Dimensionless Prandtl Research Articles

Dual Solution with Heat Transfer through Moving Porous Plate of an Unsteady Incompressible Viscous Fluid

We examine graphically the behavior of the dual solution of an unsteady incompressible viscous flow with heat transfer due to a moving porous surface. The mathematical model is developed with the implementation of conservation laws which are then tackled numerically, and the simulations are performed through the Keller–Box technique. Application of the Keller–Box technique allows the non-linear differential equations to transform to a scheme of linear differential equations which are easier to illuminate. Outcomes of velocity and thermal behavior are shown graphically for certain values of the dimensionless parameters. It is obvious from the results that temperature of fluid decreases with the increasing values of dimensionless Prandtl number Pr, whereas the velocity enhances for blowing situations.

Thermal flow analysis of self-driven temperature-sensitive magnetic fluid between partially heated parallel plates

To develop a heat transfer device based on a temperature-sensitive magnetic fluid (TSMF), it is necessary to investigate its flow and heat transfer characteristics. This study used the fractional step method to numerically investigate the flow and heat transfer characteristics of TSMF between parallel plates with small spacing when the solenoidal magnetic field is applied. Due to the influence of the magnetic field and temperature, the flow characteristics of the TSMF between the plates are significantly different from ordinary working fluids such as oil, and the fluid near the plate flows faster than the fluid near the center. We used numerical analysis to analyze the formation of this phenomenon and investigated the influence of dimensionless Prandtl number and magnetic effect parameter on this phenomenon. As the result, the heat transfer increased with the increase of the magnetic effect parameter which is affected by the magnetic field or the distance between the plates. The center between the two plates in the heating region formed a vortex under high Prandtl number conditions, and the generation of the vortex enhanced the heat transfer.

Dissipative particle dynamics with energy conservation: Isoenergetic integration and transport properties.

Simulations of nano- to micro-meter scale fluidic systems under thermal gradients require consistent mesoscopic methods accounting for both hydrodynamic interactions and proper transport of energy. One such method is dissipative particle dynamics with energy conservation (DPDE), which has been used for various fluid systems with non-uniform temperature distributions. We propose an easily parallelizable modification of the velocity-Verlet algorithm based on local energy redistribution for each DPDE particle such that the total energy in a simulated system is conserved up to machine precision. Furthermore, transport properties of a DPDE fluid are analyzed in detail. In particular, an analytical approximation for the thermal conductivity coefficient is derived, which allows its a priori estimation for a given parameter set. Finally, we provide approximate expressions for the dimensionless Prandtl and Schmidt numbers, which characterize fluid transport properties and can be adjusted independently by a proper selection of model parameters. In conclusion, our results strengthen the DPDE method as a very robust approach for the investigation of mesoscopic systems with temperature inhomogeneities.

Laminar Mixed Convection Flow from a Vertical Surface with Induced Magnetic Field and Convective Boundary

The objective of this investigation is to study the influence of thermal radiation and radiation absorption parameter on a mixed convection flow over a continuously moving porous vertical plate under the action of transverse applied magnetic field taking into account the induced magnetic field with convective boundary. Under certain assumptions, the solutions for the velocity field, temperature distribution and induced magnetic field are obtained. The influences of various parameters on the velocity, temperature fields and on induced magnetic fields are studied graphically. It is also found that the dimensionless Prandtl number, Grashof number, Schmidt number and magnetic parameter have an appreciable influence on the independent variables.

Parametric solution of the Rayleigh-Benard convection model by using the PGD

Purpose – The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time. Design/methodology/approach – In this paper both parameters are introduced as model extracoordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily. Findings – Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters. Originality/value – Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.

Analysis of the turbulent law of the wall through the finite scale Lyapunov theory

This work analyzes the turbulent velocity distribution in proximity of the wall using the finite-scale Lyapunov theory just presented in previous works. This theory is here applied to the steady boundary layer under the hypothesis of moderate pressure gradient and fully developed flow along the streamwise direction. The analysis gives an equation for the velocities correlation and identifies the parameters of the expression of the average velocity through the statistical properties of the velocity correlation functions. In particular, the von Kármán constant, theoretically calculated, is about 0.4, and the dimensionless Prandtl’s length is in function of the Taylor-scale Reynolds number. The study provides the average velocity distribution and gives also the variation laws of the other variables, such as Taylor scale and Reynolds stress. The obtained results show that the finite-scale Lyapunov theory is adequate for studying the turbulence in the proximity of the wall.

Acoustic wave transmission loss mechanisms in poroelastic media, modeling, and experiment.

