scholarly journals Convection in an internally heated stratified heterogeneous reservoir

2019 ◽  
Vol 870 ◽  
pp. 67-105 ◽  
Author(s):  
Angela Limare ◽  
Claude Jaupart ◽  
Edouard Kaminski ◽  
Loic Fourel ◽  
Cinzia G. Farnetani
Keyword(s):  
Heat Source ◽  
Scaling Laws ◽  
Lower Layer ◽  
Thermal Structure ◽  
Internal Heat ◽  
Source Distribution ◽  
Heat Sources ◽  
Homogeneous Fluid ◽  
Earth’S Mantle ◽  
Lower Fluid

The Earth’s mantle is chemically heterogeneous and probably includes primordial material that has not been affected by melting and attendant depletion of heat-producing radioactive elements. One consequence is that mantle internal heat sources are not distributed uniformly. Convection induces mixing, such that the flow pattern, the heat source distribution and the thermal structure are continuously evolving. These phenomena are studied in the laboratory using a novel microwave-based experimental set-up for convection in internally heated systems. We follow the development of convection and mixing in an initially stratified fluid made of two layers with different physical properties and heat source concentrations lying above an adiabatic base. For relevance to the Earth’s mantle, the upper layer is thicker and depleted in heat sources compared to the lower one. The thermal structure tends towards that of a homogeneous fluid with a well-defined time constant that scales with $Ra_{H}^{-1/4}$, where $Ra_{H}$ is the Rayleigh–Roberts number for the homogenized fluid. We identified two convection regimes. In the dome regime, large domes of lower fluid protrude into the upper layer and remain stable for long time intervals. In the stratified regime, cusp-like upwellings develop at the edges of large basins in the lower layer. Due to mixing, the volume of lower fluid decreases to zero over a finite time. Empirical scaling laws for the duration of mixing and for the peak temperature difference between the two fluids are derived and allow extrapolation to planetary mantles.

scholarly journals Trapped modes of internal waves in a channel spanned by a submerged cylinder

1993 ◽  
Vol 254 ◽  
pp. 113-126 ◽  
Author(s):  
Nikolay Kuznetsov
Keyword(s):  
Internal Waves ◽  
Lower Layer ◽  
Constant Density ◽  
Infinite Length ◽  
Operator Family ◽  
Trapped Modes ◽  
Homogeneous Fluid ◽  
Quadratic Operator ◽  
Finite Set ◽  
Lower Fluid

A horizontal channel of infinite length and depth and of constant width contains inviscid, incompressible, two-layer fluid under gravity. The upper layer has constant finite depth and is occupied by a fluid of constant density ρ*. The lower layer has infinite depth and is occupied by a fluid of constant density ρ > ρ*. The parameter ε = (ρ/ρ*)–1 is assumed to be small. The lower fluid is bounded internally by an immersed horizontal cylinder which extends right across the channel and has its generators normal to the sidewalls. The free, time-harmonic oscillations of fluid, which have finite kinetic and potential energy (such oscillations are called trapped modes), are investigated. Trapped modes in homogeneous fluid above submerged cylinders and other obstacles are well known. In the present paper it is shown that there are two sets of frequencies of trapped modes for the two-layer fluid. The frequencies of the first finite set are close to the frequencies of trapped modes in the homogeneous fluid (when ρ* = ρ). They correspond to the trapped modes of waves on the free surface of the upper fluid. The frequencies of the second finite set are proportional to ε, and hence, are small. These latter frequencies correspond to the trapped modes of internal waves on the interface between two fluids. To obtain these results the perturbation method for a quadratic operator family was applied. The quadratic operator family with bounded, symmetric, linear, integral operators in the space L2(−∞, +∞) arises as a result of two reductions of the original problem. The first reduction allows to consider the potential in the lower fluid only. The second reduction is the same as used by Ursell (1987).

scholarly journals Numerical Investigation on Two-Phase Flow Heat Transfer Performance and Instability with Discrete Heat Sources in Parallel Channels

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4408
Author(s):  
Changming Hu ◽  
Rui Wang ◽  
Ping Yang ◽  
Weihao Ling ◽  
Min Zeng ◽  
...  
Keyword(s):  
Heat Source ◽  
Heat Transfer Performance ◽  
Source Distribution ◽  
Phase Flow ◽  
Heat Sources ◽  
Two Phase ◽  
Discrete Heat Sources ◽  
Discrete Heat Source ◽  
Parallel Channels ◽  
Heat Source Distribution

