Transient Natural Convection of Water in a Horizontal Pipe With Constant Cooling Rate Through 4°C

1976 ◽  
Vol 98 (4) ◽  
pp. 581-587 ◽  
Author(s):  
K. C. Cheng ◽  
M. Takeuchi
Keyword(s):  
Natural Convection ◽  
Transient Flow ◽  
Temperature Fields ◽  
Freezing Process ◽  
Horizontal Pipe ◽  
Transfer Rates ◽  
Transient Natural Convection ◽  
Anomalous Density ◽  
Horizontal Cylinders ◽  
Relationship Of

A theoretical analysis is carried out to study the influence of an anomalous density-temperature relationship of water on the transient natural convection in horizontal cylinders with wall temperature decreasing at a uniform rate. Numercial solutions are obtained for three cases involving different cooling rates, pipe diameters, and initial uniform water temperatures for temperature conditions between 0 and 7°C. The transient flow and temperature fields, and local and overall heat transfer rates are presented to study the inversion of flow patterns caused by the maximum density at 4°C. The numerical results are compared with the experimental measurements and predictions of a quasi-steady boundary-layer model reported by Gilpin [2], and generally a good agreement is observed. Some implications on the subsequent freezing process are pointed out.

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.

An Experimental Apparatus to Investigate Natural Convection Heat Transfer From a Vertical Array of Isothermal Horizontal Cylinders

2010 ◽  
Author(s):  
S¸evket O¨zgu¨r Atayılmaz ◽  
Hakan Demir ◽  
O¨zden Ag˘ra ◽  
I˙smail Teke
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Vertical Array ◽  
Transfer Rates ◽  
Surface Temperatures ◽  
Experimental Apparatus ◽  
Horizontal Cylinders

Steady natural convection heat transfer from vertical array of equally-spaced isothermal horizontal cylinders has been investigated experimentally and numerically. Experimental study was carried out at different ambient temperatures in a conditioned room which can be maintained at a stable required value and inside a sufficiently designed test cabin. The ambient and cylinders’ surface temperatures varied 20°C to 30°C and 30°C to 60°C respectively. The experimental apparatus was designed to adjust different operating parameters such as number of cylinders, cylinders’ surface temperatures, distance between the cylinders and environmental temperature. Each cylinder surface temperature can be accurately adjusted to the desired temperature by means of specially designed measurement and control system. Copper test cylinders have length of 1 m and outer diameter of 4.8 mm. The uncertainty analysis method proposed by Kline and McClintock was used and explained elaborately. Detailed information and algorithm of numerical method are given to ease the understanding of the numerical part of the study. The problem was solved numerically by means of a CFD program in 2D. Average Nusselt numbers are given based on the experimental data for single and each two horizontal cylinders. Heat transfer rates obtained from experimental and numerical studies for upper and lower cylinders were compared with each other. The deviation of experimental and numerical heat transfer rates are in a good agreement and stay in the range ± 20%. It is seen that heat transfer from the lower cylinder is close to the single cylinder case. However, higher temperature of the passing air reduces the heat transfer from the upper cylinder for S/D = 2.

Radiation-Natural Convection Interactions in Two-Dimensional Complex Enclosures

1983 ◽  
Vol 105 (1) ◽  
pp. 89-95 ◽  
Author(s):  
L. C. Chang ◽  
K. T. Yang ◽  
J. R. Lloyd
Keyword(s):  
Natural Convection ◽  
Finite Thickness ◽  
Wide Band ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Transfer Rates ◽  
Gas Radiation ◽  
Radiation Exchange ◽  
Radial Flux ◽  
Physical Phenomena

A numerical finite-difference study has been carried out for the two-dimensional radiation-natural convection interaction phenomena in square enclosures with equal vertical finite-thickness partitions located at the centers of the ceiling and floor. Both participating gases (CO2 and NH3) and nonparticipating gas (air) are considered. In the radiation calculations, the nongray exponential wide-band models for CO2 and NH3 are used, together with a radial flux method utilizing a more realistic polar description for the radiation exchange in the enclosure. Results on the effects of both surface and gas radiation on the velocity and temperature fields and the overall heat transfer rates as functions of the partition heights at two levels of the Grashof number are presented and discussed in terms of the physical phenomena.

