all considered values of Darcy number. Furthermore, the form drag stabilizes the fluid flow with Pr≥7, however, it acts other way up to a threshold value for fluid flow with Pr<1. Finally, scale analysis reveals that for thermal-shear or interactive instability the minimum critical ΔT for parallel mixed convection flow is less than the same for parallel natural convective flow and it is other way for thermal-buoyant instability. As an example of thermal-buoyant instability, when the channel is filled with a porous medium having permeability 2.5 ×10−6m2 and half-width 5 cm, the mixed convective flow of water remains stable up to a temperature difference of 13.3oC between the walls, whereas the natural convective flow of water remains stable up to a temperature difference of 8.58oC between the walls.

Prandtl number dependence of convective fluids in tall laterally heated slots

The influence of the Prandtl number on the stable stationary and periodic flows of the fluids contained in laterally heated slots under realistic conditions, namely non-slip boundaries, insulated top and bottom horizontal limits and perfectly conducting lateral sides, is analyzed by using continuation methods. The branches of solutions are computed by decreasing the Prandtl number, for four Rayleigh numbers. The dynamical behavior depends strongly on both parameters. For a Rayleigh number, Ra = 103, the steady flow remains stable in the wide range of Prandtl numbers computed. At Ra = 104 and O(105) the first bifurcations are of Hopf type giving rise to a type of oscillations that affects the bulk of the fluid, alternating from a general circulation to multi-vortex solutions, or the boundary layer, respectively. However, it is found that, in any case, the location of the shear determines the type of the oscillations. Moreover, at Ra = 104 the critical multipliers at the secondary bifurcations on the main branch of POs are real, giving rise to different kinds of very bounded stable periodic states of different symmetries and periods. At Ra of order 105 the instability of the periodic orbits gives rise directly to quasi-periodic flows.

The influence of low Prandtl numbers on the turbulent mixed convection in an horizontal channel flow: DNS and assessment of RANS turbulence models

In this paper, the turbulent mixed convection in a channel flow with differentially heated walls is considered for a fixed Richardson number (Rib=0.5) and three different Prandtl numbers (Pr=1,0.1and0.01). Numerical simulations are conducted assuming constant fluid properties and the effect of the buoyancy is taken into account by means of the Boussinesq approximation. Direct Numerical Simulations (DNS) are performed first and the effect of the buoyancy on the first and second order statistics of the fluid and thermal fields is highlighted. Furthermore, it is found that in mixed convection the Prandtl number has a much larger effect on the results than in the case of forced convection. The obtained DNS results are then used as a validation database for two different RANS turbulent heat flux models, i.e. the classical Reynolds analogy and a recently proposed three-equation algebraic heat flux models called AHFM-NRG+. It is observed that, as expected, the Reynolds analogy fails to predict the thermal field even for unitary Prandtl numbers fluids. On the other hand, it is shown that the AHFM-NRG+ is in a reasonable agreement with the reference DNS over the entire range of Prandtl numbers considered in the study.

Boundary Layer Flow of Magnetic Nanoliquids due to a Radially Rotating Stretchable Plate

The effects of stretchable rotating flat surface on the time dependent 3-dimensional boundary layer flow of magnetic nanoliquid in the presence of thermal radiation have been investigated. The modelled set of nonlinear coupled ODEs governing the flow is solved numerically by finite difference scheme and shooting technique. For understanding the effects of geothermal viscosity, stretching parameter and thermal radiation on the flow and temperature fields, a range of Prandtl number is taken into account. The heat transfer rate and skin frictions due to the above physical parameters are also computed. A significant enhancement in the resistance of the fluid flow is noticed due to the viscosity variations and the stretching of the plate. Further, the heat dissipation becomes faster with the enhancement of the thermal radiation and the Prandtl number.