With the rapid development of integrated circuit technology, the heat flux of electronic chips has been sharply improved. Therefore, heat dissipation becomes the key technology for the safety and reliability of the electronic equipment. In addition, the electronic chips are distributed discretely and used periodically in most applications. Based these problems, the characteristics of the heat transfer performance of flow boiling in parallel channels with discrete heat source distribution are investigated by a VOF model. Meanwhile, the two-phase flow instability in parallel channels with discrete heat source distribution is analyzed based on a one-dimensional homogeneous model. The results indicate that the two-phase flow pattern in discrete heat source distribution is more complicated than that in continuous heat source distribution. It is necessary to optimize the relative position of the discrete heat sources, which will affect the heat transfer performance. In addition, compared with the continuous heat source, the flow stability of discrete heat sources is better with higher and lower inlet subcooling. With a constant sum of heating power, the greater the heating power near the outlet, the better the flow stability.

scholarly journals RESULTS OF SIMPLIFIED MATHEMATICAL MODELING OF LIQUID TEMPERATURE DISTRIBUTIONIN THE HEAT EXCHANGE CHANNEL OF AN ELECTRIC HEATER WITH AN INTERNAL HEAT SOURCE

2021 ◽  
pp. 117-122
Author(s):  
A.A. Bagaev ◽  
◽  
S.O. Bobrovskiy ◽  
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Heat Exchange ◽  
Heat Source ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Heat Sources ◽  
Internal Heat Sources ◽  
Coil Heat Exchanger ◽  
Coil Heat

Indirect electrical resistance heating systems are heat-ers with internal heat sources and are widely used in agri-culture for heating gaseous and liquid media. Such sys-tems are characterized by insufficient intensity of heat ex-change processes. This implies a large heat transfer sur-face area and significant geometric size. Earlier, an attempt was made to solve the problem of increasing the efficiency of heat transfer processes and minimizing the geometric size of the heat exchanger. For this purpose, the heat ex-change characteristics were simulated and the geometric dimensions of three heat exchange systems were deter-mined: “pipe with internal heat sources in a dielectric pipe”, “pipe with an internal heat source -a membraneof heated liquid” and “cylindrical coil -heated liquid”. The analysis of these heat exchange systems has shown that the most promising is a coil-type heat exchanger. This system has the best heat transfer characteristics and the most compact size. To confirm the correctness of the applied method of calculating the heat exchange and geometric parameters of the heat exchanger, the simulation of the temperature dis-tribution of the heated liquid in the channel of the coil heat exchanger is implemented in this work. The verification calculations carried out under the formulated assumptions, using the example of a coil heat exchanger, show that the method for determining the heat exchange and geometric parameters of heat exchangers is correct. As a result of the simulation, it has been found that the error in determining the required channel length of the coil heat exchanger, the number of turns and the height of the coil to reach the liq-uid temperature at the outlet of 75°C does not exceed 4%. A similar conclusion can be made regarding the heat ex-changers of the types “pipe with internal heat sources -heated liquid” and “pipe with an internal heat source -a membraneof heated liquid”.

scholarly journals The influence of heat source distribution on the space cooling load oriented to local thermal requirements

2019 ◽  
pp. 1420326X1989163
Author(s):  
Chao Liang ◽  
Arsen Krikor Melikov ◽  
Xianting Li
Keyword(s):  
Heat Source ◽  
Source Distribution ◽  
Thermal Plume ◽  
Cooling Load ◽  
Heat Sources ◽  
Local Cooling ◽  
Thermal Requirements ◽  
Space Cooling ◽  
Airflow Field ◽  
Heat Source Distribution

Existing studies have shown that the space cooling load oriented to local thermal requirements is significantly influenced by different heat source distributions. However, numerical methods have been mainly used in the analysis based on a fixed airflow field and ignoring the thermal plume. Here, an experiment in a chamber with mixing ventilation was conducted. The heat sources were simulated by metal barrels and an oil-filled radiator, 13 types of heat source distributions were designed and the local cooling load (LCL) was used as the evaluation index. The results show that (1) the LCL is equal to the total amount of heat sources at the steady state in a room with mixing ventilation only if the heat sources are also distributed uniformly; (2) the LCL decreases with a decrease in the intensity of heat sources, achieving a decrease rate of 47.4%–70.8% in the experiment with different intensities; (3) the LCL is 9.2%–22.3% lower than the total amount of heat sources when these are located near the exhaust diffuser or far away from the target zone; (4) owing to its smaller surface area, the LCL with an oil-filled radiator is 7% lower than that with five metal barrels.

