Constructal Optimization of Microchannel Heat Sinks With Noncircular Cross Sections

This article reports the numerical geometric optimization of three-dimensional microchannel heat sinks with rectangular, elliptic, and isosceles triangular cross sections. The cross-sectional areas of the mentioned microchannels can change according to the degrees of freedom, that is, the aspect ratio and the solid volume fraction. Actually, the purpose of geometric optimization is to determine the optimal values of these parameters in such a way that the peak temperature of the wall is minimized. The effects of solid volume fraction and pressure drop upon the aspect ratio, hydraulic diameter, and peak temperature of the microchannels are investigated. Moreover, these microchannel heat sinks are compared with each other at their optimal conditions. Considering the constraints and geometric parameters for the optimization of the present study, it is revealed that microchannel heat sinks with rectangular and elliptic cross sections have similar performances, while microchannels with isosceles triangular cross sections show weaker performances. The optimal shapes of all three kinds of channels are achieved numerically and compared with the approximate results obtained from scale analysis, for which good agreements are observed.     

Numerical analysis of laminar heat transfer performance of in-plane spiral ducts with various cross-sections at fixed cross-section area

A numerical approach is carried out to investigate the heat transfer performance of in-plane spiral ducts with various cross sections – rectangular, square, triangular, trapezoidal, circular and half circular. Simulations were carried out at a constant inlet Reynolds number at fixed cross section area for both constant wall temperature and constant wall heat flux conditions. Results are compared to straight ducts of the same cross sections and at the same length as the coiled ducts. The effects of Reynolds number and Prandtl number are also discussed for various geometries. The results are presented and are aimed to determine the advantages, limitations and effects of in-plane spiral ducts of various cross sections on the flow and heat transfer characteristics when the cross section area is fixed.     

Effects of design parameters on the performance of channel-type solar energy air heaters with corrugated plates

This experimental investigation of corrugated, channel-type solar air heaters is more concerned with design than environmental or operating parameters. The main system parameters considered include the corrugation geometry (i.e. rectangular, triangular and circular cross sections) and the flow arrangements which include the flow above and/or below, or within, the absorber plate. These design parameters were investigated for various flow rates, numbers of glass covers and inlet air temperatures.     

Estimation of Nusselt Number in Microchannels of Arbitrary Cross Section with Constant Axial Heat Flux

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly connected cross sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully developed, laminar flow in microchannels of arbitrary cross sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross sections with a maximum difference on the order of 9%.     

Surveying the hybrid of radiation and magnetic parameters on Maxwell liquid with TiO2 nanotube influence of different blades

In this paper, the impacts of Maxwell nanoliquid transmission, rectangular with titanium oxide nanoparticles are explored over the triangular, chamfer blades. The innovation of this paper is the use of the number of chamfers, rectangular, and triangular blades at the top and bottom of a stretched plate to study physical nanofluid parameters such as temperature and the effects of magnetism. Also, by determining the appropriate height and length for the blades, we achieve the best optimization of temperature and velocity of nanofluid between the plate and the blades, which improves heat transfer and with a more and better effect of magnetic effects. The finite element method is utilized for the calculated differential equations. In this paper, by utilizing the reaction surface strategy, we optimized the titanium oxide nanofluid velocity and temperature, and magnetic parameter passing from the extending sheet. On average, the titanium oxide nanoparticle velocity around the two rectangular blades at the beginning of the sheet is 73.09% higher than triangular blades and 66.98% higher than chamfer blades. Based on the outcomes got from the titanium oxide nanofluid speed charts and the warm exchange cantors and magnetic impacts within the Design-Expert computer program, the most excellent optimization occurred for TiO₂ nanofluid speed and TiO₂ nanofluid temperature and TiO₂ magnetic parameter with u = 0.523, T = 3.25, and H = 2.671.     

