Temperature distribution over the cross section of liquid heat transfer films

Thermal conductivity of rocks is typically measured on core samples and cannot be directly measured from logs. We have developed a method to estimate thermal conductivity from logging data, where the key parameter is rock elasticity. This will be relevant for the subsurface industry. Present models for thermal conductivity are typically based primarily on porosity and are limited by inherent constraints and inadequate characterization of the rock texture and can therefore be inaccurate. Provided known or estimated mineralogy, we have developed a theoretical model for prediction of thermal conductivity with application to sandstones. Input parameters are derived from standard logging campaigns through conventional log interpretation. The model is formulated from a simplified rock cube enclosed in a unit volume, where a 1D heat flow passes through constituents in three parallel heat paths: solid, fluid, and solid-fluid in series. The cross section of each path perpendicular to the heat flow represents the rock texture: (1) The cross section with heat transfer through the solid alone is limited by grain contacts, and it is equal to the area governing the material stiffness and quantified through Biot’s coefficient. (2) The cross section with heat transfer through the fluid alone is equal to the area governing fluid flow in the same direction and quantified by a factor analogous to Kozeny’s factor for permeability. (3) The residual cross section involves the residual constituents in the solid-fluid heat path. By using laboratory data for outcrop sandstones and well-log data from a Triassic sandstone formation in Denmark, we compared measured thermal conductivity with our model predictions as well as to the more conventional porosity-based geometric mean. For outcrop material, we find good agreement with model predictions from our work and with the geometric mean, whereas when using well-log data, our model predictions indicate better agreement.

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A Comparison Between 2-D and 3-D Conduction Shape Factors

Heat Transfer: Volume 1 ◽

10.1115/ht2003-47337 ◽

2003 ◽

Author(s):

Devashish Shrivastava ◽

Robert Roemer

Keyword(s):

Heat Transfer ◽

Temperature Distribution ◽

Cross Section ◽

Three Dimensional ◽

Cylindrical Vessel ◽

Shape Factors ◽

Axial Conduction ◽

Power Deposition ◽

Tissue Matrix

Conduction shape factors are frequently used in a variety of heat transfer applications to evaluate heat transfer from one three-dimensional body to another three-dimensional body. Previous investigators have used conduction shape factors derived using the 2-D cross-section of the 3-D geometries for non-heating conditions as approximations to 3-D conduction shape factors with heating and no-heating present. This paper investigates the suitability of neglecting the axial conduction and power deposition in deriving expressions for conduction shape factors for the case of a single, cylindrical vessel imbedded concentrically in a cylindrical, uniformly heated tissue matrix. It is shown that 1) conduction shape factors are functions of the deposited power and the temperature distribution and 2) the magnitudes of conduction shape factors are affected significantly by axial conduction.

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The variation of the metal/mold heat transfer coefficient along the cross section of cylindrical shaped castings

Inverse Problems in Science and Engineering ◽

10.1080/17415970600573650 ◽

2006 ◽

Vol 14 (5) ◽

pp. 467-481 ◽

Cited By ~ 6

Author(s):

Eduardo N. Souza ◽

Noé Cheung ◽

Carlos A. Santos ◽

Amauri Garcia

Keyword(s):

Heat Transfer ◽

Heat Transfer Coefficient ◽

Transfer Coefficient ◽

Cross Section ◽

Metal Mold ◽

The Cross

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Numerical Simulation on Temperature Field of CFST Member under Solar Radiation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.354-355.1241 ◽

2011 ◽

Vol 354-355 ◽

pp. 1241-1244

Author(s):

Yan He ◽

Man Ding ◽

Qian Zhang

Keyword(s):

Numerical Simulation ◽

Temperature Field ◽

Temperature Distribution ◽

Solar Radiation ◽

Cross Section ◽

Temperature Difference ◽

Steel Tube ◽

Concrete Filled Steel Tube ◽

Nonlinear Temperature ◽

The Cross

In this paper the temperature field of Concrete Filled Steel Tube (CFST) member under solar radiation is simulated. The results show that temperature distribution caused by solar radiation is nonlinear over the cross-section of CFST member, and it is significantly varied with time and sections, the largest nonlinear temperature difference is over 26.3°C.

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On the Convective Heat Transfer in a Tube of Elliptic Cross Section Maintained Under Constant Wall Temperature

Journal of Heat Transfer ◽

10.1115/1.3246901 ◽

1986 ◽

Vol 108 (1) ◽

pp. 33-39 ◽

Cited By ~ 8

Author(s):

M. A. Ebadian ◽

H. C. Topakoglu ◽

O. A. Arnas

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Temperature Distribution ◽

Convective Heat Transfer ◽

Cross Section ◽

Convective Heat ◽

Wall Temperature ◽

Elliptic Cross Section ◽

Constant Wall Temperature ◽

Elliptic Cross

The convective heat transfer problem along the portion of a tube of elliptic cross section maintained under a constant wall temperature where hydrodynamically and thermally fully developed flow conditions prevail is solved in this paper. The successive approximation method is used for the solution utilizing elliptic coordinates. Analytical expressions for temperature distribution and Nusselt number corresponding to the first cycle of approximation are obtained in terms of the ellipticity of the cross section. In the case of a circular section, the first cycle approximation of the Nusselt number is obtained as 3.7288 compared to the exact value of 3.6568. Representative temperature distribution curves are plotted and compared to those corresponding with constant wall heat flux conditions.

