Cylindrical Tank Filled With a Liquid in a Three-Dimensional Temperature Field

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.

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Short Helical Combustor: Flow Control in a Combustion System With Angular Air Supply

Volume 4A: Combustion, Fuels and Emissions ◽

10.1115/gt2017-63037 ◽

2017 ◽

Author(s):

Behdad Ariatabar ◽

Rainer Koch ◽

Hans-Jörg Bauer

Keyword(s):

Temperature Field ◽

Angular Momentum ◽

Three Dimensional ◽

The Novel ◽

Combustion System ◽

Flow Angle ◽

Air Supply ◽

Inhomogeneous Flow ◽

Generic Design ◽

Industrial Optimization

The concept of the novel Short Helical Combustor (SHC) was investigated in our previous work [1, 2]. Based on the insight gained from these previous investigations, we propose a generic design improvement to address the tremendous loss of initial angular momentum as well as inhomogeneous flow and temperature field at the outlet of the SHC. In the present paper, the main features of this design are introduced. It is shown that a three-dimensional shaping of the sidewalls, the dome, and the liners can effectively counteract the suboptimal interaction of the swirl flames with these surrounding walls. As a result, the flow at the outlet of the combustor features a high angular momentum and exhibits a uniform flow angle and temperature field. The insight gained from these generic investigations, and the resulting design optimization provides a useful framework for further industrial optimization of the SHC.

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Finite element modeling of transient three-dimensional temperature field of workpiece with a sharp board in laser heat treatment

10.1117/12.575385 ◽

2005 ◽

Author(s):

Yunchang Fu ◽

Junchang Li ◽

Dongxiong Ling ◽

Kun Ma ◽

Martin Bruno

Keyword(s):

Heat Treatment ◽

Finite Element ◽

Temperature Field ◽

Finite Element Modeling ◽

Three Dimensional ◽

Laser Heat Treatment ◽

Element Modeling ◽

Laser Heat

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Spectral properties of magnetohydrodynamic convection with mean horizontal temperature gradient

Proceedings of the International Astronomical Union ◽

10.1017/s1743921307001032 ◽

2006 ◽

Vol 2 (S239) ◽

pp. 513-513

Author(s):

D. Skandera ◽

W.-Ch. Müller

Keyword(s):

Temperature Field ◽

Rayleigh Number ◽

Temperature Gradient ◽

Numerical Simulations ◽

Spectral Properties ◽

Three Dimensional ◽

Numerical Code ◽

Dimensional System ◽

Horizontal Temperature Gradient ◽

Mhd Turbulence

AbstractSpectral properties of convective magnetohydrodynamic (MHD) turbulence in two and three dimensions are studied by means of direct numerical simulations (Skandera D. & Müller W.-C. 2006). The investigated system is set up with a mean horizontal temperature gradient in order to avoid a development of elevator instabilities in a fully periodic box. All simulations are performed without mean magnetic field. The applied resolution is 5123 and 20482. The MHD equation are solved by a numerical code (Müller & Biskamp 2000) that uses a standard pseudospectral scheme. For removing of aliasing errors a spherical truncation method is employed. Obtained results are compared with predictions of various existing phenomenological theories for magnetohydrodynamic and convective turbulence (Müller & Biskamp 2000). While the three-dimensional system is found to operate in a Kolmogorov-like regime where buoyant forces have a negligible impact on the turbulence dynamics (relatively low Rayleigh number achieved in the simulation; Ra ∼106), the two-dimensional system exhibits interesting irregular quasi-oscillations between a buoyancy dominated Bolgiano-Obukhov-like regime of turbulence and a standard Iroshnikov-Kraichnan-like regime of turbulence (Müller & Biskamp 2000). The most important parameter determining the turbulent regime of 2D magnetoconvection, apart from a high Rayleigh number, seems to be the mutual alignment of velocity and magnetic fields. The non-linear dynamics and the interplay between individual fields are examined with different transfer functions that confirm basic assumptions about directions of energy transfer in spectral space. Kinetic, magnetic and temperature energy are transported by a turbulent cascade from large to smaller scales. The local/nonlocal character of the transport is tested for several individual terms in the governing equations. Moreover, other statistical quantities, e.g. probability density functions, are computed as well. A passive character of the temperature field in the investigated three-dimensional magnetoconvection is supported by computations of intermittency using extended self-similarity. The intermittency of the Elsasser field z+ is in agreement with results from numerical simulations of isotropic MHD turbulence (Müller & Biskamp 2000). The intermittency of the temperature field is found to approximately agree with results of passive scalar measurements in hydrodynamic turbulence (Ruiz-Chavarria, Baudet & Ciliberto 1996).

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