Analytical heat diffusion models for different micro-channel heat sink cross-sectional geometries

This study explores heat diffusion effects in micro-channel heat sinks intended for electronic cooling applications. Detailed analytical models are constructed for heat sinks having micro-channels with rectangular, inverse trapezoidal, triangular, trapezoidal, and diamond-shaped cross sections. Solutions are presented for both monolithic heat sinks and heat sinks with perfectly insulating cover plates. The analytical results are compared to detailed two-dimensional numerical models of the same cross-sections over a broad range of cover plate thermal conductivities for different micro-channel aspect ratios, fin spacings and Biot numbers. These comparisons show the analytical models provide accurate predictions for Biot numbers of practical interest. This study proves the analytical models are very effective tools for the design and thermal resistance prediction of micro-channel heat sinks found in electronic cooling applications.     

Effects of fin shapes on heat transfer in microchannel heat sinks

In the present study, compact water cooling of high‐density, high‐speed, very‐large‐scale integrated (VLSI) circuits with the help of microchannel heat exchangers were investigated analytically. This study also presents the result of mathematical analysis based on the modified Bessel function of laminar fluid flow and heat transfer through combined conduction and convection in a microchannel heat sink with triangular extensions. The main purpose of this paper is to find the dimensions of a heat sink that give the least thermal resistance between the fluid and the heat sink, and the results are compared with that of rectangular fins. It is seen that the triangular heat sink requires less substrate material as compared to rectangular fins, and the heat transfer rate per unit volume has been almost doubled by using triangular heat sinks. It is also found that the effectiveness of the triangular fin is higher than that of the rectangular fin. Therefore, the triangular heat sink has the ability to dissipate large amounts of heat with relatively less temperature rise for the same fin volume. Alternatively, triangular heat sinks may thus be more cost effective to use for cooling ultra‐high speed VLSI circuits than rectangular heat sinks.     

SIMULATION OF THE MELT FRONT ADVANCEMENT IN INJECTION MOLDED PLATE WITH A RIB OF SEMICIRCULAR CROSS SECTION

Two algorithms are developed to predict the polymer melt front advancement in the thin plate with ribs of semicircular cross section. In the first method, rod-like elements of equivalent hydraulic diameter representing a semicircular rib are superimposed on the triangular shell element mesh used for the thin section. In the second approach, rectangular elements having the same width as the diameter of the semicircular rib and representing mixed one- and two-dimensional flow characteristics are used and interlinked with triangular elements. In both algorithms, control volume /finite element formulation is applied to trace the melt front advancement. Both simulations result in similar predictions and also show reasonably good consistency with experimental observation.     

An up to date review of continuously variable speed wind turbines with mechatronic variable transmissions

As a promising and potential alternative to conventional fixed or variable speed wind turbines, continuously variable speed wind turbines (CVSWTs) with variable transmissions offer improved power efficiency and enhanced power control capabilities. The CVSWTs can be generally achieved by adapting mechatronic variable transmissions in the turbine drive train for continuously variable speed operations for wind turbines. Therefore, this paper serves to provide an up to date and exhaustive review of the CVSWTs with mechatronic variable transmissions such as mechanical variable transmission, electrical variable transmission, and power splitting transmission. In this paper, the analysis of CVSWTs with different mechatronic transmission topologies is performed regarding basic configurations, dynamic characteristics, control principles, and experimental or simulation results. Review results indicate the feasibility of applying CVSWTs with such mechatronic transmissions and highlight superiorities of the CVSWTs with power splitting transmission. The CVSWT with power splitting transmission will be particularly suitable for megawatt‐scale turbine systems and will hence increase the economic competitiveness of these turbines due to its large power capacity and high reliability. The directions or challenges for future investigations of CVSWTs with such mechatronic transmissions are also presented to foster in‐depth understanding of such CVSWTs and their control strategies.     

Optimization of constructal economics for volume-to-point transport

The constructal economic optimization for a given area is carried out in this paper with minimum transport cost objective by using a triangular elemental area. A number of triangular elements are assembled to form a new larger rectangular area and optimized by relaxing the angle constraint. The results obtained herein are discussed and compared with those in recent references.     

