Review on thermal energy storage with phase change: materials, heat transfer analysis and applications

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

An introduction to heat transfer

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Numerical Heat Transfer And Fluid Flow

This paper explores the recent research developments in high-heat-flux thermal management. Cooling schemes such as pool boiling, detachable heat sinks, channel flow boiling, microchannel and mini-channel heat sinks, jet-impingement, and sprays, are discussed and compared relative to heat dissipation potential, reliability, and packaging concerns. It is demonstrated that, while different cooling options can be tailored to the specific needs of individual applications, system considerations always play a paramount role in determining the most suitable cooling scheme. It is also shown that extensive fundamental electronic cooling knowledge has been amassed over the past two decades. Yet there is now a growing need for hardware innovations rather than perturbations to those fundamental studies. An example of these innovations is the cooling of military avionics, where research findings from the electronic cooling literature have made possible the development of a new generation of cooling hardware which promise order of magnitude increases in heat dissipation compared to today's cutting edge avionics cooling schemes.

Assessment of high-heat-flux thermal management schemes

This work is a contribution to a larger program that seeks to improve computation of unsteady flows in Stirling engines. It presents flow visualization results from an experiment that replicates important features of oscillatory flows; such as large-scale separation and adverse and favorable, spatial and temporal acceleration. The geometry is a tube perpendicular to a space between two circular discs, one of which the tube penetrates such that the end of the tube is flush with the disc inner surface. The flow, driven by a piston in the tube, is oscillatory and acts on the exhaust stroke as a jet impinging on the center of a circular disc and on the intake stroke as a sink flow drawn into a tube from the space between the two discs. Time-varying recirculation zones and periodic appearances of highly turbulent flow are observed. In addition to a characterization of oscillatory, separating flow, this program provides code validation support for Stirling engine design models. The project goals are to identify the areas where 1-D modeling is especially weak and to provide support for developing more sophisticated design models that can be used with greater confidence. A complete description of the experiment and results is given. It is shown that a change in geometry can affect the flow in major way; i.e. whether a recirculation eddy survives an entire cycle or is eliminated upon flow reversal. Future work is outlined.

Measurements in oscillatory flows with separation in support of Stirling engine model development

CFD experiments were conducted for heat transfer with jet impingement over solid surfaces. The parameters include: 1) Jet Reynolds number from 3,000 to 23,000, 2) Jet-to-target-plate spacing (z/d), from 2 to 14 (single jet), d is jet diameter, 3) Target plate shape: 3a) flat, 3b) concave, 3c) convex, (single jet), 4) One row of seven jets impinging on a flat surface, the channel has one end closed (at 24d away from the most upstream jet axis), 5) Three rows of seven jets each in-line arrangement impinging on a flat surface, the channel has one end closed (at 24d away from the most upstream jet axis). Four CFD models (utilizing FLUENT commercial code) have been considered: 1) laminar flow (no turbulent transport), and turbulent flow with turbulence modeling by 2) the standard k–e model, 3) the k–ω model, and 4) the v2 –f model. The predictions of Nu number for each case were compared with experimental data available from the literature. It is shown that the v2 –f model gives the best overall performance, though the k–ω model gives good predictions for most of the flow, with the exception of near the stagnation zone for some cases. The models are in much better agreement (with the data) as z/d grows and at larger radial locations from the jet axis, as expected. For multiple jets in one row (z/d = 2), again the v2 –f showed the best overall agreement with the experimental data. The k–ω model is not as good while k–e clearly overpredicts the Nusselt numbers. For multiple jets in three inline rows (z/d = 5), all the three models were in overall agreement with the experimental data. However, k–e and k–ω exhibit an important phenomenon, reported by the experiments: a decrease of the stagnation Nu from the upstream jet to the downstream ones. The v2 –f model did not reproduce this feature.Copyright © 2005 by ASME

CFD for Jet Impingement Heat Transfer With Single Jets and Arrays

Air-cooled heat sinks prevail in microelectronics cooling due to their high reliability, low cost, and simplicity. But, their heat transfer performance must be enhanced if they are to compete for high-flux applications with liquid or phase-change cooling. Piezoelectrically-driven agitators and synthetic jets have been reported as good options in enhancing heat transfer of surfaces close to them. This study proposes that agitators and synthetic jets be integrated within air-cooled heat sinks to significantly raise heat transfer performance. A proposed integrated heat sink has been investigated experimentally and with CFD simulations in a single channel heat sink geometry with an agitator and two arrays of synthetic jets. The single channel unit is a precursor to a full scale, multichannel array. The agitator and the jet arrays are separately driven by three piezoelectric stacks at their individual resonant frequencies. The experiments show that the combination of the agitator and synthetic jets raises the heat transfer coefficient of the heat sink by 80%, compared with channel flow only. The 3D computations show similar enhancement and agree well with the experiments. The numerical simulations attribute the heat transfer enhancement to the additional air movement generated by the oscillatory motion of the agitator and the pulsating flow from the synthetic jets. The component studies reveal that the heat transfer enhancement by the agitator is significant on the fin side and base surfaces and the synthetic jets are most effective on the fin tips.Copyright © 2011 by ASME

Enhancing Heat Transfer of Air-Cooled Heat Sinks Using Piezoelectrically-Driven Agitators and Synthetic Jets

Experiments on nucleate boiling heat transfer with a highly-wetting dielectric fluid. Effects of pressure, subcooling and dissolved gas content

This work describes the CFD portion of an overall plan to examine a modern type of Stirling engine regenerator matrix both computationally and experimentally. An experimental program has already started at the University of Minnesota (UMN) to examine a stacked-screen regenerator. A 2-D axisymmetric computational model was developed to simulate the UMN rig encompassing a piston/cylinder, cooler tube, plenum, regenerator matrix and heater. The CFD-ACE+, a commercial CFD-code, has been utilized for this study. A systematic approach was taken where CFD results were obtained for the following: 1) Turbulence modeling (low Re k-/spl epsiv/) of a unidirectional pipe flow with sudden expansion (expansion ratio D/d=1.95). Good agreement was achieved with the experimental data; 2) Laminar flow with porous media for a flow over and through a stack of rectangular parallel plate fins (porosity=0.579 & permeability=2.28E-08 m/sup -2/). Good agreement was achieved with published CFD data; 3) Good agreement was achieved for prediction of the oscillatory velocity field, in the plenum, with the UMN data and without the regenerator matrix where a low Re k-/spl epsiv/ turbulence model was used; 4) Results for the oscillatory flow data with the regenerator matrix in place showed that the laminar flow model overpredicted the centerline velocity (as expected), since the flow is turbulent. The laminar flow model with permeability of 1.65E-08 m/sup -2/ seems to show velocity uniformity in the matrix as early as 15 screen-layers deep into the regenerator matrix (from the cooler side). This is consistent with the UMN temperature data. A combined study of a turbulence model and a porous media model is underway to provide accurate data both in the plenum and the regenerator matrix. Our next step is to apply this model and include the energy equation to predict not only velocity but also temperature profiles as well.

Terrence W. Simon

Papers

Measurements in oscillatory flows with separation in support of Stirling engine model development

CFD for Jet Impingement Heat Transfer With Single Jets and Arrays

Enhancing Heat Transfer of Air-Cooled Heat Sinks Using Piezoelectrically-Driven Agitators and Synthetic Jets

Experiments on nucleate boiling heat transfer with a highly-wetting dielectric fluid. Effects of pressure, subcooling and dissolved gas content

A 2-D CFD model of oscillatory flow with jets impinging on a random wire regenerator matrix