Prandlt Number Research Articles

The effect of thermal radiation, heat generation and suction/injection on the mechanical properties of unsteady continuous moving cylinder in a nanofluid

The effect of thermal radiation, heat generation, suction/injection, nanoparticles type, and nanoparticle volume fraction on heat transfer characteristics and the mechanical properties of unsteady moving cylinder embedded into cooling medium consist of water with Cu; Ag or Al2O3 particles are studied. The governing time dependent boundary layer equations are transformed to ordinary differential equations containing unsteadiness parameter, thermal radiation parameter, heat source parameter, suction/injection parameter, curvature parameter, nanoparticle volume fraction and Prandlt number. These equations are solved numerically. The velocity and Temperature profiles within the boundary layer are plotted and discussed in details for various values of the different parameters. Also the effects of the cooling medium and the external thermal forces on the mechanical properties of the cylinder are investigated.

Unsteady Permeable Magnetohydrodynamic (MHD) Radiating Fluid Flow Bounded by an Oscillating Porous Plate with Slip Flow Condition and Heat Generation

The problem of unsteady Magnetohydrodynamic (MHD) radiating fluid flow through a porous medium bounded by an oscillating porous plate with slip flow condition with heat generation was investigated. Boundary layer equations were derived and the resulting approximate non-linear ordinary differential equations were solved analytically using perturbation technique.  The numerical results reveal that the radiation induces a rise in velocity with a decrease in temperature. Also the heat generation increases at the points – 0.13, 0.5 and 0.13  and decreases at the point  -0.1 and 0.1 together with an increase in temperature. Some of the physical parameters like Grashof number, radiation, Prandlt number and chemical reaction has an influence on velocity, temperature and Concentration.

Study on MHD Boundary Layer Flow of Combined Heat and Mass Transfer Over a Moving Inclined Plate in a Porous Medium With Suction and Viscous Dissipation in Presence of Hall Effect

The Hall effects on the steady MHD boundary layer flow of an incompressible fluid of combined heat and mass transfer over a moving inclined plate in a porous media with suction and viscous dissipation has studied. An external magnetic field is applied perpendicular to the surface and the fluid motion is subjected to a uniform suction and injection. A closed form solutions of the equations governing the flow are obtained for the velocity, secondary velocity, and temperature and concentration profiles. The dimensionless governing equations are solved using RK method along with shooting technique. The velocities, temperature and concentration profiles are presented graphically for different values of governing flow parameters. The results presented graphically illustrate that primary velocity field decrease due to increase of magnetic parameter, angle of inclination, permeability parameter and suction parameter while secondary velocity also decrease for magnetic parameter, Hall parameter and permeability parameter .Other parameters increase the velocities of the fluid flow. Temperature field increases in the presence of Magnetic parameter, Grashof number, Modified Grashof number and permeability parameter and decreases for Prandlt number and suction parameter. Also, concentration profiles decreases for increasing the values of magnetic parameter, Hall parameter, Schmid number and suction parameter but there is no effect on concentration of the remaining parameters. Also the skin friction coefficient, the local Nusselt number and the local Sherwood number are presented in Tables 1-3.

Analyze of fluid flow and heat transfer of nanofluids over a stretching sheet near the extrusion slit

The objective of the present study is to analyze the boundary layer flow and heat transfer of nanofluids over a stretching sheet near the extrusion slit in the presence of variable thermal conductivity. The effects of Brownian motion and thermophoresis are taken into account. The governing partial differential equations are reduced to dimensionless form and solved numerically using finite difference scheme and Point Successive Over Relaxation algorithm. The critical Reynolds number is introduced to distinguish the non-similar region from the self-similar region of velocity and temperature profiles. Furthermore, the effects of dimensionless parameters such as Prandlt number, Schmidt number, variable thermal conductivity parameter, Brownian motion and thermophoresis parameters on the velocity and temperature profiles and also on reduced Nusselt number, reduced Sherwood number and critical Reynolds number are investigated. It is found that the critical Reynolds number for the temperature profile is significantly affected by Prandtl number. In addition, the reduced Nusselt and Sherwood numbers found to be much higher in non-similar regions near the extrusion slit than that of self-similar region.

