Effect of Wall Conduction on Natural Convection in Symmetrically Heated Vertical Parallel Plates With Discrete Heat Sources

2002 ◽  
Author(s):  
Oronzio Manca ◽  
Sergio Nardini ◽  
Vincenzo Naso
Keyword(s):  
Heat Conduction ◽  
Natural Convection ◽  
Wall Temperature ◽  
Channel Wall ◽  
Stokes Equations ◽  
Vertical Channel ◽  
Navier Stokes ◽  
Temperature Profiles ◽  
Computational Domain ◽  
Parallel Plates

The effect of heat conduction on air natural convection in a vertical channel, symmetrically heated, with flush-mounted strips at the walls, was numerically analyzed. Reference was made to laminar two-dimensional steady-state flow and to full elliptic Navier-Stokes equations on a I-shaped computational domain. Solutions were carried out by means of the FLUENT code. Results are presented in terms of wall temperature profiles, air velocity and temperature profiles in the channel. The wall temperature is affected by the location of the strip on the channel wall and maximum wall temperature is far larger when the heater is located in the upper region of the channel. Heat conduction in the channel wall lowers maximum wall temperature below the heater and the thicker the wall the larger the temperature reduction.

Transient Analysis of Natural Convection in a Horizontal Open Ended Cavity

2002 ◽  
Author(s):  
Assunta Andreozi ◽  
Oronzio Manca ◽  
Yogesh Jaluria
Keyword(s):  
Natural Convection ◽  
Stokes Equations ◽  
Chemical Vapor ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Penetration Length ◽  
Energy Equations

The configuration of two horizontal parallel walls can be found in many applications, such as the cooling of electronic components, solar energy systems and chemical vapor deposition systems (CVD). In the present investigation a transient numerical analysis for laminar natural convection in air between two horizontal parallel plates, with the upper plate heated at uniform heat flux and the lower one unheated, is carried out by means of the finite volume method. The model was assumed to be two-dimensional. The full two-dimensional Navier-Stokes equations together with the continuity and energy equations are solved by a numerical scheme derived from a SIMPLE-like algorithm in an H-shaped domain. Results are presented in terms of velocity and temperature profiles, wall temperature profiles and the temporal behavior of several significant variables, such as the penetration length, is reported for different Rayleigh numbers and aspect ratio values.

Transient Natural Convection in Convergent Vertical Channels With Porous Media

2008 ◽  
Author(s):  
Bernardo Buonomo ◽  
Oronzio Manca ◽  
Sergio Nardini
Keyword(s):  
Porous Medium ◽  
Nusselt Number ◽  
Steady State ◽  
Natural Convection ◽  
Wall Temperature ◽  
Initial Time ◽  
Computational Domain ◽  
Parallel Plates ◽  
Convergent Channel ◽  
Transient Natural Convection

In this paper transient natural convection in a vertical convergent channel with or without saturated porous medium is studied numerically. The investigation is carried out in laminar, two dimensional regime and employing the Brinkman-Forchheimer-extended Darcy model. The physical domain consists of two non-parallel plates which form a convergent channel. Both plates are heated at uniform heat flux. The solutions are achieved using the commercial code FLUENT. A finite-extension computational domain is employed to simulate the free-stream condition. The results are obtained for different convergence angles, for 0° to 5°, and porosity coefficient (0.4, 0.6 and 0.9), a channel aspect ratio equal to 10, a Rayleigh number equal to 104 and a Darcy number equal to 0.01. The dimensionless results are reported in terms of average and maximum wall temperatures, average Nusselt number as a function of time and at steady state wall temperature, local Nusselt number and temperature and stream function fields. The cases with porous medium in the channel shows that in conductive regime dominant, at initial time, average and maximum wall temperatures are lower than the case without porous medium in the channel. For the convective regime dominant, the lowest average and maximum wall temperatures are attained for the case without porour medium in the channel. At steady state, in the inlet zone the cases with porous medium present wall temperature lower than the no porous case. In the other part of the channel the opposite behaviour is detected.

Numerical Investigation of the Natural Convection Flows for Low-Prandtl Fluids in Vertical Parallel-Plates Channels

2005 ◽  
Vol 73 (1) ◽  
pp. 96-107 ◽  
Author(s):  
Antonio Campo ◽  
Oronzio Manca ◽  
Biagio Morrone
Keyword(s):  
Natural Convection ◽  
Computational Procedure ◽  
Navier Stokes ◽  
Computational Domain ◽  
Parallel Plates ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Rate Maximum ◽  
Induced Flow ◽  
Energy Equations

Laminar natural convection of metallic fluids (Pr⪡1) between vertical parallel plate channels with isoflux heating is investigated numerically in this work. The full elliptic Navier-Stokes and energy equations have been solved with the combination of the stream function and vorticity method and the finite-volume technique. An enlarged computational domain is employed to take into account the flow and thermal diffusion effects. Results are presented in terms of velocity and temperature profiles. The investigation also focuses on the flow and thermal development inside the channel; the outcomes show that fully developed flow is attained up to Ra=103, whereas the thermal fully developed condition is attained up to Ra=104. Further, correlation equations for the dimensionless induced flow rate, maximum dimensionless wall temperatures, and average Nusselt numbers as functions of the descriptive geometrical and thermal parameters covering the collection of channel Grashof numbers 1.32×103⩽Gr∕A⩽5.0×106 and aspect ratios 5⩽A⩽15. Comparison with experimental measurements has been presented to assess the validity of the numerical computational procedure.