Experimental investigation of natural convection heat transfer characteristics in MWCNT-thermal oil nanofluid

The carbon nanotubes are considered as one of the highest thermal conductive material which is having a variety of heat transfer applications. The suitability of carbon nanotubes in convective heat transfer is examined using multi-wall carbon nanotubes (MWCNT)-thermal oil-based nanofluids. Stable nanofluids are prepared in the concentration range of 0–1 mass% and Prandtl number range of 415 ≤ Pr ≤ 600 using ultrasonication. The natural convection heat transfer behavior is studied experimentally in a vertical rectangular enclosure with aspect ratio 4. The heat transfer experiments are conducted at varying heat flux in the range of 1594–3150 W m−2. The heat transfer coefficient, Nusselt number and Rayleigh number are estimated for MWCNT-thermal oil-based nanofluids and are compared with pure thermal oil. A significant deterioration in heat transfer coefficient is observed at higher concentrations of nanofluids. The study signifies the adverse impact on the cooling performance of MWCNT-thermal oil-based nanofluids in natural convection heat transfer, even though higher thermal conductivities are observed in nanofluids. It is found that not only thermal conductivity is essential property in heat transfer, but other thermophysical properties are also influential towards thermal management.

The effects of bottom wall heating on mixed convection of yield stress fluids in cylindrical enclosures with a rotating end wall

Steady-state laminar mixed convection of Bingham fluids in cylindrical enclosures with a rotating top cover has been numerically analysed for the configuration where the bottom cover is kept at a higher temperature than the rotating top cover. The numerical investigations have been carried out based on steady-state axisymmetric incompressible flow simulations for a range of different values Reynolds, Richardson, and Prandtl number given by 500⩽Re⩽3000, 0⩽Ri⩽1 and 10⩽Pr⩽500 respectively. The aspect ratio (i.e. height: radius = AR = H/R) of the cylindrical container is considered to be unity (i.e. AR = H/R = 1). The mean Nusselt number Nu‾ has been found to decrease sharply with increasing Bn owing to flow resistance arising from yield stress, but subsequently Nu‾ asymptotically approaches a value of unity, which is indicative of a conduction-driven transport. In addition, the mean Nusselt number Nu‾ has been found to increase with increasing Reynolds number due to the strengthening of advective transport. However, the mean Nusselt number Nu‾ exhibits a non-monotonic trend (i.e. increases with increasing Ri for small values of Richardson number before showing a weak decreasing trend) with increasing Ri for Newtonian fluid (i.e. Bn=0), whereas Nu‾ increases with increasing Ri for small values of Richardson number before becoming a weak function of Ri for Bingham fluids. A step change in the mean Nusselt number has also been observed with an increase in Richardson number for some Bingham number values due to a change in flow pattern. The influences of Prandtl, Reynolds, Richardson, and Bingham numbers on the mean Nusselt number have been explained in detail based on both physical and scaling arguments. The simulation data and scaling relations have been utilised to propose a correlation for the mean Nusselt number, which has been shown to capture the numerical findings satisfactorily for the parameter range considered here.

Natural Convection and Separation Points of a Non-Newtonian Fluid Along a Rotating Round-Nosed Body

The purpose of the present study is to present a numerical solution for the natural-convection flow of Ostwald/de Waele-type power-law non-Newtonian fluid along the surface of a rotating axisymmetric round-nosed body. For computational purpose, a rotating hemisphere is used as the case study to examine the effects of transverse curvature on heat transfer mechanism. The numerical scheme is applied after converting the dimensionless system of equations into primitive variable formulations. Implicit finite difference method is used to integrate the equations numerically. The numerical simulations performed are valid for shear-thickening fluids with a wide range of Prandtl numbers [i.e., ]. A detailed discussion is provided to understand the effects of buoyant forces and power-law exponent on the rate of heat transfer and skin-friction coefficient. A comparison of the present numerical results for different values of the buoyancy ratio parameter with other published data is shown in graphical form. The flow separation occurs when a portion of the boundary layer closest to the wall or leading edge reverses in flow direction. It is observed from our results that an increase in the power-law index and Prandtl number leads to an increase in the friction factor, as well as the rate of heat transfer.