Capillary-assisted flow and evaporation inside circumferential rectangular micro groove

To introduce capillary-assisted evaporation from micro-size fields to normal-size fields, an inclined circumferential micro groove with rectangular cross sections is investigated analytically and a systematic mathematical model is developed. The model is composed of five sub-models: a natural convection model, a liquid axial flow model, a heat transfer model in and below the intrinsic meniscus, an evaporation thin film region model and an adsorbed region model. In this model, for the extended meniscuses formed at groove cross sections, both the intrinsic meniscus and evaporation thin film region are considered when calculating heat absorbing. Through solving the model, the influences of dynamic contact angle on the heat absorbing in the intrinsic meniscus and evaporation thin film region are investigated. Moreover, the factors affecting the whole-groove equivalent heat transfer coefficient have been investigated.     

Influence of Shape,Number, and Position of Horizontal Minifins on Thermal-Hydraulic Performance of Minichannel Heat Sink Using Nanofluid

In the first part of present study, an experimental setup with constant heat flux is used to investigate the thermal performance of the water inside a horizontal triangular pin fin channel. For the sake of validation of the computational fluid dynamics (CFD) study, a simulation is conducted according to the geometry and operating conditions of the experimental work. The numerical model consists of a study that has been established based on the geometrical parameters and operating conditions similar to the experimental work. The influence of four different cross sections of minifins (shaped as square, trapezoidal, triangular, and sinusoidal) and of number of triangular minifins (1, 3, 5, 7, and 9) and their positions (in the regions of entrance, central, and terminal) on the heat transfer rate and pressure drop in a minifin minichannel heat sink are numerically investigated by a two-dimensional CFD model. The coolant is Cu–water nanofluid at a volumetric concentration of 2%. The results demonstrated that the sinusoidal minifin minichannel heat sink has the highest convective heat transfer coefficient in comparison with other shapes, while the trapezoidal minifin minichannel showed the highest thermal resistance. The highest pressure drop was observed for the triangular minifin inside minichannel. By increasing the number of fins, thermal resistance considerably decreased. Likewise, at the central and entrance positions, respectively, the highest Nusselt number and friction factor inside the minichannel was observed. This study can provide useful guidelines for the design of the cooling devices.     

Heat transfer characteristics of impinging jets: The influence of unsteadiness with different waveforms

A series of experiments are conducted in which specially designed periodic air jets are applied to a heated surface for the purpose of enhancing heat transfer relative to the corresponding steady air jet. The periodic jets are produced by a mass flow rate controller. The experiments are performed for steady jets and for specially designed periodic jets, including a combination of sinusoidal, triangular and rectangular jets at frequencies from 1.25 to 20 Hz, the triangular signal having a different symmetry (representing the ratio of time to increasing velocity in one cycle to total cycle time) and the rectangular jets having a variable duty cycle (representing the ratio of the pulse cycle on-time to off-time) at frequencies of 10 Hz and 20 Hz. Various unsteady jets show distinguishing frequency dependences and the step change, i.e. the sudden increase or decrease of signal, shows some advantageous influence on heat transfer improvement, especially negative step change. Therefore, the enhancement of combined signals lies between the performances of the individual signals. The enhancement for triangular (or sinusoidal) plus rectangular signals shows some improved performance compared with that of rectangular plus triangular (or sinusoidal) signals. The heat transfers are enhanced as Strouhal number increases from 0.004 to 0.068 on the whole for impinging jet with such combined signals. The signals of triangular jet with symmetry parameter of 0 and 1 have improved heat transfer, and the latter has a slightly better result than the former. The instantaneous changing rate of velocity also has an influence on heat transfer improvements. Thus the duty cycle of 1:2 has the best performance in terms of heat transfer enhancement in this study.     

透明蜂窝结构太阳辐射透过率的简化分析

对透明蜂窝结构太阳辐射透过率进行理论分析，提出一个适用于工程应用的近似公式，该方法忽略了对透过率贡献极小的透明蜂窝材料的散射，漫反射和漫透射，认为进入蜂窝单元底部的太阳辐射由三部分组成：１）经壁面的多次透射，２）经本单元壁面多次反射，３）经相邻单元的多次透射与反射，其中第一部分是主要的，据此，可导出横截面为四边形的蜂窝结构的透过率随太阳辐射入射角变化的近似公式，并由实验结果得到验证。     