Numerical Investigation on Transient Natural Convection in Vertical Channels With Heated and Cooled Walls

2007 ◽  
Author(s):  
Assunta Andreozzi ◽  
Bernardo Buonomo ◽  
Oronzio Manca
Keyword(s):  
Natural Convection ◽  
Average Nusselt Number ◽  
Fluid Motion ◽  
Uniform Heat Flux ◽  
Temperature Profiles ◽  
Computational Domain ◽  
Parallel Plates ◽  
Symmetric Motion ◽  
Transient Natural Convection ◽  
Transient Problem

A description of transient natural convection in air in a vertical parallel plates channel, with one plate heated and the other one cooled at uniform heat flux, is numerically accomplished. The transient problem is two-dimensional and laminar with constant thermophysical properties. The numerical solution is carried out employing the commercial CFD code Fluent. The computational domain is made up of the physical configuration and two reservoirs, placed downstream and upstream the channel. Results are obtained for Rayleigh number between 103 and 106 and they are presented in terms of wall temperature profiles as a function of time, velocity and temperature profiles along transversal channel sections. The simulation allows to describe the fluid motion structures inside and outside the channel. A complete skew-symmetric motion is detected. For Ra≥105 temperature profiles as a function of time show periodical oscillations. For Ra≥104 overshoots are observed along the profiles and for corresponding average Nusselt number profiles dips are present.

Numerical Simulation of Transient Natural Convection in a Channel-Chimney System

2005 ◽  
Author(s):  
Assunta Andreozzi ◽  
Bernardo Buonomo ◽  
Oronzio Manca
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Wall Temperature ◽  
Velocity Profiles ◽  
Channel Height ◽  
Uniform Heat Flux ◽  
Temperature Profiles ◽  
Parallel Plates ◽  
Transient Heating ◽  
Steady State Condition

In the present numerical investigation, a transient numerical analysis for natural convection in air, between two vertical parallel plates (channel), heated at uniform heat flux, with adiabatic parallel plates downstream (chimney), is carried out by means of the finite volume method. The analyzed transient problem is two-dimensional and laminar. Results are presented in terms of wall temperature, mass flow rate and air velocity profiles. They are given at different Rayleigh number and expansion ratios (chimney gap/channel gap) for a fixed channel aspect ratio (channel height/channel gap) equal to 10 and extension ratio (channel-chimney height/channel height) equal to 2.0. Wall temperature profiles vs time show the presence of overshoots and undershoots. The comparison among the maximum wall temperatures shows that the simple channel is the most critical configuration at steady state condition, but the best configuration during the transient heating at the first overshoot. Velocity profiles in the chimney allow for identification of some different fluid dynamic behaviors such as the vortex in lower corner and the cold inflow in the chimney. According to the temperature profiles, average Nusselt number profiles as a function of time show minimum and maximum values and oscillations before the steady state.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

ANALYSIS OF A HETEROGENEOUS DOMAIN DECOMPOSITION FOR COMPRESSIBLE VISCOUS FLOW

2001 ◽  
Vol 11 (04) ◽  
pp. 565-599 ◽  
Author(s):  
CRISTIAN A. COCLICI ◽  
WOLFGANG L. WENDLAND
Keyword(s):  
Domain Decomposition ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Near Field ◽  
Outer Region ◽  
Navier Stokes ◽  
Far Field ◽  
Computational Domain ◽  
Linearized Euler Equations ◽  
Naca0012 Airfoil

We analyze a nonoverlapping domain decomposition method for the treatment of two-dimensional compressible viscous flows around airfoils. Since at some distance to the given profile the inertial forces are strongly dominant, there the viscosity effects are neglected and the flow is assumed to be inviscid. Accordingly, we consider a decomposition of the original flow field into a bounded computational domain (near field) and a complementary outer region (far field). The compressible Navier–Stokes equations are used close to the profile and are coupled with the linearized Euler equations in the far field by appropriate transmission conditions, according to the physical properties and the mathematical type of the corresponding partial differential equations. We present some results of flow around the NACA0012 airfoil and develop an a posteriori analysis of the approximate solution, showing that conservation of mass, momentum and energy are asymptotically attained with the linear model in the far field.

scholarly journals Stochastic Analysis of Natural Convection in Vertical Channels with Random Wall Temperature

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Ryoichi Chiba
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Random Process ◽  
Wall Temperature ◽  
Correlation Time ◽  
Channel Wall ◽  
Velocity Fields ◽  
Transient Temperature ◽  
Horizontal Distance ◽  
Mean Square

This study attempts to derive the statistics of temperature and velocity fields of laminar natural convection in a heated vertical channel with random wall temperature. The wall temperature is expressed as a random function with respect to time, or a random process. First, analytical solutions of the transient temperature and flow velocity fields for an arbitrary temporal variation in the channel wall temperature are obtained by the integral transform and convolution theorem. Second, the autocorrelations of the temperature and velocity are formed from the solutions, assuming a stationarity in time. The mean square values of temperature and velocity are computed under the condition that the fluctuation in the channel wall temperature can be considered as white noise or a stationary Markov process. Numerical results demonstrate that a decrease in the Prandtl number or an increase in the correlation time of the random process increases the level of mean square velocity but does not change its spatial distribution tendency, which is a bell-shaped profile with a peak at a certain horizontal distance from the channel wall. The peak position is not substantially affected by the Prandtl number or the correlation time.

Numerical Investigation of Blade Flutter at or Near Stall in Axial Flow Turbomachines

2001 ◽  
Author(s):  
Wolfgang Höhn
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Computational Domain ◽  
Compressor Cascade ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Blade Flutter

During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.

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