Field synergy analysis for helical ducts with rectangular cross section

This paper proposes a new approach based on VSP method (Vorticity–Stream function–Poisson equation method), to study numerically fully developed laminar flow characteristics and heat transfer behaviors of helical ducts with rectangular cross section. The aim is to guide heat transfer enhancement for helical rectangular ducts. Based on the numerical results, synergies between velocity field and temperature field have been investigated through field synergy principle. The effects of curvature, torsion, aspect ratio, Reynolds number, and Prandlt number on velocity field, temperature field and field synergy have been examined. The results show that the secondary flow of the central regions is weaker than that in other locations of the cross section. With reference to the entire cross section, the best values of synergy between velocity field and temperature field can be found in the center of the section. Increasing the curvature, Reynolds number and Prandtl number causes the mean synergy angles of the cross section to increase. This result indicates that it is more important to improve the field synergy for high Prandlt number fluid, especially at high Reynolds number. As the torsion increases, the average synergy angles decreases. The mean synergy angles reach the maximum value when the aspect ratio is equal to one; therefore, one can conclude that the field synergy of helical ducts with square cross section is the worst. To enhance heat transfer performance of helical rectangular ducts, for small aspect ratio, the main important aspect is to improve the secondary flow in the center of the cross section. On the contrary, for moderate values of the aspect ratio, the most important aspect is to improve the field synergy of the region near the upper and the lower wall. The correlations of friction factor and Nusselt number have been also developed for helical ducts with rectangular cross section.

Modeling and Simulation of Heat and Mass Transfer During Convective Drying of Wastewater Sludge with Introduction of Shrinkage Phenomena

Wastewater sludge is dried in a convective dryer using air temperatures varying from 80°C to 200°C, velocities changing from 1 m · s−1 to 2 m · s−1, and humidities ranging from . The convective dryer is equipped with a camera and an infrared pyrometer to follow respectively the external surface and the temperature of the product. The experimental results show that drying kinetic can be divided into three phases: two short first phases, called adaptation and constant drying phases, and a long third phase, called falling drying rate phase. As the moisture content decreases, the camera confirms simultaneous shrinkage effect with the volume reduction of the product of about 30–45% of the initial volume. Moreover, an increase of the product temperature towards air temperature was measured with the infrared pyrometer. In a second step of this study, the experimental results are modeled and simulated using heat and mass balances applied to the product and the heated air. The drying curve is rightly expressed with fourth-degree polynomial model with a correlation coefficient that approximates the unity and with low calculated errors. An outstanding determination of the heat transfer coefficient has permitted calculating the product temperature with good agreement with experimental results. The heat transfer coefficient expressed by means of Nusselt number is presented as a function of Reynolds and Prandlt numbers, changeable with air and product characteristics taking into account shrinkage effect. Moreover, as the applied air temperatures are sufficiently high, transfer by radiation is not neglected and is introduced in the mathematical model.

Species separation of a binary mixture in the presence of mixed convection

In this paper, an analytical and numerical study to determine the species separation process in a binary fluid mixture by decoupling the thermal gradient from the convective velocity was performed. The configuration considered is a horizontal rectangular cavity of large aspect ratio, filled with a binary fluid. A constant tangential velocity is applied to the upper horizontal wall. The two horizontal impermeable walls are maintained at different and uniform temperatures T1 and T2 with ΔT = T2 − T1. Species separation is governed by two control parameters, the temperature difference and the velocity of the upper plate Uex→. The intensity of the thermodiffusion is controlled by the temperature gradient, while the velocity Uex→ controls the convective flow. This problem depends on six dimensionless parameters, namely, the separation ratio ψ, the Lewis number Le, the Prandlt number Pr, the aspect ratio of the cell A and two control parameters: the thermal Rayleigh number, Ra and the Péclet number Pe. In this study, the separation (mass fraction difference between the two ends of the cell) is obtained analytically as a function of mass Péclet number (Pem = PeLe) and mass Rayleigh number (Ram=ψRaLe). The optimal separation m=42/15≈0.432 is obtained for Pem=42 and Ram = 540. The numerical results, obtained using the full governing equations, are in good agreement with the analytical results based on a parallel flow approximation.

Effects of viscous dissipation on natural convection flow along a sphere with radiation and heat generation

The effects of viscous dissipation on free convection flow along a sphere with radiation and heat generation have been investigated in this paper. The governing equations with associated boundary conditions for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method. Numerical results of the velocity and temperature profiles, skin friction coefficient and surface temperature profiles for different values of the of viscous dissipation parameter Vd ( 0.0 to 4.0), radiation parameter Rd (0.0 to 1.0), the Prandlt number Pr (0.72 to7.0)and the heat generation parameter Q (0.2 to 0.6) are presented graphically. Detailed discussion is given for the effects of the aforementioned parameters. Significant effect is found in the velocity and temperature profiles, skin friction coefficient and surface temperature distribution for the Prandtl number, heat generation and radiation parameters. DOI: http://dx.doi.org/10.3329/jname.v10i1.12809

Conjugate Effects of Heat and Mass Transfer on Natural Convection Flow along an Isothermal Sphere with Radiation Heat Loss

Conjugate effects heat and mass transfer on free convection flow across an isothermal sphere immersed in a viscous incompressible fluid in the presence of species concentration with radiation heat loss has been investigated in this paper. The governing boundary layer equations are first transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are then solved numerically using Finite—difference method with Keller-box Scheme. We have focused our attention on the evaluation velocity profiles, temperature profiles and species concentration profiles of the fluid as well as the local skin friction coefficient, local heat transfer rate and local species concentration transfer rate for a wide range of radiation parameter Rd, Schmidt number Sc and Prandlt number Pr.

