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.

Axisymmetric Stagnation—Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration

2006 ◽  
Vol 129 (1) ◽  
pp. 106-115 ◽  
Author(s):  
A. B. Rahimi ◽  
R. Saleh
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Angular Velocity ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer ◽  
Self Similar

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Γ. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers, Re=Γa2∕2υ, ranging from 0.1 to 1000 for different values of Prandtl number and for selected values of dimensionless transpiration rate, S=U0∕Γa, where a is cylinder radius and υ is kinematic viscosity of the fluid. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder rotating with certain exponential angular velocity function and at particular value of Reynolds number is azimuthally stress-free. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number, and Prandtl number. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration.

Temporally- and Spatially-Periodic Laminar Flow and Heat Transfer in Staggered-Plate Arrays

2007 ◽  
Author(s):  
Alexandre Lamoureux ◽  
B. Rabi Baliga
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Plate Thickness ◽  
Geometrical Parameters ◽  
Reduced Pressure ◽  
Flow And Heat Transfer ◽  
Spatially Periodic

A computational investigation of temporally- and spatially-periodic laminar two-dimensional fluid flow and heat transfer in staggered-plate arrays is presented in this paper. The objective and the novel aspect of this study is the investigation of the influence (on the numerical solutions) of including single and multiple representative geometric modules in the calculation domain, with spatially-periodic boundary conditions imposed on the instantaneous velocity and temperature fields in both the streamwise and the lateral directions. The following geometrical parameters, normalized with respect to a representative module height, were studied: a dimensionless plate length equal to 1, and a dimensionless plate thickness of 0.250. This relatively high value of dimensionless plate thickness, compared to those commonly encountered in rectangular offset-fin cores of compact heat exchangers, was deliberately chosen to induce and enhance the unsteady features of the fluid flow and heat transfer phenomena. Different specified values of the time-mean modular streamwise gradient of the reduced pressure were investigated, yielding values of Reynolds number (Kays and London definition) in the range of 100 to 625. The Prandtl number was fixed at 0.7. In the multiple-module simulations, for Reynolds number values exceeding 400, it was found that multiple solutions are possible: the particular solution which is obtained in any one simulation depends on the specified initial conditions. The results presented include time-mean modular friction factors, modular Colburn factors, and Strouhal numbers.

Effects of Suction and Blowing on Flow and Heat Transfer Between Two Rotating Spheres With Time-Dependent Angular Velocities

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Omid Mahian ◽  
Asgahr B. Rahimi ◽  
Ali Jabari Moghadam
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Flow Parameters ◽  
Flow And Heat Transfer ◽  
Concentric Spheres ◽  
Different Temperatures ◽  
Angular Velocities ◽  
Viscous Torque ◽  
Suction And Blowing ◽  
Special Case

The effect of suction and blowing in the study of flow and heat transfer of a viscous incompressible fluid between two vertically eccentric rotating spheres is presented when the spheres are maintained at different temperatures and rotating about a common axis while the angular velocities of the spheres are arbitrary functions of time. The resulting flow pattern, temperature distribution, and heat transfer characteristics are presented for the various cases including exponential and sinusoidal angular velocities. These presentations are for various values of the flow parameters including rotational Reynolds number Re, and the blowing/suction Reynolds number Rew. The effects of transpiration and eccentricity on viscous torques at the inner and outer spheres are studied, too. As the eccentricity increases and the gap between the spheres decreases the viscous torque remains nearly unchanged. Results for special case of concentric spheres are obtained by letting eccentricity tend to zero.

scholarly journals Periodically fully developed laminar flow and heat transfer in a two-dimensional horizontal channel with staggered fins

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2443-2455 ◽  
Author(s):  
Oğuz Turgut ◽  
Kamil Arslan
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Prandtl Number ◽  
Friction Factor ◽  
Horizontal Channel ◽  
Flux Boundary Condition ◽  
Working Fluids ◽  
Flow And Heat Transfer ◽  
Smooth Channel

