Heat transfer physics

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In an isolated system, given heat is always equal to taken heat or heat change in the system is equal to zero. If two objects having different temperatures are in contact, heat transfer starts between them. The amount of heat given is equal to the amount of heat taken. Object one has mass m 1 , temperature t 1 and specific heat capacity c 1 , object two has mass m 2 , temperature t 2 and specific heat capacity c 2.

Flow boiling process is a ubiquitous thermal transport technique that has played a key role in many technological and industrial applications for more than half a century. The unique ability of this mechanism in transferring substantial amount of heat from a heated surface has enabled critical technologies ranging from HVAC systems to large boilers that power electricity generation plants. In recent years, major advancements of manufacturing technologies in areas such as power and RF electronics, high performance computers and solid-state lasers have led to extremely high heat generation rates in small volumes 1 , 2 , 3 , 4 which in turn have prompted the scientific community to implement the flow boiling process in microchannels 5 , 6 , 7 , 8 , 9 , 10 , To achieve this goal, numerous studies have been conducted to characterize and enhance heat transfer performance of microchannel heat sinks.

These studies 4 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 have identified different mechanisms responsible for heat transfer enhancement in the microchannel flow boiling process. Liquid rewetting of the surface 4 , 14 , 15 , 18 , bubble nucleation and growth 4 , 14 , 15 , 16 , and thin film evaporation 12 , 13 , 17 can have a significant impact on heat transfer in microchannels, depending on the flow regime, wall temperature and input heat flux.


Integration of surface structures on the microchannels walls has been suggested as a means of enhancing the heat transfer coefficient and the critical heat flux CHF. These structures have been proven to enhance the heat transfer coefficient and the CHF in the pool boiling process 6 , 7 , 8 , 9 , 10 , 11 , 20 , 21 , 22 , The reported enhancement in heat transfer and CHF was mainly attributed to improved surface wickability 10 , 21 , increase in active nucleation sites 23 and enhanced heat transfer area 8 , 9 , 22 associated with such structures.

However, their implementation on microchannels walls has produced mixed results ranging widely from a decline to a substantial increase in performance. Li et al.

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The authors suggested that substantial ebullition from the nanowires at the microchannel entrance resulted in a rapid transition of flow to an annular flow regime. The authors then argued that at the higher mass fluxes, a liquid film forms more easily on the microchannel surface and is able to persist over the duration of the annular flow resulting in enhanced boiling heat transfer. But, at the lowest mass flux, the liquid film disappears more quickly, and the consequent dryout leads to an inferior heat transfer performance to that of the microchannels with plain walls.

Yang et al.

Second Law of Thermodynamics

Unfortunately, Yang et al. They argued that the vapor core formed within the channel rapidly grows and eventually approaches the microchannel walls. As a result, the unsaturated nanowires in the downstream instantly act as wicking structures to activate capillary flows along the channels walls. In a more recent study, through an analysis of different forces inertia, surface tension, shear, buoyancy and evaporation momentum forces , Alam et al.

They argued that a low contact angle on walls with nanowires results in a higher surface tension and therefore a lower Weber number compared to the flow in a microchannel with a plain surface, leading to a uniform and more stable liquid film over a surface with nanowires. Nanowires have also been utilized to enhance the flow boiling heat transfer performance of the FC liquid. Shin et al.

The results indicated a decline in CHF in all test conditions. The changes in the heat transfer coefficient followed a complicated pattern ranging from a decline to enhancement depending on the nanowires height, flow Re number, and surface superheat temperature and heat flux. The authors argued that enhanced nucleation as well as convective effects could be responsible for the observed enhancement of the surface heat transfer coefficient in the case of long nanowires.

Evidently, the existing literature is lacking a mechanistic description of the role of surface structures on the microchannel flow boiling heat transfer process.

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Here, through experiment and modeling, it is clearly shown how surface structures impact a key mechanism of heat transfer in the flow boiling process i. In the following section, first, a unique experimental approach is employed to identify details of the individual heat transfer events in the microchannel flow boiling heat transfer process.

The evaporation time scale of the liquid film formed within the surface structures is directly measured in an experiment involving a single instrumented microchannel and controlled flow conditions. A model is then introduced that provides the key parameters dictating the flow and evaporation of the liquid film within the surface structures. Finally, a second experimental study is introduced to demonstrate the efficacy of the proposed model in predicting the optimal spacing of the patterned surface structures in a typical microchannel heat sink.

Recently 12 , 13 , the authors have studied the thermal field underneath a moving bubble and demonstrated that the evaporation of a thin liquid film formed on the microchannel surface is a key heat transfer mechanism. This process is hypothesized to be affected when the surface of a microchannel is patterned. Hence, an experiment is designed to directly measure the local surface heat flux and the dryout time of the thin liquid films formed on a plain as well as five textured surfaces.

A unique experimental approach is utilized which is capable of measuring the local heat flux. Details of the test article are shown in Fig. The test device consists of two temperature sensor arrays top and bottom RTD arrays depicted in Fig. These sensors are calibrated prior to the experiments in a uniform temperature oven to obtain the resistance-temperature relationship of each sensor.