Scaling of Transient Natural Convection Cooling in a Side-Cooled Cavity: The Effect of Variable Viscosity

2011 ◽  
Author(s):  
Obai Younis ◽  
Feng Xu ◽  
Chengwang Lei ◽  
John C. Patterson ◽  
Jordi Pallares ◽  
...  
Keyword(s):  
Natural Convection ◽  
Transient Flow ◽  
Variable Viscosity ◽  
Initial Growth ◽  
Transient Natural Convection ◽  
Constant Viscosity ◽  
Side Walls ◽  
Convection Cooling ◽  
Cubical Cavity ◽  
Good Agreement

The transient natural convection of variable and constant viscosity fluids in a side cooled cubical cavity is studied experimentally. The convective flow in the cavity is visualized by the shadowgraph technique. The fluid was initially preheated and enough time is allowed to assure uniform temperature distribution. Temperature difference is introduced by a sudden cooling of the two side walls. The results indicate that the transient flow development is characterized by the following distinct processes: the initial growth of the vertical boundary layer and horizontal intrusions, the interaction of the horizontal intrusions and the stratification. New scaling relations are introduced to include the effect of the viscosity variation with temperature. The new suggested scalings showed good agreement with the measurements based on the shadowgraph images.

Effet du maximum de densité sur la convection libre de l'eau dans une cavité fermée

1979 ◽  
Vol 6 (4) ◽  
pp. 481-493 ◽  
Author(s):  
L. Robillard ◽  
P. Vasseur
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Wall Temperature ◽  
Transient Flow ◽  
Coupled System ◽  
Flow Patterns ◽  
Maximum Density ◽  
Temperature Fields ◽  
Constant Wall Temperature ◽  
Square Enclosure

One of the most important factors affecting the rate of heat transfer by natural convection is the temperature–density relationship of the convecting fluid. The importance of this factor is greatly amplified when the heat is being transferred to a medium that has a maximum density at a given temperature. Water at low temperatures offers such a behavior, its density attaining a maximum value near 3.98 °C. thereafter decreasing with decreasing temperature. This phenomenon is responsible for unusual flow patterns in areas of water exposed to near freezing temperatures.This investigation is a theoretical analysis of the transient natural convection of water contained in a square enclosure with constant wall temperature. Initially the water is assumed to be at a uniform temperature above 0 °C, the wall temperature being suddenly applied.An alternating direction implicit finite-difference schema was used to solve the coupled system of partial differential equations. The transient flow and temperature fields, and local and overall heat transfer are greatly affected by the inversion of flow patterns caused by the maximum density. Their respective values for different flow situations are presented in this study.

Vector eigenfunction expansion in the integral transform solution of transient natural convection

2019 ◽  
Vol 29 (8) ◽  
pp. 2684-2708 ◽  
Author(s):  
Kleber Marques Lisboa ◽  
Jian Su ◽  
Renato M. Cotta
Keyword(s):  
Natural Convection ◽  
Eigenvalue Problem ◽  
Eigenfunction Expansion ◽  
Stokes Equations ◽  
Integral Transform ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Transient Natural Convection

Purpose The purpose of this work is to revisit the integral transform solution of transient natural convection in differentially heated cavities considering a novel vector eigenfunction expansion for handling the Navier-Stokes equations on the primitive variables formulation. Design/methodology/approach The proposed expansion base automatically satisfies the continuity equation and, upon integral transformation, eliminates the pressure field and reduces the momentum conservation equations to a single set of ordinary differential equations for the transformed time-variable potentials. The resulting eigenvalue problem for the velocity field expansion is readily solved by the integral transform method itself, while a traditional Sturm–Liouville base is chosen for expanding the temperature field. The coupled transformed initial value problem is numerically solved with a well-established solver based on a backward differentiation scheme. Findings A thorough convergence analysis is undertaken, in terms of truncation orders of the expansions for the vector eigenfunction and for the velocity and temperature fields. Finally, numerical results for selected quantities are critically compared to available benchmarks in both steady and transient states, and the overall physical behavior of the transient solution is examined for further verification. Originality/value A novel vector eigenfunction expansion is proposed for the integral transform solution of the Navier–Stokes equations in transient regime. The new physically inspired eigenvalue problem with the associated integmaral transformation fully shares the advantages of the previously obtained integral transform solutions based on the streamfunction-only formulation of the Navier–Stokes equations, while offering a direct and formal extension to three-dimensional flows.

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