Constructal multi-scale structure of PCM-based heat sinks

This paper inquires the effectiveness of a PCM-based heat sink as a reliable solution to portable electronic devices. This sink is composed of a PCM with low thermal conductivity and fins to boost its conductivity. The optimization is subjected to fixed heat sink volume filled with PCM between vertical equidistant fins. New fins are installed in the unheated space existing in each enclosure which is not involved in thermal distribution from vertical fins to the PCM. Based on the same principle, new fins generations are augmented stepwise to the multi-scale structure. The steps of adding fins will continue up to the point that the objective function reaches its maximal value, i.e., maximizing the longest safe operation time without allowing the electronics to reach the critical temperature. The results indicate that in each length of the enclosure, the optimum volume fraction and the best fins distance values exist in which the heat sink performance becomes maximum, and adding more fins lowers the performance of the heat sink. Increasing the enclosure’s length by \(2^{n}\) does not change them. For an enclosure with constant length, the optimal number of steps for adding fins within the enclosure is a function of the fin thickness. The results indicate that increasing the thickness changes the optimal number of adding fins inside the enclosure (normally a decrease). As the fin thickness is lowered, there will be a higher effect by adding vertical fins in the enclosure. Numerical simulations cover the Rayleigh number range \(2\times 10^{5}\le \hbox {Ra}_{\mathrm{H}} \le 2.7\times 10^{8}\), where H is the heat sink height.     

Analytical and numerical solution along with PC spreadsheets modeling for a composite fin

Heat transfer through composite fins is investigated by both analytical and numerical methods. In this regard, governing differential equations of the two dimensional fin and one dimensional cladding are studied to examine the effect of Biot number and ratio of thermal conductivities of the fin material to the cladding, on the dimensionless temperature profiles. The results show that one dimensional analysis, traditionally used in fin analysis, is not applicable for composite fins, particularly when the conductivity ratio of the composite fin materials is low. In addition, the use of spreadsheet programs in solving the fin problem is investigated in somewhat more detail with regard to the solution as well as presentation of the graphical results.     

Thermal performance of a carbon fiber composite material heat sink in an FC-72 thermosyphon

This study analyzes the use of a carbon fiber epoxy heat sink for evaporator surface enhancement in a FC-72 thermosyphon. The pin-fin heat sink features 945 small-cross-section (1.27 mm by 0.965 mm) fins fabricated with an integral base plate. These fins have a high thermal conductivity (500 W/m K) along the length of the fin. The influence of heat load, thermosyphon fill volume, and condenser operating temperature on the overall thermal performance is examined. The results of this experiment provide significant insight into the possible implementation and potential benefits of carbon-fiber heat sink technology in two-phase flow leading to significant improvements in thermal management strategies for advanced electronics.     

L- and U-shaped heat pipes thermal modules with twin fans for cooling of electronic system under variable heat source areas

This study utilizes a versatile superposition method with thermal resistance network analysis to design and experiment on a thermal module with embedded six L-shaped or two U-shaped heat pipes and plate fins under different fan speeds and heat source areas. This type of heat pipes-heat sink module successively transfer heat capacity from a heat source to the heat pipes, the heat sink and their surroundings, and are suitable for cooling electronic systems via forced convection mechanism. The thermal resistances contain all major components from the thermal interface through the heat pipes and fins. Thermal performance testing shows that the lowest thermal resistances of the representative L- and U-shaped heat pipes-heat sink thermal modules are respectively 0.25 and 0.17 °C/W under twin fans of 3,000 RPM and 30 × 30 mm² heat sources. The result of this work is a useful thermal management method to facilitate rapid analysis.     