The 2-D periodically fully developed laminar forced convection fluid flow and heat transfer characteristics in a horizontal channel with staggered fins are investigated numerically under constant wall heat flux boundary condition. Study is performed using ANSYS Fluent 6.3.26 which uses finite volume method. Air (Pr @ 0.7) and Freon-12 (Pr @ 3.5) are used as working fluids. Effects of Reynolds number, Prandtl number, fin height, and distances between two fins on heat transfer and friction factor are examined. Results are given in the form of non-dimensional average Nusselt number and average Darcy friction factor as a function of Reynolds number for different fin distances and Prandtl numbers. The velocity and temperature profiles are also obtained. It is seen that as the fin distance increases, behavior approaches the finless channel, as expected. Also, thermal enhancement factors are given graphically for working fluids. It is seen that heat transfer dominates the friction as both the distance between two fins and Prandtl number increase. It is also seen that fins having blockage ratio of 0.10 in 2-D periodically fully developed laminar flow is not advantageous in comparison to smooth channel without fins.

Mixed Convection Heat Transfer From a Square Cylinder to Power-Law Fluids in Cross-Flow

2006 ◽  
Author(s):  
N. Anjaiah ◽  
A. K. Dhiman ◽  
R. P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Steady Flow ◽  
Power Law ◽  
Richardson Number ◽  
Square Cylinder ◽  
Flow And Heat Transfer ◽  
Power Law Fluids

Laminar mixed convection flow and heat transfer to power-law fluids from a square cylinder has been analyzed numerically in the steady flow regime. The full momentum and energy equations along with the Boussinesq approximation have been solved by using a SMAC implicit finite difference method implemented on an uniform staggered grid arrangement for the range of Reynolds number 5 to 40, power-law index 0.6 to 1.4, Prandtl number 1 to 10 and Richardson number 0 to 0.5 in both bounded and unbounded flow configurations. The wall effects have been studied for a fixed blockage ratio of 1/15. The effects of buoyancy on the flow and heat transfer characteristics of power-law fluids have been elucidated. It is found that the mixed convection can initiate an asymmetry in the flow and temperature fields even within the steady flow regime. The variation of drag coefficients, and of the Nusselt number have been reported for a range of values of the Reynolds number, Prandtl number and Richardson number for both shear thickening and shear thinning fluids.

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.

A Numerical Study of Unsteady Laminar Flow and Heat Transfer Through an Array of Rotating Rectangular Microchannels

2011 ◽  
Author(s):  
Pratanu Roy ◽  
N. K. Anand ◽  
Debjyoti Banerjee
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Fluid Transport ◽  
Stokes Equations ◽  
Numerical Study ◽  
Simple Algorithm ◽  
Centrifugal Microfluidics ◽  
Rectangular Microchannels ◽  
Flow And Heat Transfer

Centrifugal microfluidics plays an important role for enabling many novel applications in life sciences. By controlling the rotating frequency, fluids can be handled and controlled without any actual pumps, actuators or active valves, resulting in cost effective and miniaturized techniques for fluid transport, valving, metering, switching, splitting and separation of fluids. In order to get a vivid picture of the underlying physics of centrifugal microfluidics, we have modeled and simulated fluid flow and heat transfer for water flowing through an array of rotating rectangular microchannels. A finite volume technique based on semi implicit pressure based equation (SIMPLE) algorithm has been developed to solve the Naiver-Stokes equations for unsteady laminar flow. The energy equation has been solved by applying repeated thermal boundary conditions at the wall in cross stream direction. The simulations show significant deviation of velocity and temperature profiles for rotating flow than those of non-rotating case. The results are presented for different flow Reynolds number and rotational Reynolds number.