Thermal Evolution of Hot Spots in Thermally Nonlinear Carbon Graphite Sliders

1989 ◽  
Vol 111 (4) ◽  
pp. 591-596 ◽  
Author(s):  
Young Gill Yune ◽  
M. D. Bryant
Keyword(s):  
Heat Source ◽  
Fast Moving ◽  
Thermal Evolution ◽  
Hot Spot ◽  
Frictional Heating ◽  
Extreme Temperature ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Source Distribution ◽  
Graphite Block

Frictional heating of a thermal mound (or hot spot) present on the interface between a carbon graphite block sliding against a fast moving conductor is simulated. Heating of this mound due to frictional power dissipation is modeled as a collection of internal heat sources uniformly distributed within a very shallow volume (or layer) located directly beneath the sliding contact interface. The thermal mound, assumed to be motionless on and originating from the carbon graphite block, possesses the extreme temperature dependent thermal conductivity and heat capacity common to carbon graphite materials. Evolution of thermal mound temperatures from cold to hot is studied as a function of the intensity of the internal heat source distribution and the thickness of the heat source layer. For a fast moving conducting body sliding against the graphite block, it is shown that (a) an optimal heat source layer thickness exists, whereby temperatures maximize for this thickness and (b) for a sufficiently high heat source intensity, thermal instability of the mound is possible.

Optimal Distribution of Heat Sources in Convergent Channels Cooled by Laminar Forced Convection

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
E. Jassim ◽  
Y. S. Muzychka
Keyword(s):  
Heat Source ◽  
Leading Edge ◽  
Constructal Theory ◽  
Source Distribution ◽  
Heat Sources ◽  
Optimal Distribution ◽  
Convergent Channel ◽  
Freestream Velocity ◽  
Heat Source Distribution ◽  
Laminar Forced Convection

The constructal theory is applied to the flow in a convergent channel. The primary goals of this work are to analyze the heat source distribution and generalize the formula concerning such configurations, to study the spacing between consecutive elements, and to verify the analysis by comparing the proposed configuration with numerical simulations. The results show that nonuniform distributions enhance the performance of the system by allowing the heat source element to work near its maximum condition. Furthermore, the optimal distribution occurs when the heat sources are placed closer to each other near the leading edge of the channel. While the literature shows that the spacing between any consecutive element increases as the sources move downstream from the leading edge, the present results proved that such conclusions are restricted, depending on the ratio of outlet to inlet freestream velocity. Accordingly, the spacing has a maximum value when the exit freestream velocity is more than twice that of the inlet. For design issues, the study also addresses the minimum heat required to achieve optimal system performance. The results show that the amount of heat needed by the system to work close to its optimal performance varies exponentially with the convergent angle and increases with the increase in the heating element’s width. The comparison of the present distribution of the heat source elements with a regular one (fixed spacing) is performed numerically to demonstrate the efficiency of the proposed configuration. The results show that the present model forces the system to work more efficiently than the uniform distribution.

Melting from heat sources flush mounted on a conducting vertical wall

2000 ◽  
Vol 10 (3) ◽  
pp. 286-307 ◽  
Author(s):  
Bruno Binet ◽  
Marcel Lacroix
Keyword(s):  
Heat Source ◽  
Numerical Study ◽  
Vertical Wall ◽  
Melting Process ◽  
Source Distribution ◽  
Heat Sources ◽  
Aspect Ratios ◽  
Electric Equipment ◽  
Convection Dominated ◽  
Storage Units

A numerical study is conducted for natural convection dominated melting inside discretely heated rectangular enclosures. This study finds applications in the design and operation of thermal energy storage units and the cooling of electric equipment. Results show the benefits of discrete heating over uniform heating for optimizing the melting process. For enclosures of high aspect ratios (A ∼> 4), configurations leading to well controlled heat source temperatures and long melting times are obtained. For cavities of low aspect ratios (A ∼< 4), it is found that the source span η is the most influential parameter. For η ∼ < 0.45, the melting times are shorter and the heat source temperatures remain equal and moderate during the entire melting process. A map for determining the cavity size and the source distribution that optimizes the melting process is presented.

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