No description available.

<p>In an effort to better understand the physical mechanisms responsible for pool boiling heat transfer, an analytical model is developed that better describes the changing shape and size of a growing bubble. Indeed, any analysis of thermal transport due to nucleate pool boiling requires bubble frequency predictions which are intimately linked to bubble volume. The model is developed and validated for quasi-static bubble growth due to gas injection and for bubble growth due to vaporization within the heat-transfer controlled growth regime; it highlights the need to include the asymmetric nature of growing bubbles when modeling bubble growth.</p> <p>In addition, a numerical study of quasi-static bubble shape for both adiabatic bubble growth and vapour bubble growth provides insight into the dependence the bubble shape evolution has on the Bond number. In so doing, bubble profiles generated from a numerical treatment of the Capillary equation are benchmarked to quasi-static gas injected bubble formations and to heat-transfer controlled vapour bubble formations.</p> <p>The numerical treatment of bubble shape evolution leads to a simplifying bubble geometry for low Bond number applications. The geometric model accounts for bubble shape transformation throughout the bubble growth cycle including the necking phenomenon. An analytical model of quasi-static adiabatic bubble growth is accordingly developed based on the proposed low Bond number geometric model; it is coupled with a geometric detachment relation and a force balance detachment criterion that are dependent on the Bond number. The resulting predicted bubble growth characteristics, such as profile, volume, centre of gravity and aspect ratio, are validated with the benchmarked numerical treatment of the problem.</p> <p>Furthermore, the low Bond number geometric model is applied to bubble growth due to vaporization. In order to solve the mass-energy balance at the vapour bubble interface, a spherical surface area is commonly assumed. This leads to the need for correction factors and provides little insight into the physical mechanism responsible for bubble shape. In this study, the transitioning shape of a vapour bubble is considered in the integral analysis of the interfacial mass-energy balance. The model predicts the following bubble growth characteristics: profile, volume, centre of gravity, and aspect ratio.</p> / Doctor of Philosophy (PhD)

The effect of using high voltage DC and AC on the heat transfer process during the melting of a Phase Change Material (PCM) in a rectangular enclosure was studied experimentally and numerically. The experiments were conducted for two configurations: (a) a horizontal rectangular enclosure in which the initial melting process is governed by heat conduction, (b) a vertical rectangular enclosure in which the initial melting process is governed by heat convection. The level of heat transfer enhancement was quantified by using a novel experimental facility for the horizontal configuration. The experimental methodology was verified first against non-EHD melting cases and then was further expanded to include the EHD effects. The experiments showed that EHD forces can be used to enhance a conduction dominated melting up to a maximum of 8.6-fold locally and that the level of enhancement is directly related to the magnitude of the applied voltage. It was found that the main mechanism of enhancement in these cases can be attributed to the electrophoretic forces and that the role of the dielectrophoretic forces is minimal under the applied voltages. In the vertical configuration, the effect of the magnitude of the applied voltage, the applied voltage wave-form, the gravitational Rayleigh number, Stefan number and the aspect ratio of the enclosure on the heat transfer enhancement were investigated experimentally. A novel shadowgraph experimental measurement system was developed and verified against the analytical correlations of natural convection in rectangular enclosures and the non-EHD melting performance was verified against the bench mark experiments of Ho (1984). The shadowgraph system was used to measure the local heat transfer coefficient across the heat source wall (the heat exchanger surface). The local heat transfer measurements along with the melting temporal profiles were used to explain and visualize the coupling between the Electrohydrodynamics (EHD) forces and the gravitational forces. It was found that the EHD forces could still enhance the melting process even for an initially convection dominated melting process. The mechanism of enhancement was found to be a bifurcation of the initial convection cell into multiple electro-convective cells between the rows of the electrodes. The shadowgraph system was used to assess the interaction between the electrical and the gravitational forces through the visualization of these cells and quantifying their size. The EHD heat transfer enhancement factor was found to increase by the increase of the applied voltage, reaching a 1.7 fold enhancement at the lower gravitational Rayleigh number tested and 1.45 fold for the highest gravitational Rayleigh and Stefan number. The effect of the polarity of the applied voltage was tested for the different cases and it was found that there was no significant difference between the positive and the negative polarities when the magnitude of the applied voltage was below 4 kV. At higher voltages- 6kV- the negative polarities showed better level of enhancement when compared to the positive applied voltage. It was again found that the main mechanism of enhancement is attributed to charge injection from the high voltage electrodes. A scaling analysis was conducted based on the previous conclusions and the dominant mechanism of enhancement to describe the problem in non-dimensional form. An electrical Rayleigh number was introduced and its magnitude was correlated to the magnitude of the injected current. The melt volume fraction was then represented against the non-dimensional parameter (n+1)(H/W)Fo.Ste.RaE^0.25 and the melt fraction temporal profiles for the different voltages collapsed well against this parameter. Finally, a numerical analysis was conducted on the role of the dielectrophoretic forces during the melting of Octadecane and when they would become of significant importance. The results of the numerical model supported the experimental findings and suggested that a minimum of 15 kV is needed in order to realize the effect of the dielectrophoretic forces. The numerical model was used to understand the interaction between the gravitational and the dielectrophoretic forces at different ranges of both gravitational Rayleigh number and electrical Rayleigh number. The model was complemented with scaling analysis to determine the governing scales of the problem and the dielectrophoretic Rayleigh number was deduced from the study. / Thesis / Doctor of Philosophy (PhD)