도관내 원형관의 자연대류 열전달에서 입구 및 출구 길이 효과

굴뚝내 수직 원형관의 자연대류에서 굴뚝의 입구길이, 출구길이, 그리고 굴뚝의 직경에 따른 열전달 변화를 실험적으로 연구하였다. 상사성을 이용하여 열전달 실험 대신 물질전달 실험을 수행하였다. 직경 0.054 m, 높이 0.03, 0.07, 0.10 m의 원형관에 대하여 굴뚝의 직경을 0.06 m에서 0.14 m까지, 높이를 0.30 m에서 1.10 m까지 변화시켰다. 이는 Pr 수 2,094, <TEX>$Ra_L$</TEX> 수 <TEX>$4.55{\times}10^9$</TEX>, <TEX>$5.79{\times}10^{10}$</TEX>, 그리고 <TEX>$1.69{\times}10^{11}$</TEX>에 해당한다. 굴뚝이 없을 때, 수직 원형관의 열전달은 Le Ferve의 수직평판에 대한 층류 자연대류 상관식과 일치하였다. 출구길이를 증가시키며 실험한 결과, 열전달은 증가하다가 특정 출구길이 이상에서는 일정해 졌다. 반면, 입구길이를 증가시킬 때는 열전달은 감소하다가 특정 입구길이 이상에서는 일정해졌다. 굴뚝효과로 증가된 열전달은 굴뚝의 직경을 증가시킬수록 감소하다가 굴뚝이 없을 때와 같아졌다. This work investigated the influence of the chimney dimensions(exit and entrance length, and diameter) on the heat transfer of a vertical cylinder in a duct. The measured mass transfer rates for the natural convection of vertical cylinder in a duct were presented for Prandlt number 2,094, Rayleigh number in the range of <TEX>$4.55{\times}10^9$</TEX>, <TEX>$5.79{\times}10^{10}$</TEX>, and <TEX>$1.69{\times}10^{11}$</TEX>. Experiments were performed using a copper sulfate electroplating system to simulate heat transfer based upon the analogy concept. The diameter of the duct was varied from 0.06 m to 0.14 m, and the heights from 0.30 m to 1.10 m. Nusselt numbers measured at open channel condition agreed well with the existing laminar heat transfer correlations for vertical plate developed by Le Fevre. The increase of the exit length enhanced the heat transfer up to a certain duct height but further increase does not affects the heat transfer. The heat transfer decreased with increasing the entrance length up to a certain duct height and was constant at further increase. The Nusselt number decreased with increasing the diameter of duct, until Nusselt number becomes similar to that at open channel beyond a certain diameter.

A STUDY OF THE DYNAMO TRANSITION IN A SELF-CONSISTENT NONLINEAR DYNAMO MODEL

Using the magnetohydrodynamic (MHD) description, we develop a nonlinear dynamo model that couples the evolution of the large scale magnetic field with turbulent dynamics of the plasma at small scale by electromotive force (e.m.f.) in the induction equation at large scale. The nonlinear behavior of the plasma at small scale is described by using a MHD shell model for velocity field and magnetic field fluctuations.The shell model allow to study this problem in a large parameter regime which characterizes the dynamo phenomenon in many natural systems and which is beyond the power of supercomputers at today. Under specific conditions of the plasma turbulent state, the field fluctuations at small scales are able to trigger the dynamo instability. We study this transition considering the stability curve which shows a strong decrease in the critical magnetic Reynolds number for increasing inverse magnetic Prandlt number $\textrm{Pm}^{-1}$ in the range $[10^{-6},1]$ and slows an increase in the range $[1,10^{8}]$. We also obtain hysteretic behavior across the dynamo boundary reveling the subcritical nature of this transition. The system, undergoing this transition, can reach different dynamo regimes, depending on Reynolds numbers of the plasma flow. This shows the critical role that the turbulence plays in the dynamo phenomenon. In particular the model is able to reproduce the dynamical situation in which the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field, reproducing the magnetic reversals as observed in geomagnetic dynamo and in the VKS experiments.