Among factors that determine acoustic wave transmission loss in poroelastic media are incident wave energy loss due to acoustic impedance mismatch, between pore fluid and solid frame, and their density ratio, in addition to frequency dependence of dissipation in viscous boundary layers of fluid-solid interface for compression and surface waves. Model for prediction of transmission loss mechanisms includes the use of dimensionless Prandtl and Strouhal numbers for momentum and heat transfers, respectively. Other mechanisms considered are transmission losses by resonant and wave localization in the pore spaces. Wave filtering by poroelastic media as well as transmission loss by mode conversion, scattering, diffraction, interference, absorption, and thermal conduction are considered. Mechanical and electrical models of low-pass, band-pass, and high-pass filters applied to poroelastic media lead to the type of parameters to be included in this model as a function of frequency and pore size. Experimental measurements to test the prediction on acoustic wave transmission loss in similar poroelastic media of constant uniform porosity, but of different thicknesses and pore sizes, are presented to test transmission loss as a function of pore size, media thickness, and acoustic wave frequency.

AGN Accretion Disks with Finite Turbulent Prandtl Number

The present paper reports results of a study of turbulent energy transport in AGN accretion disks. We follow the spirit of the papers by Shakura et al. and Rüdiger et. al in which the concept of an eddy heat conductivity was introduced and developed. For the viscosity we use a standard α− description with the main component of the stress tensor trø proportional to the gas pressure. The dimensionless Prandtl number Pr given as the ratio of turbulent kinematic viscosity and turbulent heat conductivity enters the model as a free parameter. The disk structure depends sensitively on material properties such as opacities and specific heats. In our calculations we have used an equation of state and mean opacities taking into account a list of the most important ionization processes as well as the radiation contributions to thermodynamic quantities.

Solution of the boussinesq equations by the finite element method

A finite element procedure is presented for the calculation of two-dimensional transient convective/conductive heat transfer in a fluid region. The governing equations are expressed in terms of the primitive variables; the flow is assumed to be laminar, and the fluid incompressible within the Boussinesq approximation. Three typical problems are examined: flow through a sudden enlargement, natural convection in rectangular enclosures, and natural convection between horizontal concentric cylinders. An assessment of the characteristics of the flow regime is made in association with varying dimensionless Prandtl and Rayleigh numbers, as well as cavity aspects ratios. The upper limit for the Rayleigh number in the present paper is 10 7. Wherever possible, the results are compared with existing solutions obtained by other numerical methods.

A finite element numerical solution of natural convection in enclosed cavities

Steady state free convective flow enclosed within a cavity and subjected to a temperature gradient is predicted using the finite element method. The matrix equations resulting from the finite element discretisation and formulation are solved using both an iterative and a modified Newton-Raphson scheme. An assessment of the variation in the characteristics of the flow regime is made in association with the dimensionless Prandtl and Rayleigh numbers. A further parameter of interest in such problems is the cavity aspect ratio. The upper limit for the Rayleigh number (based on cavity width) presented in the present paper is 10 7 . The flow patterns are obtained for Prandtl numbers in the range 10 −2 ⩽ Pr ⩽ 10 3 and for aspect ratios 1, 10, 20. Where possible the results are compared with existing solutions obtained using the finite difference method. A satisfactory correlation exists where such comparisons can be made. The results complement and extend those obtained during previous theoretical and numerical investigations.

Convection of a viscous incompressible gas in rectangular regions with inlet and outlet channels

A study is made of two-dimensional problems of thermal convection of a viscous incompressible gas in rectangular regions that have gas inlet and outlet channels in the presence of a temperature difference between the bottom and the top (the bottom is heated). In contrast to the well-studied case of natural convection, when no-slip conditions are specified on all boundaries of the region and motion in the region occurs only through the temperature difference [1–4], the heat transfer in the investigated flows is complicated by the additional influence of the forced convection of the gas due to the motion of gas through the inlet and outlet channels. Flows of such type simulate well the processes that take place in many heat transfer devices and in ventilated and air-conditioned industrial premises. Two formulations of the problem are considered. In the first, the gas flow through the inlet and outlet channels is assumed given, and the solution of the problem is determined by the dimensionless Prandtl, Grashof, and Reynolds numbers. In the second case, this flow rate is not given but determined during the solution of the problem. The motion in the region arises from the difference between the temperatures of the bottom and the top of the region, and the motion, in its turn, causes a flow of gas through the inlet and outlet channels. As in the case of natural convection, the solution of the problem in this case is determined by only two dimensionless numbers — the Grashof and Prandtl numbers. By numerical solution of the boundary-value problems for the equations of heat transfer a study is made of the influence of the characteristic dimensionless numbers on the hydrodynamic and temperature fields and the heat fluxes through the boundaries of the region. The solutions of the problems in the two formulations are compared for different positions of the outlet channels.