Validation of a Thermal Spreading/Constriction Resistance Model for a Convectively Cooled Plate With an Applied Heat Flux

2008 ◽  
Author(s):  
P. Y. C. Lee ◽  
W. H. Leong
Keyword(s):  
Heat Flux ◽  
General Solution ◽  
Neumann Boundary ◽  
Solution Technique ◽  
Two Dimensional ◽  
Experimental Heat ◽  
Experimental Heat Transfer ◽  
Present Solution ◽  
Resistance Model ◽  
Dimensional Boundary

A thermal resistance model of a two-dimensional boundary value problem (BVP) that is commonly found in engineering/experimental heat transfer is presented. The problem consists of two different convectively cooled sub-sections along one boundary, and a heat flux distribution imposed on a portion of another (opposite) boundary, coupled with adiabatic conditions (Neumann boundary conditions) along the remaining boundaries under steady-state conditions. In solving this BVP, the solution technique is highlighted. Consistent with theory, the solution to this problem depends on two Biot numbers, dimensionless heat flux and other dimensionless geometric parameters related to the problem. The present solution is an exact general solution to an existing two-dimensional problem found in literature, and as a special case, the general solution reduces exactly to the existing solution. Also, the present model is validated by comparing the present solution with measured data, and in terms of a temperature difference between two locations on the plate, the analytical solution is well within the experimental error of 0.03 K.

Design of Two-Dimensional Free Streamline Suction Slots for Parallel Channels

1965 ◽  
Vol 16 (3) ◽  
pp. 243-259
Author(s):  
W. T. F. Lau
Keyword(s):  
General Solution ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Potential Flow ◽  
Adverse Pressure Gradient ◽  
Flow Theory ◽  
Two Dimensional ◽  
Present Solution ◽  
Free Streamlines ◽  
Parallel Channels

SummaryA general solution is obtained by using potential flow theory for the design of two-dimensional suction slots for parallel channels. These slots are formed by free streamlines and are so arranged that the channel walls are free from adverse pressure gradient. Where suction slots are intended for the control of boundary layers, the present solution can only be used as a basis for experiment. It is interesting to note that the results also suggest a new method for the design of diffusers by suction.

Turbulent Heat Transport in a Boundary Layer Behind a Junction of a Streamlined Cylinder and a Wall

1992 ◽  
Vol 114 (4) ◽  
pp. 840-849 ◽  
Author(s):  
D. E. Wroblewski ◽  
P. A. Eibeck
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Vortex Shedding ◽  
Turbulent Heat Flux ◽  
Temperature Fields ◽  
Turbulent Heat ◽  
Two Dimensional ◽  
Wake Region ◽  
Dimensional Boundary ◽  
Shedding Frequency

Measurements of the turbulent velocity and temperature fields were made in a heated boundary layer 14 diameters downstream of a junction of a tapered cylinder and a wall (ReD = 24,700). The boundary layer is strongly affected by the presence of large-scale unsteadiness arising from vortex shedding, which appears in the measurements as “turbulence” with a strong spectral component at the shedding frequency. The boundary layer exhibits three distinct spanwise regions: (1) the innerwake region, z/D<0.8, where vortex shedding effects are observed only in the spanwise component of the fluctuations; (2) the middle-wake region, 0.8<z/D<1.6, where strong vortex shedding is seen in all three components of the fluctuations; and (3) the outer-wake region, z/D>1.6, where the flow is approaching a two-dimensional boundary-layer flow. Cross-spectra of νθ indicate that vortex shedding increases the turbulent heat flux in the middle-wake region. However, peak values of the Stanton number and the eddy diffusivity are observed in the inner-wake region, where the cross-spectra of turbulent heat flux do not exhibit a peak near the shedding frequency, but do show an increase compared to a two-dimensional boundary layer over a much broader frequency range.

scholarly journals Explicit Solution of Elastostatic Boundary Value Problems for the Elastic Circle with Voids

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Ivane Tsagareli
Keyword(s):  
General Solution ◽  
Boundary Value Problems ◽  
Simple Structure ◽  
Boundary Value ◽  
System Of Equations ◽  
Two Dimensional ◽  
System Of Differential Equations ◽  
Elementary Functions ◽  
Regular Solutions ◽  
Dimensional Boundary

We solve the static two-dimensional boundary value problems for an elastic porous circle with voids. Special representations of a general solution of a system of differential equations are constructed via elementary functions which make it possible to reduce the initial system of equations to equations of simple structure and facilitate the solution of the initial problems. Solutions are written explicitly in the form of absolutely and uniformly converging series. The question pertaining to the uniqueness of regular solutions of the considered problems is investigated.

Inverse Solution of Radiative Heat Transfer in Two-Dimensional Irregularly Shaped Enclosures

2000 ◽  
Author(s):  
Hakan Ertürk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Industrial Applications ◽  
Dominant Mode ◽  
Inverse Solution ◽  
Solution Technique ◽  
Complex Geometries ◽  
Two Dimensional

Abstract An inverse solution technique is used to predict the necessary temperature and heat flux distributions of the heater section of a two-dimensional enclosure so the heater satisfies the specified heat flux and temperature distributions of design surfaces, while satisfying one thermal boundary condition for the other walls. Radiation is the dominant mode of heat transfer in systems where high temperatures are present; therefore, it is considered as the only mode of heat transfer in this study. The two-dimensional enclosures considered in this study are made up of straight segments, positioned so that they form irregularly shaped enclosures approximating situations for many of the real cases in industrial applications. The enclosure walls are gray, emitting diffusely and reflecting either diffusely or specularly. The medium inside the enclosure may be transparent, absorbing-emitting or absorbing-emitting and isotropically scattering. For the participating medium cases, the gray medium is considered as isothermal, homogeneous and isotropically scattering. The Monte Carlo method is used for formulation of radiative heat transfer. The method is preferred for its accuracy and ease of handling complex geometries and various surface and medium properties. The main contribution of this study is to solve inverse design problems for complex geometries that contain blockage and shading effects, as could be the case in many real industrial applications. The resulting system of equations, which includes Fredholm equations of the first kind, is known to be highly ill-conditioned in nature. The solution for this ill-conditioned system is handled by the conjugate gradient method, an iterative solution method, which obtains smooth and very accurate solutions in a few steps for linear systems.

On the solution to a two-dimensional boundary value problem of heat conduction in a degenerating domain

2020 ◽  
Vol 98 (2) ◽  
pp. 100-109
Author(s):  
Minzilya T. Kosmakova ◽  
◽  
Valery G. Romanovski ◽  
Dana M. Akhmanova ◽  
Zhanar M. Tuleutaeva ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Two Dimensional ◽  
Dimensional Boundary
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