A semi-analytical modeling approach for three-dimensional heat transfer in sparsely fractured rocks with water flow and distributed heat source

2014 ◽  
Vol 38 (11) ◽  
pp. 1149-1171 ◽  
Author(s):  
Zhang Yong ◽  
Xiang Yan-yong
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Water Flow ◽  
Fractured Rocks ◽  
Analytical Modeling ◽  
Three Dimensional ◽  
Modeling Approach

Analytical Modeling of Temperature Distribution in Interposer-Based Microelectronic Systems

2013 ◽  
Author(s):  
Leila Choobineh ◽  
Dereje Agonafer ◽  
Ankur Jain
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Analytical Modeling ◽  
Three Dimensional ◽  
Heat Transfer Process ◽  
Thermal Design ◽  
Research Attention ◽  
On Chip

Heterogeneous integration in microelectronic systems using interposer technology has attracted significant research attention in the past few years. Interposer technology is based on stacking of several heterogeneous chips on a common carrier substrate, also referred to as the interposer. Compared to other technologies such as System-on-Chip (SoC) or System-in-Package (SiP), interposer-based integration offers several technological advantages. However, the thermal management of an interposer-based system is not well understood. The presence of multiple heat sources in various die and the interposer itself needs to be accounted for in any effective thermal model. While a finite-element based simulation may provide a reasonable temperature prediction tool, an analytical solution is highly desirable for understanding the fundamentals of the heat transfer process in interposers. In this paper, we describe our recent work on analytical modeling of heat transfer in interposer-based microelectronic systems. The basic governing energy conservation equations are solved to derive analytical expressions for the temperature distribution in an interposer-based microelectronic system. These solutions are combined with an iterative approach to provide the three-dimensional temperature field in an interposer. Results are in excellent agreement with finite-element solutions. The analytical model is utilized to study the effect of various parameters on the temperature field in an interposer system. Results from this work may be helpful in the thermal design of microelectronic systems containing interposers.

Anisotropic Behavior of Different Three-Dimensional Structures Materials under Thermal Stress Effect

2019 ◽  
Vol 297 ◽  
pp. 95-104
Author(s):  
Sihem Bouzid ◽  
Nacer Hebbir ◽  
Yamina Harnane
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Three Dimensional ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Equation System ◽  
Stress Effect ◽  
Field Calculation ◽  
Heat Transfer Theory ◽  
The Galerkin Method

This work concerns the numerical modeling of stationary conduction heat transfer in a 3D three-dimensional anisotropic material subjected to an internal heat source, based on the finite element method MEF and using the Galerkin method. The field of study is a cube representing the seven crystalline systems subjected to an internal heat source and convective boundaries. The obtained equation system is solved by the LU method. The automatic mesh is managed for all the domain nodes via the program which we have written in FORTRAN language. This program allowed temperature field calculation and was applied for different crystalline systems: monoclinic, triclinic, orthorhombic, trigonal, cubic that are identified by their thermal conductivity tensors [kij]. The obtained temperature profiles obtained are in accordance with heat transfer theory and clearly illustrate the crystalline structure symmetry; this calculation permits to predict the possible thermal deformations in an anisotropic solid.

Mixed Convection of Impinging Air Cooling Over Heat Sink in Telecom System Application

2004 ◽  
Vol 126 (4) ◽  
pp. 519-523 ◽  
Author(s):  
Siddharth Bhopte ◽  
Musa S. Alshuqairi ◽  
Dereje Agonafer ◽  
Gamal Refai-Ahmed
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Mixed Convection ◽  
Heat Sink ◽  
Three Dimensional ◽  
Source Surface ◽  
Air Cooling ◽  
Transfer Rates ◽  
Nusselt Numbers ◽  
Air Jet

The current numerical investigation will examine the effect of an impinging mixed convection air jet on the heat transfer rate of a parallel flat plate heat sink. A three-dimensional numerical model was developed to evaluate the effects of the nozzle diameter d, nozzle-to-target vertical placement H/d, Rayleigh number, and the jet Reynolds number on the heat transfer rates from a discrete heat source. Simulations were performed for a Prandtl number of 0.7 and for Reynolds numbers ranging from 100 to 5000. The governing equations were solved in the dimensionless form using a commercial finite-volume package. Average Nusselt numbers were obtained, at H/d=3 and two jet diameters, for the bare heat source, for the heat source with a base heat sink, and for the heat source with the finned heat sink. The heat transfer rates from the bare heat source surface have been compared with the ones obtained with the heat sink in order to determine the overall performance of the heat sink in an impingement configuration.