Effects of the heat transfer fluid velocity on the storage characteristics of a cylindrical latent heat energy storage system: a numerical study

A numerical study of the effects of the thermal fluid velocity on the storage characteristics of a cylindrical latent heat energy storage system (LHESS) was conducted. Due to the low thermal conductivity of phase change materials (PCMs) used in LHESS, fins were added to the system to increase the rate of heat transfer and charging. Finite elements were used to implement the developed numerical method needed to study and solve for the phase change heat transfer (melting of PCM) encountered in a LHESS during charging. The effective heat capacity method was applied in order to account for the large amount of latent energy stored during melting of the PCM and the moving interface between the solid and liquid phases. The effects of the heat transfer fluid (HTF) velocity on the melting rate of the PCM were studied for configurations having between 0 and 18 fins. Results show that the overall heat transfer rate to the PCM increases with an increase in the HTF velocity. However, the effect of the HTF velocity was observed to be small in configurations having very few fins, owing to the large residual thermal resistance offered by the PCM. However, the effect of the HTF velocity becomes more pronounced with addition of fins; since the thermal resistance on the PCM side of the LHESS is significantly reduce by the large number of fins in the system.     

Analytical approximation for solidification processes in PCM storage with internal fins: imposed heat flux

Uses of thermal energy storage systems have expanded notably in recent decades. In thermal energy systems, internal heat transfer enhancement techniques such as fins are often used because of the low thermal conductivity of the phase change materials (PCMs). In this paper, solidification of a PCM is studied in a rectangular storage with horizontal internal plate fins and an imposed constant heat flux on the vertical walls. A simplified analytical solution is presented and its results are compared to those for a numerical approach based on an enthalpy method. The fraction of solidified PCM in storage is calculated with the derived analytical model which determines how much of the storage is solidified after a certain time. The results show that the analytical model satisfactorily estimates the solid–liquid interface and the temperature distribution for the fin, which are useful in the design of PCM-based thermal energy storage or cooling systems.     

Effects of the number and distribution of fins on the storage characteristics of a cylindrical latent heat energy storage system: a numerical study

A numerical study of the effects of the number and distribution of fins on the storage characteristics of a cylindrical latent heat energy storage system (LHESS) was conducted. Due to the low thermal conductivity of phase change materials (PCMs) used in LHESS, fins were added to the system to increase the rate of heat transfer and charging. Finite elements were used to implement the developed numerical method needed to study and solve for the phase change heat transfer (melting of PCM) encountered in a LHESS during charging. The effective heat capacity method was applied in order to account for the large amount of latent energy stored during melting of the PCM and the moving interface between the solid and liquid phases. The effects of increasing the number and distribution of fins on the melting rate of the PCM were studied for configurations having between 0 and 27 fins for heat transfer fluid (HTF) velocities of 0.05 and 0.5?m/s. Results show that the overall heat transfer rate to the PCM increases with an increase in the number of fins irrespective of the HTF velocity. It was also observed that the total amount of energy stored after 12?h increases nearly linearly with the addition of fins up to 12 fins; further addition of fins increasing the total energy stored by ever smaller amounts.     

Analytical model for melting in a semi-infinite PCM storage with an internal fin

The most PCMs with high energy storage density have an unacceptably low heat conductivity and hence internal heat transfer enhancement techniques such as fins or other metal structures are required in latent heat thermal storage (LHTS) applications. Previous work has concentrated on numerical and experimental examination in determining the influence of the fins in melting phase change material. This paper presents a simplified analytical model based on a quasi-linear, transient, thin-fin equation which predicts the solid-liquid interface location and temperature distribution of the fin in the melting process with a constant imposed end-wall temperature. The analytical results are compared to the numerical results and they show good agreement. Due to the assumptions made in the model, the speed of the solid-liquid interface during the melting process is slightly too slow.     

Performance analysis and optimization of radiating fins with a step change in thickness and variable thermal conductivity by homotopy perturbation method

Although tapered fins transfer more rate of heat per unit volume, they are not found in every practical application because of the difficulty in manufacturing and fabrications. Therefore, there is a scope to modify the geometry of a constant thickness fin in view of the less difficulty in manufacturing and fabrication as well as betterment of heat transfer rate per unit volume of the fin material. For the better utilization of fin material, it is proposed a modified geometry of new fin with a step change in thickness (SF) in the literature. In the present paper, the homotopy perturbation method has been used to evaluate the temperature distribution within the straight radiating fins with a step change in thickness and variable thermal conductivity. The temperature profile has an abrupt change in the temperature gradient where the step change in thickness occurs and thermal conductivity parameter describing the variation of thermal conductivity has an important role on the temperature profile and the heat transfer rate. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found. The derived condition of optimality gives an open choice to the designer.     

