Heat Transfer between Eccentric Rotating Cylinders

1980 ◽  
Vol 102 (2) ◽  
pp. 347-350 ◽  
Author(s):  
M. Singh ◽  
S. C. Rajvanshi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Temperature Distribution ◽  
Prandtl Number ◽  
Energy Equation ◽  
Dimensionless Parameter ◽  
Velocity Ratio ◽  
Rotating Cylinders ◽  
Clearance Ratio ◽  
Small Clearance

The heat transfer between eccentric rotating cylinders is studied using a modified bipolar coordinate system. The energy equation has been solved by expressing the temperature in the form of a perturbation in terms of α, the dimensionless parameter defining the clearance ratio; and Rm, the modified Reynolds number. The effect of Prandtl number, eccentricity and velocity ratio on temperature distribution has been shown graphically. The results are valid for small clearance ratio. There is no restriction on eccentricity.

An Analysis of Laminar Forced Convection Between Concentric Spheres

1976 ◽  
Vol 98 (4) ◽  
pp. 601-608 ◽  
Author(s):  
K. N. Astill
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Temperature Distribution ◽  
Prandtl Number ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Radius Ratio ◽  
Flow And Heat Transfer ◽  
Concentric Spheres ◽  
Inner Surface

A numerical solution for predicting the behavior of laminar flow and heat transfer between concentric spheres is developed. Axial symmetry is assumed. The Navier-Stokes equations and energy equation are simplified to parabolic form and solved using finite-difference methods. Hydrodynamic and energy equations are uncoupled, which allows the hydrodynamic problem to be solved independently of the heat-transfer problem. Velocity and temperature are calculated in terms of the two spatial coordinates. Solutions depend on radius ratio of the concentric spheres, Reynolds number of the flow, Prandtl number, initial conditions of temperature and velocity, temperature distribution along the spherical surfaces, and azimuthal position of the start of the flow. The effect on flow and heat transfer of these variables, except surface temperature distribution, is evaluated. While the computer solution is not restricted to isothermal spheres, this is the only case treated. Velocity profiles, pressure distribution, flow losses, and heat-transfer coefficients are determined for a variety of situations. Local and average Nusselt numbers are computed, and a correlation is developed for mean Nusselt number on the inner surface as a function of Reynolds number, Prandtl number, and radius ratio. Flow separation is predicted by the analysis. Separation is a function of Reynolds number, radius ratio, and azimuthal location of the initial state. Separation was observed at the outer surface as well as from the inner surface under some conditions. In cases where separation occurred, the solution was valid only to the point of separation.

Numerical Study of Convective Heat Transfer From Expanding Annular Pipe Flows

2016 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Diameter Ratio ◽  
Wall Heat Transfer ◽  
Reattachment Point ◽  
Transfer Rates ◽  
Pipe Flows ◽  
Annular Pipe

Convective heat transfer from suddenly expanding annular pipe flows are numerically investigated within the steady laminar flow regime. A parametric study is performed to reveal the influence of the annular diameter ratio, k, the Prandtl number, Pr, and the Reynolds number, Re, over the following range of parameters: k = {0, 0.5, 0.7}, Pr = {0.7, 1, 7, 100}, and Re = {25, 50, 100}. Heat transfer enhancement downstream of the expansion plane is only observed for Pr > 1. Peak wall-heat-transfer-rates always appear downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e. k = 0. However, for suddenly expanding annular pipe flows, i.e., k = 0.5 and 0.7, peak wall-heat-transfer-rates always appear upstream of the flow reattachment point. The observed heat transfer augmentation is more dramatic for suddenly expanding annular flows, in comparison with the one observed for suddenly expanding pipe flows. For a given annular diameter ratio and Reynolds number, increasing the Prandtl number, always results in higher wall-heat-transfer-rates downstream the expansion plane.

