Transient Natural Convection From Vertical Elements

1961 ◽  
Vol 83 (1) ◽  
pp. 61-70 ◽  
Author(s):  
B. Gebhart
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Surface Temperature ◽  
Extreme Case ◽  
Transient Behavior ◽  
Thermal Capacity ◽  
Average Surface ◽  
Transient Natural Convection ◽  
Average Surface Temperature ◽  
Prandtl Numbers

The transient natural-convection process is analyzed using an integral method of analysis. Differential equations are derived which relate average surface temperature and time for either heating or cooling for vertical elements having arbitrary thermal capacity. The equations are applicable to laminar flow for all fluids. The coefficients are Prandtl number dependent and are estimated for Prandtl numbers in the range 0.01 to 1000. A solution of the equations is presented for the extreme case of a vertical plate of negligible thermal capacity subjected to a step in flux at its surface. Fluids having Prandtl numbers of 0.01, 0.1, 0.72, 1.0, 5, 10, 100, and 1000 are considered. The results, in terms of generalized variables, are practically independent of Prandtl number. Simple one-dimensional transient behavior is followed for approximately 20 per cent of the transient with a subsequent quick approach to the asymptotic value. The results show no substantial overshoot of the average surface temperature. It is doubted that significant temperature overshoot actually occurs for vertical surfaces even for a step in flux.

Transient Natural Convection From Vertical Elements—Appreciable Thermal Capacity

1963 ◽  
Vol 85 (1) ◽  
pp. 10-14 ◽  
Author(s):  
B. Gebhart
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Boundary Layer Flow ◽  
Present Author ◽  
Thermal Capacity ◽  
Generalized Variables ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Layer Flow

Natural convection transients are considered for laminar boundary-layer flow on vertical surfaces by the method previously presented by the present author. Cases are solved for elements having finite thermal capacity as, e.g., electric heaters or reactor elements. A wide range of thermal capacity is considered for fluid Prandtl numbers in the range 0.01 to 1000; for a step in internal energy generation rate. The Prandtl number effect is shown to be very small, in the generalized variables employed, and the range of thermal capacity which results in true convection transients is clearly delineated.

Measurements and Calculations of Transient Natural Convection in Water

1982 ◽  
Vol 104 (4) ◽  
pp. 644-648 ◽  
Author(s):  
B. Sammakia ◽  
B. Gebhart ◽  
Z. H. Qureshi
Keyword(s):  
Natural Convection ◽  
Temperature Response ◽  
Vertical Surface ◽  
Constant Heat Flux ◽  
Thermal Capacity ◽  
Transient Natural Convection ◽  
Heating And Cooling ◽  
Dependent Form ◽  
Induced Flow ◽  
Explicit Finite Difference

Transient natural convection adjacent to a flat vertical surface with appreciable thermal capacity is investigated both experimentally and numerically. The surface is immersed in initially quiescent water, and has the same uniform temperature distribution. It is then suddenly loaded with a uniform and constant heat flux thereby generating a buoyancy induced flow adjacent to the surface. Surface temperature response was recorded by means of thermocouples embedded inside the surface, and boundary layer temperature measurements were also taken. An explicit finite difference numerical scheme is used to obtain solutions to the partial differential equations describing the conservation of mass, momentum, and energy in their time dependent form. Good agreement between the calculated and measured results is observed for both the heating and cooling transient processes.

Numerical Study of Three-Dimensional Oscillatory Natural Convection at Low Prandtl Number in Rectangular Enclosures

2000 ◽  
Vol 123 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Shunichi Wakitani
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Width Ratio ◽  
Three Dimensional Flow ◽  
Longitudinal Vortices ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Prandtl Numbers

Numerical investigations are presented for three-dimensional natural convection at low Prandtl numbers (Pr) from 0 to 0.027 in rectangular enclosures with differentially heated vertical walls. Computations are carried out for the enclosures with aspect ratios (length/height) 2 and 4, and width ratios (width/height) ranging from 0.5 to 4.2. Dependence of the onset of oscillation on the Prandtl number, the aspect ratio, and the width ratio is investigated. Furthermore, oscillatory, three-dimensional flow structure is clarified. The structure is characterized by some longitudinal vortices (rolls) as well as cellular pattern.

A Numerical Study of Laminar Natural Convection in Shallow Cavities

1981 ◽  
Vol 103 (2) ◽  
pp. 226-231 ◽  
Author(s):  
G. S. Shiralkar ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Numerical Study ◽  
Aspect Ratios ◽  
Shallow Cavities ◽  
Horizontal Cavity ◽  
Side Walls ◽  
Prandtl Numbers

Heat transfer by natural convection in a horizontal cavity with adiabatic horizontal walls and isothermal side walls is investigated numerically for high aspect ratios (width/height). Comparison is made with existing analytical and experimental results. Agreement is generally good at moderate and high Prandtl numbers to which most previous works have been restricted. Improvements of the existing correlation have been proposed in regions of discrepancy. Extension to the low Prandtl number case, including the range of liquid metals, has been made on the basis of an analytical model for high Rayleigh numbers as well as by numerical solution of the full equations. The agreement between the two is found to be very good. A correlation for the heat transfer is proposed for each of the two different cases of high and low Prandtl number.

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