NUMERICAL PREDICTION OF LAMINAR FORCED CONVECTION IN TRIANGULAR DUCTS WITH UNSTRUCTURED TRIANGULAR GRID METHOD

The flow and heat transfer characteristics of smooth triangular ducts with different apex angles of 15, 30, 60, and 90 under the fully developed laminar flow condition were predicted numerically using a finite volume method. The SIMPLE-like algorithm was employed together with an unstructured triangular grid method, where the grid was generated by a Delaunay method. The triangular grid was adopted instead of the traditional rectangular grid to fit better into the triangular cross section of the duct. Two kinds of boundary condition (uniform wall temperature and uniform wall heat flux) were considered. Comparison of the predictions with previous computational results indicated a very good agreement. Both the friction factor and Nusselt number (Nu) showed a strong dependence on apex angle of the triangular duct. When the apex angle was 60, the duct provided the highest steady-state forced convection from its inner surface to the airflow under the laminar flow condition.     

ON THE APPLICATION OF THE METHOD OF ORTHOGONAL PROJECTION IN HEAT CONDUCTION

The method of orthogonal projection is applied in the first stage of thermoelastic problems involving specification of the temperature field in a uniform, infinitely long, elastic bar heated by an electric current, the surface of the bar being kept at zero temperature. Three kinds of cross sections of the bar are considered: elliptical, equilateral triangular, and in the form of a circular sector. All the function-space concepts that are used are briefly explained, but the treatment is purely intuitive.     

Investigations on Forced Convection in Compact Passages With Surface Irregularities

Two-dimensional, fully developed, convective heat transfer in compact passages is investigated numerically, incorporating the effects of the surface irregularities, to analyze the influence of these irregularities on fluid flow and heat transfer. This analysis helps to bring out the differences in the performance evaluation if regular cross sections are assumed in analyzing compact and mini channels. Forced convection in compact passages with an apparent rectangular shape is analyzed using a finite-difference method. The calculation is validated experimentally using Michelson interferometry. The numerical results for the channel, incorporating surface irregularities, are compared with those assuming a regular cross-sectional geometry. The results indicate that the coefficient of friction and the Nusselt number calculated for channels, considering the irregular cross section, are less than those predicted using an assumption of regular geometry. The results provide some insight into the reasons for the observed deviations in the comparisons. The observations are attributed to the influence of the surface irregularities on the relative dominance of the surface area to the cross-sectional area, which gets pronounced in compact passages. The findings suggest that some of the observed deviations in the performance of compact passages, compared to theoretical results, may be due to the use of regular geometries to define domain shapes while performing theoretical analysis.     

Discussion on the Effect of a Fluid Domain around Fins and Grid Discretization in Buoyancy-Driven Convection

In the numerical study of heat sinks, it is known that a sufficient amount of fluid domain should be added at each side of the heat sink. However, the question in this context is: what can be defined as sufficiently far away from the heat sink? Different authors use different sizes of the computational domain around the heat sink. In this work the impact of the size and location of the fluid domain on the calculated heat transfer coefficient is investigated. Three fin row types are studied: a rectangular, an interrupted rectangular, and an inverted triangular fin row. First, the influence of adding fluid domain to the sides of the heat sink is studied. A large decrease of the heat transfer coefficient on both sides and bottom is observed. Next, the influence of adding fluid domain on both the top and the sides is studied. For the rectangular fins, the impact on the lumped heat transfer coefficient is +12% compared to the case without any fluid domain added. For the inverted triangular fin shape, no net effect is observed on the lumped heat transfer coefficient. So the impact of adding fluid domain depends on fin shape that is investigated. For the sides only, a small amount of fluid needs to be added, while for the fluid domain on top of the heat sink, 130% of the equivalent fin height is found as a good option to simulate the fin in computational fluid dynamics.     

Heat transfer in rectangular microchannels during volumetric heating of the substrate

Convective heat transfer in microchannels with rectangular and square cross sections are analyzed for volumetric heat generation in the substrate due to an imposed magnetic field. Gadolinium was used as the substrate material and water as the working fluid. Gadolinium is a magnetic material that exhibits high temperature rise during adiabatic magnetization around its transition temperature of 295 K. A thorough investigation for velocity and temperature distributions was performed by varying channel aspect ratio, Reynolds number, and heat generation rate in the substrate. With the increase in Reynolds number, the outlet temperature decreased and the average Nusselt number increased.