Final Design Parameter Settings for a Physically-Realizable Uniform Temperature Boundary Condition Specification on a Wall of an Enclosure

2013 ◽  
Author(s):  
P. Y. C. Lee ◽  
W. H. Leong
Keyword(s):  
Boundary Condition ◽  
Natural Convection ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Design Parameters ◽  
Uniform Temperature ◽  
Original Design ◽  
Temperature Boundary ◽  
Contact Width ◽  
Temperature Boundary Condition

Design parameters based on a three-dimensional internal natural convection heat transfer in a cubical apparatus are presented so that a uniform temperature boundary condition specification on a wall of the apparatus can be physically achieved. Preliminary temperature measurements based on the initial design of the apparatus where the uniform boundary condition was prescribed revealed that a temperature non-uniformity existed in the excess of 4% error. In order to complete the objective of the benchmark internal natural convection study, the apparatus had to be modified so that the temperature non-uniformity can be reduced to less than 1% error. It was decided that the original design be modified by simply adding two auxiliary heaters in the vicinity of the wall where the uniform temperature profile was desired. Before the implementation of the auxiliary heaters onto the apparatus, a detailed mathematical analysis was conducted to determine the position and the contact width of the heaters, and to establish an appropriate heat flux required to reduce the temperature non-uniformity to less than 1% along the wall of the apparatus. This analysis was achieved by using the approximate analytical temperature solution obtained from the boundary value problem of a plate (which is one part of the apparatus) with boundary conditions prescribed to model the auxiliary heaters. Previously, a specific set of design parameters were used that reduced the temperature non-uniformity to less than 1% along a wall of the modified cubical apparatus. As an extension to the previous work, this paper presents a generalized set of design parameters that can equally prescribe a physically-realizable uniform temperature setting along a wall of an enclosure to within 1% error. With the range of design parameters, this would enable any designer with the flexibility in choosing what parameters can be allocated based on their need.

On the Reduction of Wall Temperature Non-Uniformity of a Three-Dimensional Experimental Apparatus

2009 ◽  
Author(s):  
P. Y. C. Lee ◽  
W. H. Leong
Keyword(s):  
Heat Source ◽  
Temperature Difference ◽  
Mathematical Analysis ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Measured Temperature ◽  
Uniform Temperature ◽  
Original Design ◽  
Experimental Apparatus ◽  
Detailed Mathematical Analysis

This paper presents a detailed analysis that was performed for the design of a “uniform” temperature boundary condition imposed on a boundary of a three-dimensional cubical experimental apparatus for benchmark natural convection heat transfer study. The three-dimensional experimental apparatus was constructed with plates which were assembled to act as boundary conditions to the enclosure walls. Test measurements revealed that temperature non-uniformity along one of the plates (boundary) was significant enough that the benchmark study could not be carried out to the desired accuracy of about 1% error. A subsequent detailed mathematical analysis revealed that the temperature non-uniformity on the plate was a result of the effect of thermal spreading/constriction resistance. Modifications to the original design of the apparatus were made to reduce the temperature non-uniformity on the plate by adding a heat source around the plate where the uniform temperature setting was desired. Before the addition of this heat source, a careful mathematical analysis shows a significant reduction in temperature non-uniformity from about 4% (based on the initial design) to less than 1% (for the modified design). By examining the temperature difference between two locations on the plate, the predicted temperature difference obtained through mathematical analyses show excellent agreement with the measured temperature difference.

Experimental Investigation of Natural Convection Losses From Open Cavities

1984 ◽  
Vol 106 (2) ◽  
pp. 333-338 ◽  
Author(s):  
C. F. Hess ◽  
R. H. Henze
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Boundary Layer Transition ◽  
Transition To Turbulence ◽  
Layer Transition ◽  
Turbulence Flow ◽  
Temperature Boundary ◽  
Open Cavities ◽  
Rayleigh Numbers ◽  
Temperature Boundary Condition

Experimental results for natural convection in a cavity are reported. Both constrained and unconstrained cavity geometries were studied. Detailed velocity profiles were obtained using Laser doppler velocimetry for Rayleigh numbers between 3 × 1010 and 2 × 1011, corresponding to a constant elevated wall temperature boundary condition. Characteristics of two-dimensional and three-dimensional flows obtained with dye flow visualization are discussed, including boundary layer transition to turbulence, flow patterns in the cavity, and flow outside of the cavity. Local Nusselt number is correlated with local Rayleigh number for constrained and unconstrained cavities.

