scholarly journals Thermal convection with generalized friction

2021 ◽  
Author(s):  
Brian Straughan
Keyword(s):  
Global Stability ◽  
Exponential Decay ◽  
Thermal Convection ◽  
Linear Instability ◽  
Instability Threshold ◽  
Temperature Fields ◽  
Perturbation Velocity ◽  
Velocity And Temperature Fields

AbstractA model for thermal convection with generalized friction is investigated. It is shown that the linear instability threshold is the same as the global stability one. In addition, decay of the energy in the $$L^2$$ L 2 norm is shown for the perturbation velocity and temperature fields. However, due to the presence of the generalized friction we establish exponential decay in the $$L^{\beta +1}$$ L β + 1 norm for the perturbation temperature, where $$\beta >1$$ β > 1 .

scholarly journals Coriolis effect on thermal convection in a rotating bidispersive porous layer

2020 ◽  
Vol 476 (2235) ◽  
pp. 20190875 ◽  
Author(s):  
F. Capone ◽  
R. De Luca ◽  
M. Gentile
Keyword(s):  
Porous Medium ◽  
Linear Theory ◽  
Porous Layer ◽  
Nonlinear Stability ◽  
Thermal Convection ◽  
Linear Instability ◽  
Instability Threshold ◽  
Coriolis Effect ◽  
Single Temperature

We obtain the linear instability and nonlinear stability thresholds for a problem of thermal convection in a rotating bidispersive porous medium with a single temperature. We show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection.

scholarly journals Lagrangian Measurements in Turbulent Thermal Convection: About the Inhomogeneity of the Velocity and Temperature Fields

2017 ◽  
Vol 20 ◽  
pp. 112-119 ◽  
Author(s):  
Olivier Liot ◽  
Julien Salort ◽  
Fanny Seychelles ◽  
Yoann Gasteuil ◽  
Jean-François Pinton ◽  
...  
Keyword(s):  
Thermal Convection ◽  
Temperature Fields ◽  
Velocity And Temperature Fields ◽  
Lagrangian Measurements

New benchmark solutions for transient natural convection in partially porous annuli

2016 ◽  
Vol 26 (3/4) ◽  
pp. 1187-1225 ◽  
Author(s):  
Nicola Massarotti ◽  
Michela Ciccolella ◽  
Gino Cortellessa ◽  
Alessandro Mauro
Keyword(s):  
Natural Convection ◽  
Free Convection ◽  
Transient Flow ◽  
Flow Behavior ◽  
Outer Radius ◽  
Temperature Fields ◽  
Content Type ◽  
Transient Natural Convection ◽  
Velocity And Temperature Fields ◽  
Benchmark Solutions

Purpose – The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference ro-ri. Moreover, several Darcy numbers have been considered. Design/methodology/approach – A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement. Findings – For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number. Research limitations/implications – A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems. Practical implications – The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility. Originality/value – This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.

Thermally Induced Flow in a Rotating Annulus Filled With a Compressible Fluid

1988 ◽  
Vol 110 (2) ◽  
pp. 134-139 ◽  
Author(s):  
M. A. Ortega ◽  
J. T. Sielawa
Keyword(s):  
Flow Field ◽  
Inner Core ◽  
Temperature Fields ◽  
Bottom Plate ◽  
Rossby Number ◽  
Thermally Induced ◽  
Coaxial Cylinders ◽  
Induced Flow ◽  
Velocity And Temperature Fields ◽  
Induced Velocity

The thermally induced flow field, in a rapidly rotating container consisting of a pair of coaxial cylinders bounded on the top and bottom by horizontal end plates, is considered. The top plate is heated and the bottom plate is cooled, both by small amounts, so that the thermal Rossby number is small, and the cylinders are supposed to be conductive. The induced velocity and temperature fields are determined by subdivision of the flow field; the equation for the central part, the inner core, is solved numerically as well as analytically.

