Transient natural convection in a cylindrical annulus

10.2514/3.944 ◽  
1997 ◽  
Vol 11 ◽  
pp. 595-597
Author(s):  
Young-Kil Yu ◽  
Ruey-Hung Chen ◽  
Larry Chew ◽  
K. Ramamurthi ◽  
K. Ravi
Keyword(s):  
Natural Convection ◽  
Transient Natural Convection ◽  
Cylindrical Annulus

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.

Natural Convection in a Porous, Horizontal Cylindrical Annulus

1994 ◽  
Vol 116 (3) ◽  
pp. 621-626 ◽  
Author(s):  
J. P. Barbosa Mota ◽  
E. Saatdjian
Keyword(s):  
Natural Convection ◽  
Initial Conditions ◽  
Hysteresis Loops ◽  
Boussinesq Equations ◽  
Radius Ratio ◽  
Fine Grid ◽  
Cylindrical Annulus ◽  
Alternating Direction ◽  
Fluid Layers ◽  
Horizontal Cylinders

Natural convection in a porous medium bounded by two horizontal cylinders is studied by solving the two-dimensional Boussinesq equations numerically. An accurate second-order finite difference scheme using an alternating direction method and successive underrelaxation is applied to a very fine grid. For a radius ratio above 1.7 and for Rayleigh numbers above a critical value, a closed hysteresis loop (indicating two possible solutions depending on initial conditions) is observed. For a radius ratio below 1.7 and as the Rayleigh number is increased, the number of cells in the annulus increases without bifurcation, and no hysteresis behavior is observed. Multicellular regimes and hysteresis loops have also been reported for fluid layers of same geometry but several differences between these two cases exist.

Effect of magnetic field on natural convection in a vertical cylindrical annulus

2006 ◽  
Vol 44 (20) ◽  
pp. 1556-1570 ◽  
Author(s):  
M. Sankar ◽  
M. Venkatachalappa ◽  
I.S. Shivakumara
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Cylindrical Annulus
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