Study on Effective Radial Thermal Conductivity of Gas Flow through a Methanol Reactor

2015 ◽  
Vol 13 (1) ◽  
pp. 103-112 ◽  
Author(s):  
Kun Lei ◽  
Hongfang Ma ◽  
Haitao Zhang ◽  
Weiyong Ying ◽  
Dingye Fang
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Reynolds Number ◽  
Temperature Distribution ◽  
Large Scale ◽  
Gas Flow ◽  
Fixed Bed ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Particle Reynolds Number

Abstract The heat conduction performance of the methanol synthesis reactor is significant for the development of large-scale methanol production. The present work has measured the temperature distribution in the fixed bed at air volumetric flow rate 2.4–7 m3 · h−1, inlet air temperature 160–200°C and heating tube temperature 210–270°C. The effective radial thermal conductivity and effective wall heat transfer coefficient were derived based on the steady-state measurements and the two-dimensional heat transfer model. A correlation was proposed based on the experimental data, which related well the Nusselt number and the effective radial thermal conductivity to the particle Reynolds number ranging from 59.2 to 175.8. The heat transfer model combined with the correlation was used to calculate the temperature profiles. A comparison with the predicated temperature and the measurements was illustrated and the results showed that the predication agreed very well with the experimental results. All the absolute values of the relative errors were less than 10%, and the model was verified by experiments. Comparing the correlations of both this work with previously published showed that there are considerable discrepancies among them due to different experimental conditions. The influence of the particle Reynolds number on the temperature distribution inside the bed was also discussed and it was shown that improving particle Reynolds number contributed to enhance heat transfer in the fixed bed.

scholarly journals MODELING HEAT EXCHANGE DEPENDING ON THE PRANDTL NUMBER FOR VARIOUS GEOMETRIC AND REGIME PARAMETERS

2020 ◽  
Vol 46 (4) ◽  
pp. 91-101
Author(s):  
I. E. Lobanov
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Prandtl Number ◽  
Energy Equation ◽  
Transport Model ◽  
Reynolds Numbers ◽  
Structured Grids ◽  
Shear Stress Transport Model ◽  
Small Reynolds Numbers ◽  
Prandtl Numbers

Objectives. The aim is to study the dependency of the distribution of integral heat transfer during turbulent convective heat transfer in a pipe with a sequence of periodic protrusions of semicircular geometry on the Prandtl number using the calculation method based on a numerical solution of the system of Reynolds equations closed using the Menter’s shear stress transport model and the energy equation on different-sized intersecting structured grids.Method. A calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations by factored finite-volume method closed with the help of the Menter shear stress transport model, as well as the energy equation on different-scaled intersecting structured grids (fast composite mesh method (FCOM)).Results. The calculations performed in the work showed that with an increase in the Prandtl number at small Reynolds numbers, there is an initial noticeable increase in the relative heat transfer. With additional increase in the Prandtl number, the relative heat transfer changes less: for small steps, it increases; for median steps it is almost stabilised, while for large steps it declines insignificantly. At large Reynolds numbers, the relative heat transfer decreases with an increase in the Prandtl number followed by its further stabilisation.Conclusion. The study analyses the calculated dependencies of the relative heat transfer on the Pr Prandtl number for various values of the relative h/D height of the turbulator, the relative t/D pitch between the turbulators and for various values of the Re Reynolds number. Qualitative and quantitative changes in calculated parameters are described all other things being equal. The analytical substantiation of the obtained calculation laws is that the height of the turbuliser is less for small Reynolds numbers, while for large Reynolds numbers, it is less than the height of the wall layer. Consequently, only the core of the flow is turbulised, which results in an increase in hydroresistance and a decrease in heat transfer. In the work on the basis of limited calculation material, a tangible decrease in the level of heat transfer intensification for small Prandtl numbers is theoretically confirmed. The obtained results of intensified heat transfer in the region of low Prandtl numbers substantiate the promising development of research in this direction. The theoretical data obtained in the work have determined the laws of relative heat transfer across a wide range of Prandtl numbers, including in those areas where experimental material does not currently exist. 

Effect of viscous dissipation in stokes flow between rotating cylinders using BEM

2019 ◽  
Vol 30 (4) ◽  
pp. 2121-2136 ◽  
Author(s):  
Tomasz Janusz Teleszewski
Keyword(s):  
Nusselt Number ◽  
Temperature Distribution ◽  
Viscous Dissipation ◽  
Stokes Flow ◽  
Energy Equation ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Content Type ◽  
Dissipation Term ◽  
Cylinder Diameter

