Journal of Heat Transfer
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Thermally Optimum Spacing of Vertical, Natural Convection Cooled, Parallel Plates While component dissipation patterns and system operating modes vary widely, many electronic packaging configurations can be modeled by symmetrically or asymmetrically isothermal or isoflux plates. The idealized configurations are amenable to analytic optimization based on maximizing total heat transfer per unit volume or unit primary area. To achieve this anlaytic optimization, however, it is necessary to develop composite relations for the variation of the heat transfer coefficient along the plate surfaces. The mathematical development and verification of such composite relations as well as the formulation and solution of the optimizing equations for the various boundary conditions of interest constitute the core of this presentation.
Journal of Heat Transfer - Tập 106 Số 1 - Trang 116-123 - 1984
Optimal Arrays of Pin Fins and Plate Fins in Laminar Forced Convection This paper reports the optimal geometry of an array of fins that minimizes the thermal resistance between the substrate and the flow forced through the fins. The flow regime is laminar. Two fin types are considered: round pin fins, and staggered parallel-plate fins. The optimization of each array proceeds in two steps: The optimal fin thickness is selected in the first step, and the optimal thickness of the fluid channel is selected in the second. The pin-fin array is modeled as a Darcy-flow porous medium. The flow past each plate fin is in the boundary layer regime. The optimal design of each array is described in terms of dimensionless groups. It is shown that the minimum thermal resistance of plate-fin arrays is approximately half of the minimum thermal resistance of heat sinks with continuous fins and fully developed laminar flow in the channels.
Journal of Heat Transfer - Tập 115 Số 1 - Trang 75-81 - 1993
Forced Convection Heat Transfer from a Shrouded Fin Array with and without Tip Clearance An analysis is made of the laminar heat transfer characteristics of an array of longitudinal fins with an adiabatic shroud situated adjacent to the fin tips. The analysis involves the solution of the velocity field in the inter-fin space and in the shroud clearance gap beyond the tips, after which the governing energy equations for the fluid and the fins are solved simultaneously. Solutions are obtained for representative values of dimensionless parameters which describe the system geometry and the fin conductance. For the fin, the results show that the heat loss is a minimum adjacent to the base and increases along the fin in the direction of the tip. The maximum fin heat loss occurs either at the tip or intermediate between the base and the tip, depending on whether or not there is clearance between the fin tips and the shroud. The calculated heat transfer coefficients vary along the fin and, in some cases, take on negative values. Heat loss variations are also encountered along the base surface, the extent of which depends on the fin conductance, the inter-fin spacing, and the extent of the clearance gap. With regard to the overall heat loss, the fin is, on a unit area basis, a more efficient transfer surface than is the base. The results demonstrate that the conventional uniform heat transfer coefficient model is inapplicable to shrouded fin arrays.
Journal of Heat Transfer - Tập 100 Số 4 - Trang 572-579 - 1978
Heat/Mass Transfer Characteristics for Flow in a Corrugated Wall Channel Experiments based on the naphthalene sublimation technique were carried out to determine the local and average transfer characteristics for flow in a corrugated wall channel. The range of the experiments encompassed the laminar, transition, and low-Reynolds-number turbulent regimes. Local mass transfer measurements were made both in the spanwise (i.e., cross stream) and streamwise directions, and overall transfer rates were also determined. The experiments demonstrated the existence of a variety of complex transfer processes and related fluid flow phenomena. These included secondary flows and associated spanwise mass transfer variations, suppression of the secondary flow by counteracting centrifugal forces, and destruction of the secondary flow by the onset of turbulence. Flow separation on the leeward facets of the corrugated wall caused a sharp decrease in the local transfer rates, but relatively high transfer rates were in evidence in the reattachment region. In the laminar range, the average transfer coefficients for the corrugated wall channel were only moderately larger than those for a parallel-plate channel. On the other hand, in the low-Reynolds-number turbulent regime, the wall corrugations were responsible for an increase of nearly a factor of three in the average coefficient compared with the smooth wall channel.