Natural Convection from a Horizontal Cylinder—Laminar Regime

1981 ◽  
Vol 103 (3) ◽  
pp. 522-527 ◽  
Author(s):  
B. Farouk ◽  
S. I˙. Gu¨c¸eri
Keyword(s):  
Natural Convection ◽  
Horizontal Cylinder ◽  
Heat Transfer Characteristics ◽  
Convective Flows ◽  
Finite Difference Numerical Method ◽  
Temperature Boundary ◽  
Recirculation Zones ◽  
Boussinesq Fluid ◽  
Temperature Boundary Condition ◽  
Good Agreement

A finite-difference numerical method has been adopted to generate flow patterns and heat transfer characteristics for laminar, steady-state, two-dimensional natural convection around a circular cylinder submerged in an unbounded Boussinesq fluid. The approach allows the use of nonuniform as well as uniform specified temperature and heat flux distributions over the cylindrical surface. Part of the results are generated for reverse convective flows with recirculation zones which occur when part of the cylinder is below the ambient temperature while the remaining part is above. The results for uniform temperature boundary condition are in good agreement with the experimental data and other solutions available in literature.

scholarly journals An integral relationship for a fractional one-phase Stefan problem

2018 ◽  
Vol 21 (4) ◽  
pp. 901-918 ◽  
Author(s):  
Sabrina Roscani ◽  
Domingo Tarzia
Keyword(s):  
Boundary Condition ◽  
Stefan Problem ◽  
One Dimensional ◽  
Similarity Type ◽  
Integral Relationship ◽  
Temperature Boundary ◽  
Liouville Derivative ◽  
The One ◽  
Stefan Condition ◽  
Temperature Boundary Condition

Abstract A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered by using the Riemann–Liouville derivative. This formulation is more convenient than the one given in Roscani and Santillan (Fract. Calc. Appl. Anal., 16, No 4 (2013), 802–815) and Tarzia and Ceretani (Fract. Calc. Appl. Anal., 20, No 2 (2017), 399–421), because it allows us to work with Green’s identities (which does not apply when Caputo derivatives are considered). As a main result, an integral relationship between the temperature and the free boundary is obtained which is equivalent to the fractional Stefan condition. Moreover, an exact solution of similarity type expressed in terms of Wright functions is also given.

Visualization and Prediction of Natural Convection of Water Near Its Density Maximum in a Tall Rectangular Enclosure at High Rayleigh Numbers

2000 ◽  
Vol 123 (1) ◽  
pp. 84-95 ◽  
Author(s):  
C. J. Ho ◽  
F. J. Tu
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Convection Flow ◽  
Oscillatory Convection ◽  
Uniform Temperature ◽  
Density Maximum ◽  
Rectangular Enclosure ◽  
Rayleigh Numbers

An experimental and numerical investigation is presented concerning the natural convection of water near its maximum-density in a differentially heated rectangular enclosure at high Rayleigh numbers, in which an oscillatory convection regime may arise. The water in a tall enclosure of Ay=8 is initially at rest and at a uniform temperature below 4°C and then the temperature of the hot vertical wall is suddenly raised and kept at a uniform temperature above 4°C. The cold vertical wall is maintained at a constant uniform temperature equal to that of the initial temperature of the water. The top and bottom walls are insulated. Using thermally sensitive liquid crystal particles as tracers, flow and temperature fields of a temporally oscillatory convection was documented experimentally for RaW=3.454×105 with the density inversion parameter θm=0.5. The oscillatory convection features a cyclic sequence of onset at the lower quarter-height region, growth, and decay of the upward-drifting secondary vortices within counter-rotating bicellular flows in the enclosure. Two and three-dimensional numerical simulations corresponding to the visualization experiments are undertaken. Comparison of experimental with numerical results reveals that two-dimensional numerical simulation captures the main features of the observed convection flow.

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