Heat Transfer Enhancement in Narrow Channels Using Two and Three-Dimensional Mixing Devices

1995 ◽  
Vol 117 (3) ◽  
pp. 590-596 ◽  
Author(s):  
S. V. Garimella ◽  
D. J. Schlitz
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Prandtl Number ◽  
Heat Transfer Enhancement ◽  
Large Scale ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Transitional Flow ◽  
Transfer Enhancement ◽  
Roughness Elements

The localized enhancement of forced convection heat transfer in a rectangular duct with very small ratio of height to width (0.017) was experimentally explored. The heat transfer from a discrete square section of the wall was enhanced by raising the heat source off the wall in the form of a protrusion. Further enhancement was effected through the use of large-scale, three-dimensional roughness elements installed in the duct upstream of the discrete heat source. Transverse ribs installed on the wall opposite the heat source provided even greater heat transfer enhancement. Heat transfer and pressure drop measurements were obtained for heat source length-based Reynolds numbers of 2600 to 40,000 with a perfluorinated organic liquid coolant, FC-77, of Prandtl number 25.3. Selected experiments were also performed in water (Prandtl number 6.97) for Reynolds numbers between 1300 and 83,000, primarily to determine the role of Prandtl number on the heat transfer process. Experimental uncertainties were carefully minimized and rigorously estimated. The greatest enhancement in heat transfer relative to the flush heat source was obtained when the roughness elements were used in combination with a single on the opposite wall. A peak enhancement of 100 percent was obtained at a Reynolds number of 11,000, which corresponds to a transitional flow regime. Predictive correlations valid over a range of Prandtl numbers are proposed.

Three-Dimensional Magnetohydrodynamics Slip Flow of Nanofluids Over a Slendering Stretching Sheet with Heat Source or Sink Effects

2021 ◽  
Vol 10 (3) ◽  
pp. 380-387
Author(s):  
R. Jayakar ◽  
B. Rushi Kumar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Boundary Layers ◽  
Source Parameters ◽  
Slip Flow ◽  
Three Dimensional ◽  
Current Approach ◽  
Slip Effects ◽  
Nano Fluids

Aim: The research carried out in this article is based on experimenting with a 3-D MHD nanofluid flow on a sheet as slendering stretch bearing the slip effects, thermophoresis, Brownian Motion, heat source, and sink. Water-based Cuo and Cu nano-fluids were considered for the analysis. Following the suitable techniques of similarity transformation, the partial differential equations also called the governing equations are deduced into ODE (Ordinary Differential Equations). The mathematical results were estimated by applying the Methods of Newton and Runge-Kutta. The calculations along with the graphs for different parameters were also explained. Novelty: The outcomes of novel effective graphs for different parameters of interest are shown and explained. It has been found that heat-sink/source parameters depending on the temperature and space serve as heat transfer parameters. Slip effects minimize the thermal boundary layers as well as concentration development. It is discovered that CuO-Water, as well as Cu-Water nanofluids, have homogeneous boundary layers (concentration, thermal and momentum),and as contrasted with the CuO-Water nanofluids, the mass, and the heat transfer rate is higher in Cu-Water nanofluids. The paper concludes by comparing the outcomes of the current approach with findings that already existed.

scholarly journals Solvability of the Boussinesq Approximation for Water Polymer Solutions

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 611 ◽  
Author(s):  
Mikhail A. Artemov ◽  
Evgenii S. Baranovskii
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Boussinesq Approximation ◽  
Robin Boundary Condition ◽  
Flow Domain ◽  
The Galerkin Method ◽  
Robin Boundary ◽  
Dimensional Domain

We consider nonlinear Boussinesq-type equations that model the heat transfer and steady viscous flows of weakly concentrated water solutions of polymers in a bounded three-dimensional domain with a heat source. On the boundary of the flow domain, the impermeability condition and a slip condition are provided. For the temperature field, we use a Robin boundary condition corresponding to the classical Newton law of cooling. By using the Galerkin method with special total sequences in suitable function spaces, we prove the existence of a weak solution to this boundary-value problem, assuming that the heat source intensity is bounded. Moreover, some estimates are established for weak solutions.

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