Purpose The purpose of this paper is to apply the boundary element method (BEM) to Stokes flow between eccentric rotating cylinders, considering the case when viscous dissipation plays a significant role and determining the Nusselt number as a function of cylinder geometry parameters. Design/methodology/approach The problem is described by the equation of motion of Stokes flow and an energy equation with a viscous dissipation term. First, the velocity field and the viscous dissipation term were determined from the momentum equation. The determined dissipation of energy and the constant temperature on the cylinder walls are the conditions for the energy equation, from which the temperature distribution and the heat flux at the boundary of the cylinders are determined. Numerical calculations were performed using the author’s own computer program based on BEM. Verification of the model was carried out by comparing the temperature determined by the BEM with the known theoretical solution for the temperature distribution between two rotating concentric cylinders. Findings As the ratio of the inner cylinder diameter to the outer cylinder diameter (r1/r2) increases, the Nusselt number increases. The angle of inclination of the function of the Nusselt number versus r1/r2 increases as the distance between the centers of the inner and outer cylinders increases. Originality/value The computational results may be used for the design of slide bearings and viscometers for viscosity testing of liquids with high viscosity where viscous dissipation is important. In the work, new integral kernels were determined for BEM needed to determine the viscous dissipation component.

Heat transfer from a circular cylinder by acoustic streaming

1967 ◽  
Vol 30 (2) ◽  
pp. 337-355 ◽  
Author(s):  
Peter D. Richardson
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Natural Convection ◽  
Circular Cylinder ◽  
Prandtl Number ◽  
Acoustic Streaming ◽  
Mean Flow ◽  
Wide Range ◽  
Transverse Oscillations ◽  
Streaming Flow

An analysis is described for convection from a circular cylinder subjected to transverse oscillations relative to the fluid in which it is immersed. The analysis is based upon use of the acoustic streaming flow field. It is assumed that the frequency involved is sufficiently small that the acoustic wavelength in the fluid is much larger than the cylinder diameter, and that there is no externally imposed mean flow across or along the cylinder. Solutions are presented which are appropriate for a wide range of Prandtl number, and the cases of small and of large streaming Reynolds number are distinguished. The analysis compares favourably with experiments when the influence of natural convection is small.

Thermal Fluid Flow Transport Characteristics in Confined Channels With Two-Dimensional Dual Jet Impingement

2011 ◽  
Author(s):  
Caner Senkal ◽  
Shuichi Torii
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Rate ◽  
Inclination Angle ◽  
Transfer Rate ◽  
Velocity Ratio ◽  
Heated Wall ◽  
Outer Diameter ◽  
Stagnation Zone ◽  
Governing Equations

The flow and heat transfer characteristics of laminar dual circular jet impinging on a heating plate with inclined confinement surface has been investigated numerically. Governing equations in steady state are solved by a control volume based finite-difference method. The simulations have been carried out for Reynolds number (250≤Re≤418), the angle of inclination of the confined upper wall (0 ≤ θ ≤ 10), circular jet to annular jet velocity ratio (0≤VR≤2) and jet to target plate distances between 2D and 8D where D is the outer diameter of dual jet.SIMPLE algorithm was used to obtain velocity and temperature fields. Hybrid difference scheme is adopted for the discretized terms in the governing equations. The discretised equations are solved iteratively using the tridiagonal matrix algorithm line solver. Heat transfer performance along the heated wall is amplified with an increase in the velocity ratio and the Reynolds number. On the contrary, a substantial reduction in the heat transfer rate, for VR = 0.0, occurs in the stagnation zone, because the absence of the inner nozzle injection causes the recirculation in the corresponding region. The heat transfer rate in the stagnation zone is attenuated by increasing the jet nozzle to impinging plate distance. In particular, the effect of the inclination angle in the down-stream region, especially at the vicinity of outlet, is major then other effects Nusselt number distribution on the impingement plate is affected by inclined upper wall because inclination of the wall accelerates the exhaust flow. The streamwise reduction in the heat transfer rate for θ = 0° is suppressed by the presence of the inclined confinement surface and its value is intensified by the inclination angle.