Local heat transfer analysis for boiling of hydrocarbons in complex geometries: A new approach for heat transfer prediction in staggered tube bundle

This paper deals with heat transfer analysis for boiling flow in staggered tube bundle. A local analysis is performed to determine the heat transfer coefficient linked to local flow regimes by optical fibre. The first part of the paper is devoted to the literature survey of the main existing studies on the topic. We show that published heat transfer correlations deviate largely from each others and also from the experimental results that have been carried out. On these features, a new approach has been developed. It is based on the relationship between flow regimes and thermal characteristics. An experimental setup has been developed for the determination of the local heat transfer and the two-phase flow void fraction. A detailed analysis of the two-phase flow has been performed in a previous paper [1] in which two regimes were identified. In the present paper, focus is done on the heat transfer analysis in relation with the flow regime map. This new approach allows a better prediction of the heat transfer coefficient. For the bubbly flow, the heat transfer coefficient is well predicted by a classical correlation corresponding to nucleate boiling regime. For the dispersed flow, classical correlations for convective boiling are not adapted anymore for tube bundle. We evidenced that heat coefficient is mainly controlled by the vapour flow and a heat transfer law is derived using the vapour Reynolds number and vapour Prandlt number. These two heat transfer laws are used to evaluate heat transfer coefficient in the intermediate regime.

The onset of convection in a rotating layer of viscous fluid with an imposed magnetic field: the dependence on the prandlt numbers

The onset of Boussinesq convection in a horizontal layer of an electrically conducting incompressible fluid is considered. The layer rotating about a vertical axis is heated from below; a vertical magnetic field is imposed. Rigid electrically insulating boundaries are assumed. The loss of stability of the trivial steady state, which occurs as the Rayleigh numbers increase, can be accompanied by the development of a monotonic or an oscillatory instability, depending on the parameter values of the problem at hand (the Taylor number, the Chandrasekhar number, the kinematic and the magnetic Prandtl numbers). When the instability is monotonic, the emerging convective rolls themselves are also unstable if the Taylor number is sufficiently large (the so-called Kuppers-Lortz instability takes place). In the present work it is studied how the critical value of the Rayleigh number, the type of the trivial steady state instability, and the critical value of the Taylor number for the Kuppers-Lortz instability depend on the kinematic and the magnetic Prandtl numbers. We consider the values of the Prandtl number not exceeding 1, which is typical for the outer core of the Earth.

Effect of radiation on natural convection flow on a sphere in presence of heat generation

Effect of radiation on natural convection flow around a sphere in presence of heat generation has been investigated. The governing equations are transformed into dimensionless non-similar equations by using a set of suitable transformations and solved numerically by the finite difference method along with Newton's linearization approximation. We have focused our attention on the evaluation of velocity profiles, temperature profiles, shear stress in terms of local skin friction and the rate of heat transfer in terms of local Nusselt number for different values of heat generation parameter, radiation parameter and the Prandlt number and the numerical results have been shown graphically.

Experimental Analysis of Microconvective Heat Transfer in the Laminar and Transitional Regions

This article details experiments to determine the Nusselt number for laminar and transitional liquid flows (water and FC-72) through rough stainless-steel microtubes of 440-, 280-, and 146-μm inner diameter. Under laminar conditions, the average Nusselt number approaches the fully developed value for uniformly heated tubes as Reynolds decreases. For higher Reynolds, the region of thermal development increases the average convective heat transfer coefficient, which becomes a function of the Reynolds and Prandlt numbers and of the inner diameter-to-heated-length ratio. The effect of roughness is negligible in the laminar regime. Under transition, the average Nusselt steeply increases with Reynolds, more than for conventional pipes.

Momentum and heat transport in a three-dimensional transitional wake of a heated square cylinder

The transport of momentum and a passive scalar (temperature) in a three-dimensional transitional wake of a heated square cylinder has been carried out through direct numerical simulations using the lattice Boltzmann method at a Reynolds number Rd = 200 (d is the cylinder diameter) and a Prandlt number of 0.7. The simulations shows that while momentum and heat are transported by vortical structures, heat is in general more effectively transported than momentum. It is argued that the nature of the structural flow is responsible for the longitudinal heat flux uθ being larger than the lateral one vθ in the wake region extending up to 45d. It was shown that a gradient transport model could, to a first-order approximation, be used to model uv but would be less accurate for modelling vθ. Also the Reynolds analogy between momentum and heat transports is not verified in this flow. The fluctuating temperature field presents thermal structures similar to the velocity structures with, however, a different spatial organization. In addition the analogy between fluctuating turbulent kinetic energy and the temperature variance is relatively well satisfied throughout the wake flow.

Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet

A theoretical analysis of the laminar boundary-layer flow and heat transfer of power-law non-Newtonian fluids over a stretching sheet with the sheet velocity distribution of the form U w = C x m and the wall temperature distribution of the form T w = T ∞ + A x γ is presented, where x denotes the distance from the slit from which the surface emerges and C and A are constants, m and γ denote, the sheet velocity exponent and the temperature exponent, respectively. Within the framework of the boundary layer approximations, the nonlinear boundary layer momentum equation and the energy equation are reduced to a set of ordinary differential equations. It is found that when the velocity exponent m = 1 / 3 or the power-law index n = 1 , the similarity solutions are in existence for both the momentum equation and the energy equation. Analytical approximations with high accuracy for the reduced velocity and temperature profiles are obtained using a new procedure based on the homotopy analysis method. Besides, the effects of the parameters m , n and the Prandlt number P r on the flow are investigated.

Stagnation-Point Heat Transfer Near the Continuum Limit

H EAT and momentum transfer at the stagnation point is a problem of theoretical and practical interest. Solution of the Navier–Stokes equations at the stagnation point is one of oldest known solutions to the Navier–Stokes equations [1,2] and is closely related to boundary-layer flow [3]. Once the fluid flow is computed, the heat transfer can be computed in both 2-dimensional [4] and axisymmetric [5] geometries. The importance of stagnation-point heat transfer in problems such as atmospheric reentry [6] and other rarefied hypersonic flows [7] make estimating the heat transfer a problem of practical engineering interest. Initial attempts to solve stagnation-point flow and boundary-layer flow with a slip boundary condition using perturbation methods [8] suggested that the slip condition would not affect shear stress or heat transfer. Amore complete thermal analysis partially contradicted this result, suggesting that heat transfer in a laminar boundary layer decreased in the presence of a slip boundary condition [9]. The apparent lack of a change in shear stress due to the slip condition led to the conclusion that the terms added by the slip boundary condition were smaller than the discarded second-order terms in the boundary-layer equations [10]. This led to the conclusion that slip could be ignored in both laminar boundary-layer and stagnationpoint flows. These conclusions were challenged by numerical results, including solution of the linearized Boltzmann equation for stagnation-point flow [11], solution of stagnation-point flow with slip [12], and solution of the Blasius boundary-layer equations with slip flow that incorporated the loss of self-similarity [13]. All of these analyses showed decreased shear stress and boundary-layer thickness. When heat transfer was incorporated in the boundarylayer analysis, the heat transfer decreased from the equilibrium values. The present work extends previous analysis of the fluid flow and heat transfer in the presence of a slip boundary condition [12,14] to cover rarefied flow, in which the temperature jump and slip boundary conditions are coupled. This analysis provides an estimate for change in heat transfer due to rarefied-flow effects for a range of Knudsen and Prandlt numbers for both monatomic and diatomic gases.

Influence of acoustic streaming on the stability of melt flows in horizontal Bridgman configurations

Abstract We study the effect of acoustic streaming (steady flow generated by progressive acoustic waves) on the stability of convective flows associated with crystal growth from melt in horizontal Bridgman configurations. We consider two simple configurations: an extended fluid layer submitted to a horizontal temperature gradient and a laterally heated parallelepipedic cavity. In both cases, the dependence of the critical Grashof number Gr c on the acoustic intensity (monitored through the acoustic parameter A ) is determined for given values of the Prandlt number and of the dimension of the acoustic source H b . In the case of the extended fluid layer, it is shown that for rather small beam widths H b , the acoustic streaming destabilizes the buoyant flows, but for a large beam width, a range of acoustic intensities A is found for which the buoyant flows are stabilized. An adequate decentring of the beam can also enhance the stabilization. In the case of the parallelepipedic cavity, the numerical calculations for a quite large beam width have shown that the critical thresholds for the two first (steady, and then oscillatory) bifurcations clearly increase when the acoustic streaming contribution is enhanced.

Viscous Dissipation Effects on MHD Natural Convection Flow Over a Sphere in the Presence of Heat Generation

In this paper, the viscous dissipation effects on magnetohydrodynamic natural convection flow over a sphere in the presence of heat generation have been described. The governing boundary layer equations are first transformed into a nondimensional form and the resulting nonlinear system of partial differential equations are then solved numerically using finite-difference method together with Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles are shown graphically and tabular form for a selection of parameters set consisting of heat generation parameter Q, magnetic parameter M, viscous dissipation parameter N and the Prandlt number Pr.