Thermal analysis of a finned-tube LHTS module for a solar dynamic power system

 This paper investigates the transient behaviour of a finned tube latent heat thermal storage (LHTS) module that is put into use in space based power systems, or such similar energy storage applications. The shell side of the module is loaded with phase change material (PCM) while the tubes carry the heat transfer fluid (HTF). Thin circumferential fins are added externally onto the tube surface at equal spacings. The LHTS module is mathematically modeled with an enthalpy based method and the resulting system of conjugate governing equations is numerically solved for charging mode. The influence of various parameters viz. geometrical, thermophysical and various non-dimensional numbers on the performance of the unit is studied. Numerical results indicate an appreciable enhancement in the energy storage process with the addition of fins in the module for an effective utilisation of the available solar energy during the active phase of the orbit orcharging cycle. Received on 1 September 2000 / Published online: 29 November 2001     

Freezing around a finite heat sink immersed in an infinite phase change medium

Freezing around a spherical heat sink immersed in an infinite phase change medium — a free boundary problem involving growth and decay of the free boundary — is analysed here. A one-dimensional conduction model is formulated and the resulting partial differential equations are solved by finite difference methods. The energy discharged from the phase change medium during the heat transfer process is analysed for latent heat thermal energy storage applications. Results are presented for a wide range of parameters that are encountered in energy storage devices. The cases of slab/cylindrical heat sink are reexamined for a range of parameters not covered by the earlier investigators     

Heat transport of hybrid nanomaterial in an annulus with quadratic Boussinesq approximation

The convective heat transfer of hybrid nanoliquids within a concentric annulus has wide engineering applications such as chemical industries, solar collectors, gas turbines, heat exchangers, nuclear reactors, and electronic component cooling due to their high heat transport rate. Hence, in this study, the characteristics of the heat transport mechanism in an annulus filled with the Ag-MgO/H_2O hybrid nanoliquid under the influence of quadratic thermal radiation and quadratic convection are analyzed. The nonuniform heat source/sink and induced magnetic field mechanisms are used to govern the basic equations concerning the transport of the composite nanoliquid. The dependency of the Nusselt number on the effective parameters(thermal radiation, nonlinear convection,and temperature-dependent heat source/sink parameter) is examined through sensitivity analyses based on the response surface methodology(RSM) and the face-centered central composite design(CCD). The heat transport of the composite nanoliquid for the spacerelated heat source/sink is observed to be higher than that for the temperature-related heat source/sink. The mechanisms of quadratic convection and quadratic thermal radiation are favorable for the momentum of the nanoliquid. The heat transport rate is more sensitive towards quadratic thermal radiation.     

Thermodynamic analysis of a thermal storage unit under the influence of nano-particles added to the phase change material and/or the working fluid

The thermal storage unit consists of two concentric cylinders where the working fluid flows through the internal cylinder and the annulus is filled with a phase change material. The system carries out a cyclic operation; each cycle consists of two processes. In the charging process the hot working fluid enters the internal cylinder and transfers heat to the phase change material. In the discharging process the cold working fluid enters the internal cylinder and absorbs heat from the phase change material. The differential equations governing the heat transfer between the two media are solved numerically. The numerical results are compared with the experimental results available in the literature. The performance of an energy storage unit is directly related to the thermal conductivity of nano-particles. The energy consumption of a residential unit whose energy is supplied by a thermal storage system can be reduced by 43?% when using nano-particles.     

Interaction between heat dipole and circular interracial crack

The heat dipole consists of a heat source and a heat sink. The problem of an interfacial crack of a composite containing a circular inclusion under a heat dipole is investigated by using the analytical extension technique, the generalized Liouville theo-rem, and the Muskhelishvili boundary value theory. Temperature and stress fields are formulated. The effects of the temperature field and the inhomogeneity on the interracial fracture are analyzed. As a numerical illustration, the thermal stress intensity factors of the interfacial crack are presented for various material combinations and different po-sitions of the heat dipole. The characteristics of the interfacial crack depend on the elasticity, the thermal property of the composite, and the condition of the dipole.     