Numerical Simulation of Laminar Flow and Heat Transfer Over a Blunt Flat Plate in Square Channel

2001 ◽  
Vol 124 (1) ◽  
pp. 8-16 ◽  
Author(s):  
Hideki Yanaoka ◽  
Hiroyuki Yoshikawa ◽  
Terukazu Ota
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Flat Plate ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Region ◽  
Recirculation Region ◽  
Square Channel ◽  
Flow And Heat Transfer ◽  
Side Walls

Three-dimensional simulations of laminar separated and reattached flow and heat transfer over a blunt flat plate in a square channel are presented. Numerical calculations of Navier-Stokes equations and energy equation are carried out using the finite difference method. Results of three-dimensional calculation are compared with two-dimensional ones and effects of the side walls are described. It is clarified from the present results that the reattachment length increases with an increase of Reynolds number and the flow in the recirculation region becomes three-dimensional. The reattachment line is curved by the side wall effects. Two-dimensionality of the flow is reduced as Reynolds number increases. The horseshoe-vortex formed near the side walls has great effects upon the heat transfer in the redeveloping flow region. The separated shear layer around the center of plate becomes unstable with a further increase of Reynolds number and the vortices are periodically shed from the reattachment flow region. Such vortices exhibit a hairpin-like structure and greatly influence the heat transfer.

Taylor vortices between two concentric rotating spheres

1982 ◽  
Vol 119 ◽  
pp. 1-25 ◽  
Author(s):  
Fritz Bartels
Keyword(s):  
Reynolds Number ◽  
Finite Difference ◽  
Flow Field ◽  
Critical Reynolds Number ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Finite Difference Methods ◽  
Taylor Vortices ◽  
Concentric Spheres ◽  
Inner Sphere

The laminar viscous flow in the gap between two concentric spheres is investigated for a rotating inner sphere. The solution is obtained by solving the Navier-Stokes equations by means of finite-difference techniques, where the equations are restricted to axially symmetric flows. The flow field is hydrodynamically unstable above a critical Reynolds number. This investigation indicates that the critical Reynolds number beyond which Taylor vortices appear is slightly higher in a spherical gap than for the flow between concentric cylinders. The formation of Taylor vortices could be observed only for small gap widths s ≤ 0·17. The final state of the flow field depends on the initial conditions and the acceleration of the inner sphere. Steady and unsteady flow modes are predicted for various Reynolds numbers and gap widths. The results are in agreement with experiment if certain accuracy conditions of the finite-difference methods are satisfied. It is seen that the equatorial symmetry is of great importance for the development of the Taylor vortices in the gap.

Numerical Modeling and Physical Simulation of Vortex Heat Transfer Enhancement Mechanisms Over Dimpled Reliefs

2010 ◽  
Author(s):  
Alexander I. Leontiev ◽  
Sergey A. Isaev ◽  
Nikolai V. Kornev ◽  
Yaroslav Chudnovsky ◽  
Egon Hassel
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Physical Simulation ◽  
Stokes Equations ◽  
Numerical Study ◽  
Narrow Channel ◽  
Discrete Models ◽  
Navier Stokes ◽  
Heat Output ◽  
Flow And Heat Transfer

The paper presents a comprehensive analysis of conditions for numerical simulation and physical modeling of convective heat transfer in the vicinity of dimpled surface relief. Contradictory results, unreasonable assumptions, and non-justified conclusions are marked. Based on the analysis of physical experiments the correlation between the predictions and measured data is discussed. Detailed numerical study of turbulent air flow and heat transfer in the narrow channel with three types of dimples (spherical, conic and oval) was carried out. Various mathematical and discrete models, including, those based on solving Reynolds-averaged Navier-Stokes equations (RANS/URANS-SST), and also adaptive scale models (SAS-SST) are compared. The influence of flow parameters (Reynolds number) and geometric sizes (dimple diameter, depth, radius of rounding off of an edge, channel width and height) on local and integral characteristics of flow and heat transfer (total heat output and hydraulic losses) is determined. Special attention is given to reorganizing vortex structures and flow regime (with periodic fluctuations) with increasing relative dimple depth and Reynolds number. For the first time the influence of the scale factor of a constant cross-section channel is detailed. Thermal-hydraulic characteristics of various dimpled reliefs are compared, and the advantage of an oval dimple over a spherical one is shown.

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