Natural convection in an enclosure having a vertical sidewall with time-varying temperature

1996 ◽  
Vol 329 ◽  
pp. 65-88 ◽  
Author(s):  
Ho Sang Kwak ◽  
Jae Min Hyun
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Time Varying ◽  
Vertical Sidewall ◽  
Boussinesq Fluid

A numerical study is performed for time-varying natural convection of an incompressible Boussinesq fluid in a sidewall-heated square cavity. The temperature at the cold sidewall Tc is constant, but at the hot sidewall a time-varying temperature condition is prescribed, $ T_H = \overline{T_H} + \Delta T^{\prime} \sin ft $. Comprehensive numerical solutions are found for the time-dependent Navier–Stokes equations. The numerical results are analysed in detail to show the existence of resonance, which is characterized by maximal amplification of the fluctuations of heat transfer in the interior. Plots of the dependence of the amplification of heat transfer fluctuations on the non-dimensional forcing frequency ω are presented. The failure of Kazmierczak & Chinoda (1992) to identify resonance is shown to be attributable to the limitations of the parameter values they used. The present results illustrate that resonance becomes more distinctive for large Ra and Pr ∼ 0(1). The physical mechanism of resonance is delineated by examining the evolution of oscillating components of flow and temperature fields. Specific comparisons are conducted for the resonance frequency ωr between the present results and several other previous predictions based on the scaling arguments.

A Numerical Study of the Influence of Disc Geometry on the Flow and Heat Transfer in a Rotating Cavity

1990 ◽  
Author(s):  
B. L. Lapworth ◽  
J. W. Chew
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Model Calculations ◽  
Flow And Heat Transfer ◽  
Rotating Cavity ◽  
Radial Outflow

Numerical solutions of the Reynolds-averaged Navier-Stokes equations have been used to model the influence of cobs and a bolt cover on the flow and heat transfer in a rotating cavity with an imposed radial outflow of air. Axisymmetric turbulent flow is assumed using a mixing length turbulence model. Calculations for the non-plane discs are compared with plane disc calculations and also with the available experimental data. The calculated flow structures show good agreement with the experimentally observed trends. For the cobbed and plane discs, Nusselt numbers are calculated for a combination of flow rates and rotational speeds; these show some discrepancies with the experiments, although the calculations exhibit the more consistent trend. Further calculations indicate that differences in thermal boundary conditions have a greater influence on Nusselt number than differences in disc geometry. The influence of the bolt cover on the heat transfer has also been modelled, although comparative measurements are not available.

Numerical Study of an Evaporating Meniscus on a Moving Heated Surface

Volume 3 ◽  
2004 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Numerical Study ◽  
Heated Surface ◽  
Nucleate Boiling ◽  
Two Dimensions ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Wall Heat Transfer ◽  
Parallel Plates

The present study is performed to numerically analyze an evaporating meniscus on a moving heated surface. This phenomenon is similar to the one observed at the base of a vapor bubble during nucleate boiling. The complete Navier-Stokes equations along with continuity and energy equations are solved. The liquid vapor interface is captured using the level set technique. A column of liquid is placed between two parallel plates with an inlet for water at the top to feed the meniscus. The location of water inlet at the top is kept fixed and the bottom wall is imparted with a velocity. Calculations are done in two-dimensions with a fixed distance between the plates. The main objective is to study the velocity and temperature fields inside the meniscus and calculate the wall heat transfer. The results show that the wall velocity creates a circulation near the meniscus base causing increased wall heat transfer as compared to a stationary meniscus. The local wall heat transfer is found to vary significantly along the meniscus base, the highest being near the advancing contact line.

A Numerical Study of the Influence of Disk Geometry on the Flow and Heat Transfer in a Rotating Cavity

1992 ◽  
Vol 114 (1) ◽  
pp. 256-263 ◽  
Author(s):  
B. L. Lapworth ◽  
J. W. Chew
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Model Calculations ◽  
Flow And Heat Transfer ◽  
Rotating Cavity ◽  
Radial Outflow

Numerical solutions of the Reynolds-averaged Navier–Stokes equations have been used to model the influence of cobs and a bolt cover on the flow and heat transfer in a rotating cavity with an imposed radial outflow of air. Axisymmetric turbulent flow is assumed using a mixing length turbulence model. Calculations for the non-plane disks are compared with plane disk calculations and also with the available experimental data. The calculated flow structures show good agreement with the experimentally observed trends. For the cobbed and plane disks, Nusselt numbers are calculated for a combination of flow rates and rotational speeds; these show some discrepancies with the experiments, although the calculations exhibit the more consistent trend. Further calculations indicate that differences in thermal boundary conditions have a greater influence on Nusselt number than differences in disk geometry. The influence of the bolt cover on the heat transfer has also been modeled, although comparative measurements are not available.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Numerical Simulation of the Cooling Process of Cubic Shells

2011 ◽  
Author(s):  
Manabu Okura ◽  
Kiyoaki Ono
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Numerical Code ◽  
Navier Stokes ◽  
Cooling Process ◽  
Air Velocity ◽  
Navier Stokes Equations ◽  
The Difference ◽  
The Heat Transfer Coefficient

