ADAPTIVE BOUNDARY INPUT HEAT FLUX AND TEMPERATURE ESTIMATION IN A THREE-DIMENSIONAL DOMAIN

A synthesis of observations of flow in a three-dimensional lid-driven cavity is presented through the use of flow visualization pictures and velocity and heat flux measurements. The ratio of the cavity depth to width used was 1:1 and the span to width ratio was 3:1. Flow visualization was accomplished using the thymol blue technique and by rheoscopic liquid illuminated by laser-light sheets. Velocity measurements were made using a two-component laser-Doppler-anemometer and the heat flux on the lower boundary of the cavity was measured using flush mounted sensors. The flow is three-dimensional and is weaker at the symmetry plane than that predicted by accurate two-dimensional numerical simulations. Local three-dimensional features, such as corner vortices in the end-wall regions and longitudinal Taylor-Go¨rtler-like vortices, are significant influences on the flow. The flow is unsteady in the region of the downstream secondary eddy at higher Reynolds numbers (Re) and exhibits turbulent characteristics in this region at Re = 10,000.

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A complex definite integral used in the semi-analytical solution of the mass transport equation in an unbounded two- or three-dimensional domain

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(92)90333-9 ◽

1992 ◽

Vol 166 (1) ◽

pp. 170-174

Author(s):

A.B Gureghian

Keyword(s):

Analytical Solution ◽

Mass Transport ◽

Transport Equation ◽

Three Dimensional ◽

Definite Integral ◽

Mass Transport Equation ◽

Dimensional Domain

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Formation, structure, and dissociation of the ribonuclease S three-dimensional domain-swapped dimer. VOLUME 281 (2006) PAGES 9400-9406

Journal of Biological Chemistry ◽

10.1016/s0021-9258(18)95088-x ◽

2007 ◽

Vol 282 (17) ◽

pp. 13139

Author(s):

Jorge P. López-Alonso ◽

Marta Bruix ◽

Josep Font ◽

Marc Ribó ◽

María Vilanova ◽

...

Keyword(s):

Three Dimensional ◽

Dimensional Domain

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Mixed Convection Adjacent to 3-D Backward-Facing Step

10.1115/imece2000-1408 ◽

2000 ◽

Author(s):

A. Li ◽

B. F. Armaly

Keyword(s):

Heat Flux ◽

Nusselt Number ◽

Mixed Convection ◽

Buoyancy Force ◽

Three Dimensional ◽

The Other ◽

Convection Flow ◽

Backward Facing Step ◽

Grashof Number ◽

Recirculating Flow

Abstract Results from three-dimensional numerical simulation of laminar, buoyancy assisting, mixed convection airflow adjacent to a backward-facing step in a vertical rectangular duct are presented. The Reynolds number, and duct geometry were kept constant at Re = 200, AR = 8, ER = 2, and S = 1 cm. Heat flux at the wall downstream from the step was kept uniform, but its magnitude was varied to cover a Grashof number (Gr) range between 0.0 to 4000. All the other walls in the duct were kept at adiabatic condition. The flow, upstream of the step, is treated as fully developed and isothermal. The relatively small aspect ratio of the channel is selected specifically to focus on the developments of the three-dimensional mixed convection flow in the separated and reattached flow regions downstream from the step. The presented results focus on the effects of increasing the buoyancy force, by increasing the uniform wall heat flux, on the three-dimensional flow and heat transfer characteristics. The flow and thermal fields are symmetric about the duct’s centerline. Vortex generated near the sidewall, is the major contributor to the three dimensional behavior in the flow domain, and that feature increases as the Grashof number increases. Increasing the Grashof number results in an increase in the Nusselt number, the size of the secondary recirculating flow region, the size of the sidewall vortex, and the spanwise flow from the sidewall toward the center of the channel. On the other hand, the size of the primary reattachment region decreases with increasing the Grashof number. That region lifts away and partially detaches from the downstream wall at high Grashof number flow. The maximum Nusselt number occurs near the sidewalls and not at the center of the channel. The effects of the buoyancy force on the distributions of the three-velocity components, temperature, reattachment region, friction coefficient, and Nusselt number are presented, and compared with 2-D results.