Low Reynolds number heat transfer from a circular cylinder

1968 ◽  
Vol 32 (1) ◽  
pp. 21-28 ◽  
Author(s):  
C. A. Hieber ◽  
B. Gebhart
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Number Theory ◽  
Circular Cylinder ◽  
Prandtl Number ◽  
Experimental Work ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Theoretical Results

Theoretical results are obtained for forced heat convection from a circular cylinder at low Reynolds numbers. Consideration is given to the cases of a moderate and a large Prandtl number, the analysis in each case being based upon the method of matched asymptotic expansions. Comparison between the moderate Prandtl number theory and known experimental results indicates excellent agreement; no relevant experimental work has been found for comparison with the large Prandtl number theory.

scholarly journals Computation of heat transfer of a plane turbulent jet impinging a moving plate

2014 ◽  
Vol 18 (4) ◽  
pp. 1259-1271 ◽  
Author(s):  
Dahbia Benmouhoub ◽  
Amina Mataoui
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Flow Field ◽  
Velocity Ratio ◽  
Local Heat Transfer ◽  
Slight Modification ◽  
Surface Velocity ◽  
Moving Plate ◽  
Jet Velocity

This study examines the performance of one point closure turbulence models in predicting of heat and momentum transfer of impinging flows. The scope of this paper is limited to impinging jet on a moving wall and heat transfer. The impinging distance is fixed to 8 thickness of the nozzle (8e) for this study. Two parameters are considered: the jet exit Reynolds number (10000?Re?25000) and the jet-surface velocity ratio (0?Rsj?4). the flow field structure at a given surface-to-jet velocity ratio is independent of the jet Reynolds number, a slight modification of the flow field is observed for low surface-to-jet velocity ratio (Rsj<0.25) whereas at higher ratios Rsj>0.25, the flow field is significantly modified. Good agreement with experimental results is obtained for surface-to-jet velocity ratio 0?Rsj?2. the purpose of this paper is to consider the case of higher of surface-to-jet velocity Rsj>2. A further study of heat transfer is achieved and shows that the stagnation points the local heat transfer coefficient have a maximum value. The local Nusselt number at the impinging region tends to decrease significantly when Rsj?1.5. The evolution of average Nusselt number is correlated according to the surface-to-jet velocity ratios for each Reynolds number.

Numerical Analysis for Heat and Mass Transfer of Granular Flow in a Duct by the Discrete Particle Simulation

2009 ◽  
Author(s):  
Tomohiko Yamaguchi ◽  
Kuniyasu Kanemaru ◽  
Satoru Momoki ◽  
Toru Shigechi ◽  
Ryo Fujiwara
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Energy Equation ◽  
Continuous Phase ◽  
Particle Simulation ◽  
Two Dimensional ◽  
Discrete Particle ◽  
One Dimensional ◽  
Discrete Particle Simulation ◽  
Dimensional Simulation

The solid-gas or liquid-gas two phase flow has many industrial applications such as spray drying, pollution control, transport systems, fluidized beds, energy conversion and propulsion, material processing, and so on. Though the solid-gas multiphase flow has been studied experimentally and numerically, the transport phenomena have not been cleared due to its complexity, computational time and economical costs for the hardware. In this study the heat and mass transfer of solid-gas collision dominated flow is analyzed by the Discrete Particle Simulation (DPS), a kind of the Dispersed Element Method (DEM)[1]. This method describes the discrete phase and the continuous phase by Lagrange and Euler methods respectively, and has been used to simulate the multiphase flow of various geometrical systems. In order to analyze the thermal field we took account of the energy equation and heat conduction between colliding particles. The heat transfer rate is summation of conductive heat transfer and convective heat transfer. Furthermore, the fluid flow has a two dimensional velocity profile, because the void fractions are analyzed as two dimensions. But momentum space has not been resolved by the two dimensional simulation. We call this method, the quasi two-dimensional simulation in this paper. To obtain the temperature distribution of the continuous phase the energy equation is solved in addition to the momentum equations. We treated the interaction between continuous and discrete phases as one and two way couplings. The positions, the momentum and the temperature information of particles and the velocity and the temperature distribution of the fluid were obtained as functions of time from results of these numerical simulations. When the hot air that is suspending small glass particles flows in a duct from bottom up, we traced the particles and got the temperature distribution of fluid and compared with the former results of one-dimensional flow. At the beginning, the cooler particles decrease the fluid temperature near the bottom of the vessel. The temperature profile of the particles obtained by the one-dimensional simulation is as same as quasi two-dimensional simulation. After 0.5 second the particles cool the downstream air. At 1.2 second, particles do not decrease the air temperature because the temperatures of particles are close to the inlet temperature of the air.

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