Journal of Heat Transfer - Tập 99 Số 2 - Trang 187-195 - 1977
Finite-Volume Solutions for Laminar Flow and Heat Transfer in a Corrugated Duct A finite volume methodology was developed to predict fully developed heat transfer coefficients, friction factors, and streamlines for flow in a corrugated duct. The basis of the method is an algebraic coordinate transformation which maps the complex fluid domain onto a rectangle. The method can be adopted for other convection-diffusion problems in which two boundaries of the flow domain do not lie along the coordinate lines. Representative results were found for laminar flow, uniform wall temperature, and for a range of Reynolds number, Prandtl number, corrugation angle, and dimensionless interwall spacing. As seen from the streamlines, the flow patterns are highly complex including large recirculation zones. The pressure drops and friction factor results are higher than the corresponding values for a straight duct. Finally, the performance of the corrugated duct was compared with the straight duct under three different constraints—fixed pumping power, fixed pressure drop, and fixed mass flow rate. There are small differences in the heat transfer rate ratios under these constraints.
Journal of Heat Transfer - Tập 109 Số 3 - Trang 627-634 - 1987
Least-Squares Smoothing of Direct-Exchange Areas in Zonal Analysis
Journal of Heat Transfer - Tập 108 Số 1 - Trang 239-242 - 1986
Average Volumetric Concentration in Two-Phase Flow Systems A general expression which can be used either for predicting the average volumetric concentration or for analyzing and interpreting experimental data is derived. The analysis takes into account both the effect of nonuniform flow and concentration profiles as well as the effect of the local relative velocity between the phases. The first effect is taken into account by a distribution parameter, whereas the latter is accounted for by the weighted average drift velocity. Both effects are analyzed and evaluated. The results predicted by the analysis are compared with experimental data obtained for various two-phase flow regimes, with various liquid-gas mixtures in adiabatic, vertical flow over a wide pressure range. Good agreement with experimental data is shown.
Journal of Heat Transfer - Tập 87 Số 4 - Trang 453-468 - 1965
A Correlating Equation for Forced Convection From Gases and Liquids to a Circular Cylinder in Crossflow A single comprehensive equation is developed for the rate of heat and mass transfer from a circular cylinder in crossflow, covering a complete range of Pr (or Sc) and the entire range of Re for which data are available. This expression is a lower bound (except possibly for RePr < 0.2); free-stream turbulence, end effects, channel blockage, free convection, etc., may increase the rate. In the complete absence of free convection, the theoretical expression of Nakai and Okazaki may be more accurate for RePr < 0.2. The correlating equation is based on theoretical results for the effect of Pr in the laminar boundary layer, and on both theoretical and experimental results for the effect of Re. The process of correlation reveals the need for theoretical results for the effect of Pr in the region of the wake. Additional experimental data for the effect of Pr at small Pe and for the effect of Re during the transition in the point of separation are also needed.
Journal of Heat Transfer - Tập 99 Số 2 - Trang 300-306 - 1977
Improved Discrete Ordinates Method for Ray Effects Mitigation A new and improved method based on the concept of discrete ordinates scheme with infinitely small weights (DOS+ISW) is developed for modeling radiative heat transfer in three-dimensional participating media. To demonstrate the effectiveness of the method in mitigating ray effects, the ray effects caused by (1) abrupt step changes in the boundary conditions and (2) the stepwise variation of the medium emissive power are considered. In this work, angular quadrature sets with large number of discrete ordinate directions are chosen to mitigate ray effects while at the same time keeping the computational time increase to a minimum. Comparing with the conventional discrete ordinates method, the difference is that intensities in these directions are calculated by DOS+ISW method. Intensity with fine directional resolution calculated by this method is validated by comparing with that of reverse Monte Carlo method. The large number of discrete ordinate directions used in the new method becomes computationally prohibitive in the conventional discrete ordinates method due to the increased computer memory and computation time requirements.
Journal of Heat Transfer - Tập 133 Số 4 - 2011
Analysis of Radiative Heat Transfer in Complex Two-Dimensional Enclosures With Obstacles Using the Modified Discrete Ordinates Method In this work, an extension of a modified discrete ordinates method recently proposed by other researchers is presented. It is intended to counter the ray effect inherent in this method. The media analyzed are absorbing, emitting and isotropically or anisotropically scattering and the enclosure geometry is arbitrary. Cases with obstructions are emphasized. The radiative intensity is broken into two parts: the wall-related intensity and the medium-related intensity. The former is treated separately by rigorous integration over the entire solid boundary. A new differencing scheme based on quadrangular grids is also proposed and used for the treatment of the medium-related intensity. Results confirm that the proposed method is a good general remedy for anomalies caused by the ray effect due to the geometry.
Journal of Heat Transfer - Tập 123 Số 5 - Trang 892-900 - 2001
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