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Numerical Simulation Of A Microchannel For Microelectronic Cooling

Jurnal Teknologi ◽

10.11113/jt.v46.278 ◽

2012 ◽

Cited By ~ 1

Author(s):

Wai Hing Wong ◽

Normah Mohd. Ghazali

Keyword(s):

Heat Transfer ◽

Numerical Simulation ◽

Heat Flux ◽

Aspect Ratio ◽

Three Dimensional ◽

Large Temperature ◽

Rectangular Microchannel ◽

Numerical Work ◽

Solid Region ◽

Wall Interaction

Kertas kerja ini membincangkan simulasi berangka ke atas sinki haba saluran mikro dalam penyejukan alatan mikroelektronik. Model Dinamik Bendalir Berkomputer (CFD) tiga dimensi dibina menggunakan pakej komersil, FLUENT, untuk mengkaji fenomenon aliran bendalir dan pemindahan haba konjugat di dalam suatu sinki haba segi empat yang diperbuat daripada silikon. Model ditentusahkan dengan keputusan daripada uji kaji dan pengkajian berangka yang lepas untuk lingkungan nombor Reynolds kurang daripada 400 berdasarkan diameter hidraulik 86 mm. Kajian ini mengambil kira kesan kelikatan bendalir yang bersandaran dengan suhu dan keadaan aliran pra–membangun dari segi hidrodinamik dan haba. Model memberi maklumat tentang taburan suhu dan fluks haba yang terperinci di dalam sinki haba saluran mikro. Kecerunan suhu yang tinggi dicatat pada kawasan pepejal berdekatan dengan sumber. Fluks haba paling tinggi didapati pada dinding tepi saluran mikro diikuti oleh dinding atas dan bawah. Purata pekali pemindahan haba yang lebih tinggi bagi silikon menjadikan ia bahan binaan sinki haba saluran mikro yang lebih baik berbanding dengan kuprum dan aluminium. Peningkatan nisbah aspek saluran mikro yang bersegi empat memberi kecekapan penyejukan yang lebih tinggi kerana kelebaran saluran yang berkurangan memberi kecerunan halaju yang lebih tinggi dalam saluran. Nisbah aspek yang optimum yang diperoleh adalah dalam lingkungan 3.7 – 4.1. Kata kunci: Saluran mikro, CFD, FLUENT, simulasi berangka, penyejukan mikroelektron The paper discusses the numerical simulation of a micro–channel heat sink in microelectronics cooling. A three–dimensional Computational Fluid Dynamics (CFD) model was built using the commercial package, FLUENT, to investigate the conjugate fluid flow and heat transfer phenomena in a silicon–based rectangular microchannel heatsink. The model was validated with past experimental and numerical work for Reynolds numbers less than 400 based on a hydraulic diameter of 86 mm. The investigation was conducted with consideration of temperaturedependent viscosity and developing flow, both hydrodynamically and thermally. The model provided detailed temperature and heat flux distributions in the microchannel heatsink. The results indicate a large temperature gradient in the solid region near the heat source. The highest heat flux is found at the side walls of the microchannel, followed by top wall and bottom wall due to the wall interaction effects. Silicon is proven to be a better microchannel heatsink material compared to copper and aluminum, indicated by a higher average heat transfer. A higher aspect ratio in a rectangular microchannel gives higher cooling capability due to high velocity gradient around the channel when channel width decreases. Optimum aspect ratio obtained is in the range of 3.7 – 4.1. Key words: Microchannel, CFD, FLUENT, numerical simulation, microeletronics cooling

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An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

Volume 1: Heat Transfer in Energy Systems; Thermophysical Properties; Heat Transfer Equipment; Heat Transfer in Electronic Equipment ◽

10.1115/ht2009-88140 ◽

2009 ◽

Author(s):

Gisela Widmer

Keyword(s):

Linear System ◽

Radiative Transfer ◽

Transfer Equation ◽

Degrees Of Freedom ◽

Radiative Transfer Equation ◽

Three Dimensional ◽

Discrete Ordinates ◽

Five Dimensions ◽

Computational Costs ◽

Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

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