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Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and H1 Boundary Conditions

Journal of Heat Transfer ◽

10.1115/1.4032173 ◽

2015 ◽

Vol 138 (4) ◽

Cited By ~ 7

Author(s):

Pamela Vocale ◽

Gian Luca Morini ◽

Marco Spiga

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Aspect Ratio ◽

Boundary Conditions ◽

Convective Heat Transfer ◽

Cross Section ◽

Convective Heat ◽

Slip Flow ◽

The Cross ◽

Cross Section Geometry

In this work, hydrodynamically and thermally fully developed gas flow through elliptical microchannels is numerically investigated. The Navier–Stokes and energy equations are solved by considering the first-order slip flow boundary conditions and by assuming that the wall heat flux is uniform in the axial direction, and the wall temperature is uniform in the peripheral direction (i.e., H1 boundary conditions). To take into account the microfabrication of the elliptical microchannels, different heated perimeter lengths are analyzed along the microchannel wetted perimeter. The influence of the cross section geometry on the convective heat transfer coefficient is also investigated by considering the most common values of the elliptic aspect ratio, from a practical point of view. The numerical results put in evidence that the Nusselt number is a decreasing function of the Knudsen number for all the considered configurations. On the contrary, the role of the cross section geometry in the convective heat transfer depends on the thermal boundary condition and on the rarefaction degree. With the aim to provide a useful tool for the designer, a correlation that allows evaluating the Nusselt number for any value of aspect ratio and for different working gases is proposed.

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Numerical study on heat transfer and flow resistance characteristics of multi-head twisted spiral tube

Thermal Science ◽

10.2298/tsci210224206z ◽

2021 ◽

pp. 206-206

Author(s):

Zhiqun Zheng ◽

Fayi Yan ◽

Lei Shi

Keyword(s):

Heat Transfer ◽

Numerical Calculation ◽

Cross Section ◽

Heat Transfer Performance ◽

Numerical Study ◽

Smooth Tube ◽

Transfer Performance ◽

Spiral Tube ◽

Inside Diameter ◽

The Cross

A numerical calculation model of multihead twisted spiral tube (MTST) was established. In the range of Reynolds number from 5000 to 35000, the influence of different twisted structure on the flow and heat transfer characteristics of the MTST was studied by numerical calculation. Numerical calculation results indicate that the Nusselt number and friction coefficient increase with the increase in the ratio of outside and inside diameter of the cross-section, the increase in the number of twisted nodes, and the increase in the number of twisted spiral tube heads. Under the condition of the same spiral structure and the same hydraulic diameter, the heat transfer performance of the MTST is better than that of the spiral smooth tube. In addition, through artificial neural network (ANN) analysis, the ratio of outside and inside diameter of the cross-section, number of twisted nodes, and the number of twisted spiral tube heads were optimized to promote the comprehensive heat transfer performance. The performance evaluation criterion is the highest when the ratio of outside and inside diameter of the cross-section is 25/22.5, the number of twisted nodes is 3, and the number of twisted spiral tube heads is 3, which is 1.849 of the spiral smooth tube.

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Numerical Study of Conjugate Heat Transfer Due to Growth of a Vapor Bubble During Flow Boiling of Water in a Microchannel

ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference, Volume 1 ◽

10.1115/ht2007-32434 ◽

2007 ◽

Cited By ~ 1

Author(s):

A. Mukherjee

Keyword(s):

Heat Transfer ◽

Heat Flux ◽

Temperature Distribution ◽

Cross Section ◽

Vapor Bubble ◽

Conjugate Heat Transfer ◽

Flow Boiling ◽

Wall Heat Flux ◽

Channel Cross Section ◽

Flux Boundary Condition

The present study is performed to numerically investigate temperature distribution at the channel walls during growth of a vapor bubble inside a microchannel. The microchannel is of 200 μm square cross section and a vapor bubble nucleates at one of the walls, with liquid flowing in through the channel inlet. Constant heat flux boundary condition is specified at the bottom wall of the microchannel. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid vapor interface is captured using the level set technique. The conjugate heat transfer problem is solved at the bottom and side walls. The bubble grows rapidly due to heat transfer from the walls and soon turns into a plug filling the entire channel cross section. The temperature distribution at the channel walls is studied for different values of wall heat flux. The bubble growth rate is found to increase with increase in wall heat flux. High temperatures are noted at the wall below the bubble base due to vapor contact causing axial temperature gradients. Areas of high heat transfer are also seen to exist in the thin layer of liquid between bubble and the channel sidewalls.

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