Direct numerical simulation of energy separation effect in the near wake behind a circular cylinder

Based on direct numerical simulation of two-dimensional Navier-Stokes equations, the effect of energy separation in unsteady vortex flows is investigated with the reference to the problem of a compressible viscous flow past a thermally insulated circular cylinder. The range of Reynolds (Re⩽103), Prandtl (0.1⩽Pr⩽10) and Mach (M⩽0.6) numbers considered corresponds mainly to the periodic vortex shedding regime. The energy separation, associated with the vortex shedding process, manifests itself in the appearance of cold and hot (in terms of total temperature) spots in the near wake. The main attention is focused on the comparative analysis of different mechanisms of total-enthalpy variation in a fluid particle moving around the cylinder, such as the action of viscosity, thermal conductivity, and unsteadiness of the flow. It is shown that the time-averaged total-enthalpy stratification in the boundary layer is caused by dissipative mechanisms. In the vortex formation region and in the vortex street, a decrease in the time-averaged total enthalpy is attributable mainly to the streamline oscillations. The known Eckert-Weise effect of low equilibrium temperature at the rearmost stagnation point of the cylinder is associated with the non-uniformities in the temperature and density fields, created by the evolution of recirculation zones near the body surface. For both instantaneous and time-averaged flow patterns, the regions of local increase and decrease in the total enthalpy are distinguished. It turned out that, in the time-averaged flow, the region responsible for the total-enthalpy decrease in the vortex formation zone does not affect the decrease in the total enthalpy in the developed vortex wake, and vice versa.

Predicting transition ranges to fully turbulent viscous boundary layers in low Prandtl number convection flows

Characteristic properties of turbulent Rayleigh-B\'enard convection in the bulk and the boundary layers are summarized for a wide range of Rayleigh and Prandtl numbers, with a specific emphasis on low-Prandtl-number convection.

Mean temperature profiles in turbulent thermal convection

To predict the mean temperature profiles in turbulent thermal convection, the thermal boundary layer (BL) equation including the effects of fluctuations has to be solved. In Shishkina et al., Phys. Rev. Lett. 114 (2015), the thermal BL equation with the fluctuations taken into account as an eddy thermal diffusivity has been solved for large Prandtl-number fluids for which the eddy thermal diffusivity and the velocity field can be approximated respectively as a cubic and a linear function of the distance from the plate. In the present work we make use of the idea of Prandtl's mixing length model and relate the eddy thermal diffusivity to the stream function. With this proposed relation, we can solve the thermal BL equation and obtain a closed-form expression for the dimensionless mean temperature profile in terms of two independent parameters for fluids with a general Prandtl number. With a proper choice of the parameters, our predictions of the temperature profiles are in excellent agreement with the results of our direct numerical simulations for a wide range of Prandtl numbers from 0.01 to 2547.9 and Rayleigh numbers from 10^7 to 10^9.

Flow regime maps for smooth horizontal tubes at a constant heat flux

The existing constant heat flux boundary condition flow regime maps are accurate for high Prandtl number fluids, however, they are inaccurate at lower Prandtl numbers and tube diameters and specifically for water as the working fluid. The purpose of this paper was to develop a flow regime map that can be used for both high and low Prandtl number fluids for a wide range of tube diameters. Furthermore, not only to develop a map for fully developed flow, but also for developing flow. An experimental set-up was designed, built and validated against results from literature. Two smooth circular test sections with inner diameters of 4 mm and 11.5 mm, respectively, and lengths of 5.5 m and 9.5 m, respectively, were used. Heat transfer measurements were taken at a range of Reynolds numbers from laminar to turbulent. Water was used as the test fluid and the Prandtl number was limited between 3 and 7. Experimental results from literature complemented the test matrix used for this study, especially with high Prandtl number data. Six flow regime maps were developed for a constant heat flux boundary condition and a square-edged inlet, and these flow regime maps are original for four reasons. Firstly, it contains contour lines that show the Nusselt number enhancements due to free convection effects. Secondly, it is valid for a wide range of tube diameters and Prandtl numbers. Thirdly, the flow regime maps were developed as a function of temperature difference (Grashof number) and heat flux (modified Grashof number). Finally, four of the six flow regime maps are not only valid for fully developed flow, but also developing flow.

