scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

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.

Design of a Fractal Tree-Like Microchannel Net Heat Sink for Microelectronic Cooling

2006 ◽  
Author(s):  
F. J. Hong ◽  
P. Cheng ◽  
H. Ge ◽  
Teck Joo Goh
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Heat Sink ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Electronic Cooling ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Result ◽  
Parallel Microchannels

In this paper, a numerical simulation is carried to study pressure drop and heat transfer in a fractal tree-like microchannel net heat sink of 10mm×12.5mm×0.5mm in dimensions. The numerical result is obtained by solving three-dimensional Navier-Stokes equations and energy equation, taking into consideration conjugate heat transfer in the microchannel walls. A comparison of fractal tree-like microchannel net heat sink with 6 branch levels to parallel microchannels heat sink, with respect to the pressure drop, thermal resistance and temperature uniformity, was also performed under the condition of the same heat sink dimensions. The results indicates that for a mass flow rate of water less than 0.00175kg/s, the fractal tree-like microchannel is much better than parallel channel heat sink with respect to all of three aspects. Therefore, the fractal tree-like microchannels net heat sink using water as the coolant is promising to be used in the future electronic cooling industry.

Numerical Computation of Roughness Effects on Heat Transfer and Hydrodynamic Characteristics in Microchannels

2006 ◽  
Author(s):  
Heming Yun ◽  
Lin Cheng ◽  
Liqiu Wang ◽  
Binjian Chen
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Hydrodynamic Characteristics ◽  
Roughness Effects ◽  
Navier Stokes Equations ◽  
Experimental Heat ◽  
Macro Scale

In the present paper we focus our attention on the analysis of surface roughness effects. In the process of numerical simulation, a finite-volume method was used to solve the three-dimensional Navier-Stokes equations and energy equation. In turbulent region, wall-function was used to solve the temperature and velocity of coolant in the area near the wall. In all computational regions, the fluid-solid Conjugate heat transfer is used to solve the microchannel heat transfer problems. In conclusion the effect of surface roughness on heat transfer and pressure drop can not be neglected. And one should be very careful in ascribing the roughness effect to the discrepancies between experimental heat transfer and the prediction for standard macro scale channels.

Heat Transfer in Film-Cooled Turbine Blades

1993 ◽  
Author(s):  
Vijay K. Garg ◽  
Raymond E. Gaugler
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Film Cooling ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Explicit Finite Difference ◽  
Control Volumes

In order to study the effect of film cooling on the flow and heat transfer characteristics of actual turbine blades, a three-dimensional Navier-Stokes code has been developed. An existing code (Chima and Yokota, 1990) has been modified for the purpose. The code is an explicit finite difference code with an algebraic turbulence model. The thin-layer Navier-Stokes equations are solved using a general body-fitted coordinate system. The effects of film cooling have been incorporated into the code in the form of appropriate boundary conditions at the hole locations on the blade surface. Each hole exit is represented by several control volumes, thus providing an ability to study the effect of hole shape on the film-cooling characteristics. Comparison with experimental data is fair. Further validation of the code is required, however, and in this respect, there is an urgent need for detailed experimental data on actual turbine blades.

Stretching effects on the three-dimensional stability of vortices with axial flow

2002 ◽  
Vol 454 ◽  
pp. 419-442 ◽  
Author(s):  
IVAN DELBENDE ◽  
MAURICE ROSSI ◽  
STÉPHANE LE DIZÈS
Keyword(s):  
Dimensional Stability ◽  
Strain Field ◽  
Stokes Equations ◽  
Linear Equations ◽  
Three Dimensional ◽  
Axial Flow ◽  
Time Dependent ◽  
Navier Stokes ◽  
Simultaneous Action ◽  
Navier Stokes Equations

The effect of stretching on the three-dimensional stability of a viscous unsteady vortex is addressed. The basic flow, which satisfies the Navier–Stokes equations, is a vortex with axial flow subjected to a time-dependent strain field oriented along its axis. The linear equations for the three-dimensional perturbations of the stretched vortex are first reduced by using successive changes of variables to equations which are almost identical to those of the unstretched vortex but with time-dependent parameters. These equations are then numerically solved in the particular case of the Batchelor vortex with a strain field which first compresses then stretches the vortex. Through this simulation, it is qualitatively demonstrated how the simultaneous action of stretching and azimuthal vorticity may destabilize a vortex. It is also argued that it provides a possible mechanism for the vortex bursts observed in turbulence experiments.

Numerical Simulations of Three-Dimensional Flows in a Cubic Cavity With an Oscillating Lid

1993 ◽  
Vol 115 (4) ◽  
pp. 680-686 ◽  
Author(s):  
Reima Iwatsu ◽  
Jae Min Hyun ◽  
Kunio Kuwahara
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Sinusoidal Oscillations ◽  
Dependent Flow

Numerical studies are made of three-dimensional flow of a viscous fluid in a cubical container. The flow is driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions are acquired by solving the time-dependent, three-dimensional incompressible Navier-Stokes equations by employing very fine meshes. Results are presented for wide ranges of two principal physical parameters, i.e., the Reynolds number, Re ≤ 2000 and the frequency parameter of the lid oscillation, ω′ ≤ 10.0. Comprehensive details of the flow structure are analyzed. Attention is focused on the three-dimensionality of the flow field. Extensive numerical flow visualizations have been performed. These yield sequential plots of the main flows as well as the secondary flow patterns. It is found that the previous two-dimensional computational results are adequate in describing the main flow characteristics in the bulk of interior when ω′ is reasonably high. For the cases of high-Re flows, however, the three-dimensional motions exhibit additional complexities especially when ω′ is low. It is asserted that, thanks to the recent development of the supercomputers, calculation of three-dimensional, time-dependent flow problems appears to be feasible at least over limited ranges of Re.

Numerical Computation of Fluid Flow and Heat Transfer in Microchannels

2005 ◽  
Author(s):  
Ningli Liu ◽  
Rene Chevray ◽  
Gerald A. Domoto ◽  
Elias Panides
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Time Dependent ◽  
Navier Stokes ◽  
Temperature Profiles ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer

A finite difference numerical approach for solving slightly compressible, time-dependent, viscous laminar flow is presented in this study. Simplified system of Navier-Stokes equations and energy equation are employed in the study in order to perform more efficient numerical calculations. Fluid flow and heat transfer phenomena in two dimensional microchannels are illustrated numerically in this paper. This numerical approach provides a complete numerical simulation of the development of the fluid flow and the temperature profiles through multi-dimensional microchannels.

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