The test platform is a microfluidic chip Fig. The surface structures i. The structures are made from SU8 through spin coating and using the electron-beam lithography EBL technique. SEM images of the pillars are provided in Fig. A total of five structures with pillar spacings 0.

The tests are conducted with FC liquid at saturation conditions. The cavity is surrounded by a pulsed function microheater cf. This configuration allows us to generate bubbles at a desired frequency and size. The thin film heaters are also powered by the NI dc power supply. All data collection, as well as the control for the applied dc voltages of the heaters, are performed using a LabVIEW program. The working fluid is delivered to the microfluidic chip by a piezoelectric micropump Model MP6, manufactured by Bartels Mikrotechnik GmbH.

The working fluid is degassed by vigorous boiling for several hours before each experiment. Further details of the fabrication process, experimental procedures, calibration tests, and uncertainty analysis are presented in the Supplementary Materials section. To understand the role of surface patterns, the heat transfer events on a plain surface are first analyzed. This analysis is accomplished by evaluating the thermal field at sensor 14 located at the center of the channel where the local dryout is initially expected.

The corresponding local temperature and heat flux data are provided in Fig. The blue and red shadow lines indicate the times at which the front and rear ends of the bubble arrive at the sensor footprint, respectively. Therefore, the observed heat flux rise is due to the evaporation of a liquid layer formed on the surface as a result of the preceding liquid slug flow.

Test is conducted at a mass flux of As it can be seen, the surface experiences a second spike in heat flux as the rear end of the bubble rewets the sensor footprint. This sudden spike in the local heat flux resembles observations made in pool boiling studies during the bubble departure, as the liquid front advances over i.

After the liquid slug fully rewets the surface, the local heat flux gradually decreases and approaches that of the single-phase heat transfer. As the results indicate, the nature of heat transfer is predominately governed by the thin film evaporation mode of heat transfer. Figure 3a—c show images of the bubble shown in Fig. A comparison of the bubble images shown in Figs 2c and 3c indicates that the three-phase line is pulled further into the channel providing a visual verification of the effect of pillars on the liquid distribution. The corresponding local temperature and heat flux data measured at sensor 36 are shown in Fig.

While the heat transfer event observed on the patterned surface is very similar to that observed on a plain surface, the measured heat flux and drying time of the surfaces differ.

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A comparison of the drying time scales observed in Figs 2e and 3e suggests that a liquid film formed on a textured surface takes a longer time to evaporate compared to a liquid film formed on the plain surface. This observation shows that the capillary wicking effect induces the liquid micro-inflows within the pillars during the thin film evaporation process leading to a longer drying time scale.

Also, the results clearly show that the thermal characteristics of the other heat transfer events i. In the previous section, it was shown that during the flow boiling process in a microchannel vapor slugs form and interrupt the otherwise continuous liquid flow stream. Here, it is assumed that the liquid and vapor slugs are flowing at a velocity of U to estimate the exposure time of the heat transfer surface to a bubble i.

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In the test conditions of this study, heat transfer associated with the liquid slug can be predicted fairly accurately using the single-phase laminar flow theory. The thermal events associated with the vapor slug flow are the thin film evaporation and the surface partial dryout processes. Hence, the surface heat transfer associated with the vapor slug flow can be presented as:.

Figure 4a,b depict the liquid film wicking and evaporation on a textured surface as well as the meniscus formed between surface micropillars, respectively.

Temperature is just a name to describe the state of vibration of the molecules.

An average liquid layer thickness is assumed that continuously varies during the thin film evaporation process. The heating length scale, , is also introduced which factors in the fact that extended surfaces shorten the heat transfer path to the liquid-vapor interface. To determine the heating length scale, a 3D conduction heat transfer equation is numerically solved. The heating length scale is then defined as where and are the projected liquid-vapor interface area and the total heat transfer from the solid area to the liquid, respectively. The simulation results shown in Fig.

The heat flux associated with the thin film evaporation process can then be estimated by where A r is the ratio of the projected liquid-vapor interface area to that of a unit cell between the pillars cf. By combining Eqs 1 and 2 and neglecting the small heat transfer during the partial dry-out period, the two-phase heat transfer can be determined as:. Schematics showing cross-sectional and top views of surface pillars depicting a liquid wicking and evaporation, b heat flow from the walls to the liquid-vapor interface and c difference between the overall wick projected and evaporation areas.

The bubble generation frequency and parameters and f. Therefore, the above equation suggests that the two-phase heat transfer has a linear relationship with parameter with a proportionality constant of f. The drying time scale associated with the evaporation of the liquid film fed by the capillary induced micro-inflows can be determined by applying a mass balance to the control volume shown in Fig.

Through this approach, an equation was developed which could express variations in the average liquid layer thickness during combined wicking-thin film evaporation process as follows:. V is the mean imbibition velocity of the liquid wicked into the surface structures.

Heat transfer

As mentioned earlier, capillary pressure induced by narrow gaps within the surface structures generates micro-inflows that replenishes the liquid vaporized during the thin film evaporation process. When one end of a metal rod is put into a fire, the energy from the flame makes the ions in the rod vibrate faster. Since the ions in the solid metal are close together, this increased vibration means that they collide with neighbouring ions more frequently. Energy is passed on through the metal by these collisions, transmitting the energy.

More frequent collisions increase the rate of transfer.