Lagrangian Modeling of Turbulent Dispersion from Instantaneous Point Sources at the Center of a Turbulent Flow Channel

The paper is focused on the simulation and modeling of the dispersion from an instantaneous source of heat or mass located at the center of a turbulent flow channel. The flow is modeled with a direct numerical simulation, and the dispersion is modeled with Lagrangian methods based on Lagrangian scalar tracking (LST). The LST technique allows the simulation of scalar sources that span a range of Prandtl or Schmidt numbers that cover orders of magnitude. The trajectories of individual heat or mass markers are tracked, generating a probability distribution function that describes the behavior of instantaneous point sources of a scalar in the turbulent field. The effect of the Prandtl or Schmidt number on turbulent dispersion is examined, with emphasis on the dispersion pattern. Results for Prandtl or Schmidt numbers between 0.1 and 15,000 are presented. For an instantaneous source at the channel center, it is found that there are two zones of cloud development: one where molecular diffusion plays a role at very small times (early stage of the dispersion), and one where turbulent convection dominates. The asphericity of the scalar marker cloud is found to increase monotonically, in contrast to published results for isotropic, homogenous turbulence, where the asphericity goes through a maximum.

Toward the analogue of a thermally generated electromagnetic field

The evolution equations for magnetic and vorticity fields are known to display the same pattern when dissipation and sources terms are neglected. We investigate the analogy between the two fields for non-vanishing dissipation and sources. In addition to the magnetic Reynolds (ReM) and Prandtl (PrM) numbers, we define a new number (SM) that is given by the ratio of the diffusive term to the Biermann battery term and which allows for a different classification of magnetized fluid behavior. Numerical simulations of the two fields are then carried out given a parameter space made of Reynolds, Prandtl, and source numbers. We find it appropriate to present and discuss the findings against Prandtl numbers given that these provide the link between viscous and magnetic diffusion. Our simulations indicate that there exists a range of Prandtl numbers for which the fields remain analogues which raises the important question of how far the analogy goes and also raises the prospect of a theory of analogue magnetism.

An experimental study on the natural convection heat transfer in rectangular enclosure using functionalized alumina-thermal oil-based nanofluids

The nanofluids are considered as an effective medium for thermal transport in various applications due to improved properties. Limited experimental studies are accomplished on the convective heat transfer of nanofluids. Natural convective heat transfer behavior in nanofluids is experimentally studied in a vertical rectangular enclosure (aspect ratio=4) with one heating and one cooling wall. The fluid under investigation is a novel and highly stable functionalized alumina-thermal oil-based nanofluid. The investigations are carried out for different concentrations of nanofluids ranging from 0 to 3wt%. The effectiveness of the natural convection heat transfer process is mainly dependent on the properties of cooling media. The measured thermophysical properties of nanofluids are used for the estimation of heat transfer characteristics with a Prandtl number range of 228–592. The heat transfer coefficient and Nusselt number are obtained at different nanoparticle concentrations. A heat flux is applied on the hot wall with a range of 1593.75–3150W/m2. An improvement in the cooling performance of nanofluids is observed. The high nanoparticle concentrations of nanofluids exhibit higher heat transfer coefficient as compared to the pure thermal oil. A correlation is developed for the Nusselt number in terms of Rayleigh number (4.43×105–2.59×106), nanoparticle concentration and effective thermophysical properties.

Heat transfer augmentation through convergence angles in a pipe

ABSTRACTForced convection in a combined entry developing length of a convergent pipe under constant wall heat flux boundary condition is performed in this work. Influences of the convergence angle, Reynolds, and Prandtl numbers on the heat transfer and flow field have been investigated. The numerical results are obtained for a wide range of convergence angles (0°–25°), Reynolds numbers (700–2100), and Prandtl numbers (0.707, 5.83). Compared to a traditional pipe, a substantial increase in heat transfer has been achieved with an increase in the pressure drop as the convergence angle increases. In this work, the effect of convergence angle, Reynolds number, and Prandtl number on the overall flow and thermal performance for the aforementioned configuration is investigated. To the best of authors’ knowledge, this investigation has been done for the first time, and it provides new and significant information regarding heat transfer enhancement utilizing a convergent pipe.