Multigrid Numerical Solutions of Non-Isothermal Laminar Recirculating Flows

1999 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Maximilian S. Mesquita
Keyword(s):  
Numerical Solutions ◽  
Rectangular Domain ◽  
Optimal Number ◽  
Computational Effort ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Discretization Scheme ◽  
Multigrid Algorithm ◽  
Finite Volume Discretization ◽  
Velocity And Temperature Fields

Abstract The present work investigates the efficiency of the multigrid numerical method applied to solve two-dimensional laminar velocity and temperature fields inside a rectangular domain. Numerical analysis is based on the finite volume discretization scheme applied to structured orthogonal regular meshes. Performance of the correction storage (CS) multigrid algorithm is compared for different inlet Reynolds number (Rein) and number of grids. Up to four grids were used for both V- and W-cycles. Simultaneous and uncoupled temperature-velocity solution schemes were also applied. Advantages in using more than one grid is discussed. Results further indicate an increase in the computational effort for higher Rein and an optimal number of relaxation sweeps for both V- and W-cycles.

On Low-Dimensional Galerkin Modeling of Confined Twin-Jet Flow and Heat Transfer

2001 ◽  
Author(s):  
H. Gunes ◽  
K. Gocmen ◽  
L. Kavurmacioglu
Keyword(s):  
Heat Transfer ◽  
Jet Flow ◽  
Basis Functions ◽  
Galerkin Projection ◽  
Temperature Fields ◽  
Transitional Flow ◽  
Flow And Heat Transfer ◽  
Galerkin Models ◽  
Velocity And Temperature Fields ◽  
Low Dimensional

Abstract The two-dimensional incompressible non-isothermal confined twin-jet flow has been numerically studied in the transitional flow regime by a finite volume technique. Results have been obtained for the velocity and temperature distributions close to the onset of temporal oscillations. Next, the proper orthogonal decomposition (POD) is applied to the instantaneous flow and temperature data to obtain POD-based basis functions for both velocity and temperature fields. These basis functions are capable to identify the coherent structures in the velocity and temperature fields. The low-dimensional Galerkin models of the full Navier-Stokes and energy equations are constructed by the Galerkin projection onto basis functions. Since the low-dimensional Galerkin models are much easier to analyze than the full governing equations, basic insights into important mechanisms of dynamically complex flow and heat transfer (e.g. flow instabilities) can be easily studied by these models. The numerical implications, the validity of the models and their performance characteristics are discussed.

The MHD Flows for a Heated Generalized Oldroyd-B Fluid With Fractional Derivative

2010 ◽  
Author(s):  
Yaqing Liu ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fenglei Zong
Keyword(s):  
Fractional Calculus ◽  
Viscoelastic Fluid ◽  
Mhd Flow ◽  
Hankel Transform ◽  
Constitutive Relationship ◽  
Temperature Fields ◽  
Fractional Partial Differential Equations ◽  
Relation Model ◽  
Velocity And Temperature Fields ◽  
Relationship Of

In this paper, we present a circular motion of magnetohydrodynamic (MHD) flow for a heated generalized Oldroyd-B fluid. The fractional calculus approach is introduced to establish the constitutive relationship of a viscoelastic fluid. The velocity and temperature fields of the flow are described by fractional partial differential equations. Exact analytical solutions of velocity and temperature fields are obtained by using Hankel transform and Laplace transform for fractional calculus. Results for ordinary viscous flow are deduced by making the fractional order of differential tend to one and zero. It is shown that the fractional constitutive relation model is more useful than the conventional model for describing the properties of viscoelastic fluid.

Combustor Cooling Wiggle Strip and Geometrical Simplification

2008 ◽  
Author(s):  
Leiyong Jiang
Keyword(s):  
Conjugate Heat Transfer ◽  
Flow Fields ◽  
Considerable Effect ◽  
Temperature Fields ◽  
Gas Turbine Combustor ◽  
Temperature Prediction ◽  
Average Temperature ◽  
Velocity And Temperature Fields ◽  
Cooling Element ◽  
Combustor Liner

The flow fields of a combustor cooling wiggle strip and its corresponding simplified slot with conjugate heat transfer have been studied numerically. The effects of geometrical simplification on the flow fields have been analysed qualitatively and quantitatively. It is found that its effects on the flow velocity and temperature fields are limited to local regions near the cooling element, and are negligible in the far field. However, the simplification shows a considerable effect on the combustor liner temperature near the cooling element, about 8.5% of the average temperature across the cooling element. In short, using the simplified slot to replace the cooling wiggle strip in gas turbine combustor modeling is an acceptable practice if accurate liner temperature prediction is not required.

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