Simulation of metal matrix composite solidification in the presence of cooled fibers

Metal matrix composite (MMC) has been well known for its superior material properties compared with traditional composite. A new method is introduced to improve the properties of MMC in the sense that the ends of the reinforcement phase of the composite are allowed to extend out of the mold and cooled by a heat sink in order to promote the rate of heat transfer through the fibers and promote the formation of primary alpha phase around the reinforcement. This paper presents the experimental results obtained from the foundry in the University of Wisconsin-Milwaukee and some numerical simulation results of the solidification process in the cast mold.     

Interaction between heat dipole and circular interfacial crack

The heat dipole consists of a heat source and a heat sink. The problem of an interracial crack of a composite containing a circular inclusion under a heat dipole is investigated by using the analytical extension technique, the generalized Liouville theorem, and the Muskhelishvili boundary value theory. Temperature and stress fields are formulated. The effects of the temperature field and the inhomogeneity on the interracial fracture axe analyzed. As a numerical illustration, the thermal stress intensity factors of the interfacial crack are presented for various material combinations and different positions of the heat dipole. The characteristics of the interfacial crack depend on the elasticity, the thermal property of the composite, and the condition of the dipole.     

Influence of vibration in enhancement of heat transfer rates from thin plannar fins

The enhancement of heat transfer rates without an extension of heat removal surface area due to packaging and compactness is essential. This paper investigates the possibility of the enhancement of heat transfer rate from heat sink having thin planner fins by normal vibration. In this study; the heat sink was selected to be the personal computer heat sink as a test specimen. It has four similar quadrants; each quadrant has a definite number of thin planer fins. The specimen is heated by an electric heater at its bottom. A circular disc cam with an offset center is used to vibrate the specimen with different displacement amplitude and frequency. Temperature measurements for both the surface of the specimen and surrounding air were recorded and saved by using a data acquisition system at different sample times according to the vibration frequency. The effect of both vibration frequency and displacement amplitude on the enhancement of heat transfer rate was clarified. Deduced empirical correlation among Nusselt number, Strouhal number and Reynolds number was found. It was found that the normal vibration can enhance the heat transfer rate for the case study by about 85% rather than the steady flow case if both are having the same average velocity. In a comparison among the present investigation and those by the literature, the influence of vibration on heat transfer enhancement may be slightly greater than that of the pulsating flow.     

Optimization of an ammonia-cooled rectangular microchannel heat sink using multi-objective non-dominated sorting genetic algorithm (NSGA2)

The ever decreasing size of modern electronic packaging has induced researchers to search for an effective and efficient heat removal system to handle the continuously increasing power density. Investigations have involved different geometry, material and coolant to address the thermal management issues. This paper reports the potential improvement in the overall performance of a rectangular microchannel heat sink using a new gaseous coolant namely ammonia gas. Using a multi-objective general optimization scheme with the thermal resistance model as an analysis method in combination with a non-dominated sorting genetic algorithm as an optimization technique, it was found that significant reduction in the total thermal resistance up to 34?% for ammonia-cooled compared to air-cooled microchannel heat sink under the same operating conditions is achievable. In addition, a considerable decrease in the microchannel heat sink’s mass up to 30?% was achieved due to the different heat sink’s material used.     

Numerical simulation of turbulent heat transfer from perforated plate-fin heat sinks

Excessive heat from microelectronic components is essential to remove to increase the reliability of the system. In this paper, various types of perforations in the form of small channels such as square, circular, triangular and hexagonal cross sections are introduced and thermal performances are compared to improve the cooling performance of heat sink. The governing equations are solved by adopting a control volume based finite element method with an unstructured non-uniform grid system. Flow and heat transfer characteristics are presented for Reynolds numbers from 2 × 10⁴ to 4 × 10⁴ based on the fin length and Prandtl number is taken as Pr = 0.71. RANS based k-ε turbulence model is used to predict the turbulent flow parameters. The predicted results are validated by the previously published experimental data and in reasonable agreement with the experiment. Results show that fins having circular perforations have better thermal and fluid dynamic performances than the other types of fins considered here.