In order to keep the environment in an air-conditioned room comfortable, it is important to anticipate the air velocity and temperature fields precisely. The numerical code, solving simultaneously the Navier-Stokes equations governing flow field inside and outside the room and the heat conduction equation applying to walls, are developed. The assumption that the heat transfer coefficient between the fluid and the surface of solids is not used. This code is applied to investigate the cooling process of a cubic shell. The computational results agree with the experimental results. We also investigated the same process of the cubic shells whose walls are internally or externally insulated. The difference of the amount of heat transfer will be discussed.

scholarly journals Natural convection melting of nano-enhanced phase change material in a cavity with finned copper profile

2018 ◽  
Vol 240 ◽  
pp. 01006 ◽  
Author(s):  
Nadezhda Bondareva ◽  
Mikhail Sheremet
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Melting Process ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Dimensional Approximation ◽  
Change Material

Present study is devoted to numerical simulation of heat and mass transfer inside a cooper profile filled with paraffin enhanced with Al2O3 nanoparticles. This profile is heated by the heat-generating element of constant volumetric heat flux. Two-dimensional approximation of melting process is described by the Navier-Stokes equations in non-dimensional variables such as stream function, vorticity and temperature. The enthalpy formulation has been used for description of the heat transfer. The influence of volume fraction of nanoparticles and intensity of heat generation on melting process and natural convection in liquid phase has been studied.

Developing Fluid Flow and Heat Transfer in a Semi-Porous Square Channel

2003 ◽  
Author(s):  
Tien-Chien Jen ◽  
Tuan-Zhou Yan ◽  
S. H. Chan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Porous Channel ◽  
Navier Stokes ◽  
Axial Position ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer

A three-dimensional computational model is developed to analyze fluid flow in a semi-porous channel. In order to understand the developing fluid flow and heat transfer process inside the semi-porous channels, the conventional Navier-Stokes equations for gas channel, and volume-averaged Navier-Stokes equations for porous media layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain in a channel using the vorticity-velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature fields at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside semi-porous channel are also analyzed in the present study.

scholarly journals Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

1974 ◽  
Vol 65 (2) ◽  
pp. 231-246 ◽  
Author(s):  
D. E. Cormack ◽  
L. G. Leal ◽  
J. H. Seinfeld
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Excellent Agreement ◽  
Asymptotic Theory ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Shallow Cavity

Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6·983, 10 ≤ Gr 2 × 104 and 0·05 [les ] A [les ] 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A [lsim ] 0·1 and Gr2A3Pr2 [lsim ] 105. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.

Numerical Study of Lateral Merger of Vapor Bubbles During Nucleate Pool Boiling

2003 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Vijay K. Dhir
Keyword(s):  
Heat Transfer ◽  
Bubble Dynamics ◽  
Stokes Equations ◽  
Numerical Study ◽  
Heating Surface ◽  
Nucleate Boiling ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Wall Heat Transfer ◽  
Simple Method

Nucleate boiling is one of the most efficient modes of heat transfer. At the start of nucleate boiling, isolated bubbles appear on the heating surface, the regime known as partial nucleate boiling. Transition from isolated bubbles to fully developed nucleate boiling occurs with increase in wall superheat, when bubbles begin to merge in vertical and lateral directions. The laterally merged bubbles form vapor mushrooms, which stay attached to the heater surface via numerous vapor stems. The present study is performed to numerically analyze the bubble dynamics and heat transfer associated with lateral bubble merger during transition from partial to fully developed nucleate boiling. The complete Navier-Stokes equations in three dimensions along with the continuity and energy equations are solved using the SIMPLE method. The liquid vapor interface is captured using the Level-Set technique. Calculations are carried out for multiple bubble-merger in a line and also in a plane and the bubble dynamics and wall heat transfer are compared to that for a single bubble. The results show that the merger process significantly increases the overall wall heat transfer. It is also found that the orientation of the bubbles strongly influences different heat transfer mechanisms.

COMPARATIVE STUDY OF THERMAL FLOWS WITH DIFFERENT FINITE VOLUME AND LATTICE BOLTZMANN SCHEMES

2004 ◽  
Vol 15 (02) ◽  
pp. 307-319 ◽  
Author(s):  
AHMAD AL-ZOUBI ◽  
GUNTHER BRENNER
Keyword(s):  
Heat Transfer ◽  
Comparative Study ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Hybrid Approach ◽  
Navier Stokes ◽  
Steady Flows ◽  
Parallel Plates

In the present paper, a comparative study of numerical solutions for steady flows with heat transfer based on the finite volume method (FVM) and the relatively new lattice Boltzmann method (LBM) is presented. In the last years, the LB methods have challenged the classical FV methods to solve the Navier–Stokes equations and have proven to be superior in accuracy and efficiency for certain applications. Most of these studies were related to the transport of mass and momentum. In the meantime, significant effort has been invested in the application of the LBM to simulate flows including heat transfer. The studies in the present paper are the analysis of performance and accuracy aspects of LBM applied to the prediction of these flows. For a fully developed laminar flow between parallel plates, analytical solutions for the heat transfer in fully developed thermal boundary layers are available and may be compared with the respective numerical results. Finally, a hybrid approach is proposed to circumvent numerical problems of the thermal LB methods.

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