Topological bifurcations in the evolution of coherent structures in a convection model

Blob filaments are coherent structures in a turbulent plasma flow. Understanding the evolution of these structures is important to improve magnetic plasma confinement. Three state variables describe blob filaments in a plasma convection model. A dynamical systems approach analyzes the evolution of these three variables. A critical point of a variable defines a feature point for a region where that variable is significant. For a range of Rayleigh and Prandtl numbers, the bifurcations of the critical points of the three variables are investigated with time as the primary bifurcation parameter. Bifurcation curves separate the parameter planes into regions with different critical point configurations for the state variables. For Prandtl number equal to 1, the number of critical points of each state variable increases with increasing Rayleigh number. For Rayleigh number equal to 104, the number of critical points is the greatest for Prandtl numbers of magnitude 100.

New design equations for turbulent forced convection heat transfer and pressure loss in pillow-plate channels

Pillow-plate heat exchangers (PPHE) represent a stack of pillow plates characterized by a wavy surface and fully welded construction. The benefits of PPHE over conventional heat exchangers have made them increasingly attractive for numerous applications in the process industry. However, the lack of verified design methods and reference applications for PPHE hinders their widespread application. This work aims at overcoming this “bottleneck” by providing new equations for the thermo-hydraulic design of pillow plates.In particular, design methods for pressure loss and heat transfer are proposed for turbulent forced convection in pillow-plate channels over a wide range of Reynolds numbers (1000≤Re≤8000), Prandtl numbers (1≤Pr≤150) and characteristic geometry parameters (e.g., welding spot arrangement, inflation height). For the determination of heat transfer coefficients, two different approaches are presented. The first approach is based on the method typically suggested in literature, whereby the well-known Dittus-Boelter type power law function (cf. [1]) for the Nusselt number is applied and fitted to numerical data largely obtained in Ref. [2]. The second approach is based on the characteristic flow pattern in pillow plates suggested in Ref. [2]. In this pattern, the initial complex flow is broken down into two simpler flows, which can then be modeled separately. For both methods, the relative deviations between the numerical data obtained in Ref. [2] and in this study are less than 15%.

Influences of Boundary Condition on Laminar Natural Convection of Bingham Fluids in Square Cross-Sectioned Cylindrical Annular Enclosures with Differentially Heated Vertical Walls

ABSTRACTNumerical simulations have been carried out to analyze steady-state laminar natural convection of yield stress fluids obeying Bingham model in square cross-sectioned cylindrical annular enclosures with differentially heated vertical walls for both constant wall temperature and constant wall heat flux boundary conditions for active walls. The simulations have been performed under the assumption of axisymmetry for a nominal Rayleigh number range of 103 to 106 and nominal Prandtl number range of 10 to 103 for different ratio of internal cylinder radius to cylinder height range of 0.125 to 16. The mean Nusselt number on the inner periphery for the constant wall heat flux configuration has been found to be smaller than that in the case of constant wall temperature configuration for a given set of values of nominal Rayleigh and Prandtl numbers for both Newtonian and Bingham fluid cases. The mean Nusselt number normalized by the corresponding value obtained for pure conductive transport increases with increasing internal radius before approaching the corresponding mean Nusselt number for square enclosures regardless of the boundary conditions. Detailed physical explanations have been provided for the effects of the aforementioned parameters on the mean Nusselt number on the inner periphery. Finally, the new Nusselt number correlations have been proposed for laminar natural convection of both Newtonian and Bingham fluids in square cross-sectioned cylindrical annular enclosures for both constant wall temperature and constant wall heat flux boundary conditions.

Prandtl Number Effect on the Laminar Convective Heat Transfer From a Rotating Disk

Convective heat transfer in rotating disk systems is of great importance in many engineering applications. Despite the high practical relevance, there have been only a small number of experimental investigations regarding the influence of the Prandtl number larger than unity. Ever since Dorfman's pioneering work more than 50 years ago, various analytical works about the heat transfer of a rotating disk have been published. However, this study is a novelty because measurements of the laminar convective heat transfer over a free rotating disk for a wide range of Prandtl number up to Pr=5000 are presented. The accuracy of the employed experimental apparatus was assessed by heat transfer measurements in air, for which reliable literature data are widely available. Natural convection effects and temperature-dependent physical properties have been taken into consideration using the property-ratio method. The experimental results are in excellent agreement with analytical self-similar solutions and the theoretical correlation of Lin and Lin. The applicability of frequently used heat transfer correlations is assessed by the means of the new experimental data.