A framework that presents a new methodology for design-evaluation of active solar collection systems was developed. Although this methodology emphasizes the importance of detailed modeling for accurate prediction of building performance, it also presents a process through which the detailed modeling results can be reused in a simplified iterative procedure allowing the designer the flexibility of revising and improving the preliminary design. For demonstration purposes, the framework was used to design and evaluate two case studies located in Blacksburg (VA) and Minneapolis (MN). These locations were selected because they both represent a cold weather region; presenting a need for using solar energy for heating and hot water requirements. Moreover, the cold weather in Blacksburg is not as severe as in Minneapolis. Therefore, the two cases will result in different thermal loading structures enabling the framework validation process. The solar collection system supplying both case studies consisted of a low temperature flat plate solar collector and storage system. Thermal performance of the case study located in Blacksburg was conducted using detailed modeling evaluation techniques; while thermal performance of the case study located in Minneapolis was conducted using a simplified modeling evaluation technique. In the first case study, hourly evaluation of the thermal performance of the solar collection system was accomplished using finite element (FE) analysis, while hourly evaluation of the building thermal performance was made using Energy Plus software. The results of the finite element analysis were used to develop a statistical predictive design equation. The energy consumption for the second case study was calculated using the heating design day method and the energy collection for that case study was calculated using the predictive design equation developed from the first case study results. Results showed that, in the case of the building located in Blacksburg, the solar collection system can supply an average of 85% of the building's heating and hot water requirements through out the year. In the case of the building located in Minneapolis, the solar collection system can supply an average of 56% of the building's heating and hot water requirements through out the year given no night time window insulation and using similar insulation thicknesses for both cases. / Ph. D.

Smart thermal management by which ultra-high heat fluxes (i.e., q''> 100 W/cm²) are dissipated efficiently, is increasingly desirable for many applications in aerospace, electronic packaging, metallurgy, as the existing cooling solutions are highly constrained. For example, the cooling strategy for aircraft must be executed in such a way that will operate independently of orientation while also screen out external heat loads coming from the neighboring electronic boxes and/or external sources. Therefore, it is crucial to develop heat transfer devices which could effectively dump heat away while additionally shield against external heat loads. Thermal diodes, by definition, accomplish this desirable unidirectional heat transfer functionality. Nonetheless, the existing thermal diodes are currently constrained by either a low diodicity (i.e., heat transfer ratio), gravitational dependence, a one-dimensional configuration, or poor durability. Further example for the necessity of smart thermal management would be in firefighting and nuclear reactor safety. Above a critical temperature referred to as the ``Leidenfrost temperature'', the highly effective nucleate boiling is completely replaced by insulating film boiling, causing a dramatic decrease in the essential cooling rate of water pool boiling and spray quenching. In chapter 2, after noting the mechanism and shortcomings of each existing solid-state and phase-change thermal diode, we develop a unique thermal diode, called bridging-droplet thermal diode, which operates independent of orientation, is planar and durable. Our diode is comprised of two opposing copper plates separated by an insulating gasket of micrometric thickness; one plate contains a superhydrophilic wick structure while the other is smooth and hydrophobic. In the forward mode of operation, water evaporates from the heated wicked plate and condenses on the opposing hydrophobic plate. The large contact angle of the dropwise condensate enables bridging across the gap to replenish the wicked evaporator, providing sustained phase-change heat transfer. Conversely, in the reverse mode the heat source is now on the hydrophobic plate, resulting in dryout and excellent thermal insulation across the gap. An orientation-independent heat transfer ratio (i.e. diodicity (η)) of approximately 85 was experimentally measured. In chapter 3, after highlighting that our experimental proof-of-concept discussed in chapter 2, was limited to only a narrow parameter space, we develop a comprehensive thermal circuit model for both the forward and reverse modes of operation to theoretically characterize the bridging-droplet thermal diode over a broad parameter space. Parameters that are varied include the gap height, input heat flux, effective thermal conductivity of the wetted wick structure, height of the wicking micropillars, wettability of the opposing smooth surface, and heat sink temperature. Our findings show that a vapor space height of Hᵥ≈ 250 μm, short and densely packed micropillars, a higher applied heat flux in the forward mode, and a hotter heat sink temperature result in optimal diodicities of η~ 100. In chapter 4, we discuss that the Leidenfrost effect has been a two-phase phenomenon thus far: either an evaporating liquid or a sublimating solid levitates on its vapor. Here, we demonstrate that an ice disk placed on a sufficiently hot surface exhibits a three-phase Leidenfrost effect, where both liquid and vapor films emanate from under the levitating ice. Curiously, the critical Leidenfrost temperature was over three times hotter for ice than for a water drop. As a result, the effective heat flux was an order of magnitude larger when quenching aluminum with ice rather than water over a wide temperature range of 150--550 °C. An analytical model reveals the mechanism for the delayed film boiling: the majority of the surface's heat is conducted across the levitating meltwater film due to its 100 °C temperature differential, leaving little heat for evaporation. In chapter 5, we note that nucleate boiling achieves dissipative heat fluxes as high as q''~ 100 W/cm² and is widely used for power plants, spray quenching metal alloys, desalination, and electronics cooling. However, above a Leidenfrost temperature of about 150 °C for water, an insulating vapor film massively degrades the heat flux by two orders of magnitude. Here, we demonstrate that robust nucleate boiling can be maintained even at temperatures as high as 400 °C by using ice particles in place of water droplets. Ice pellets are periodically released onto a superheated stage and compared to spray quenching at an equivalent mass flow rate. Ice quenching was twice as fast as spray quenching at low superheats, and at large superheats, only ice quenching is successful. Our results demonstrate that ice quenching can maintain groundbreaking heat fluxes of q''~ 100--1,000,W/cm² over a broad range of superheats, far superior than classical spray quenching. / Doctor of Philosophy / Smart thermal management by which enormous heat generated in avionics, electronic packaging, wildfire, etc are removed efficiently, is increasingly desirable as the current cooling solutions are highly constrained. For example, in the context of aircraft, equipment must be cooled down independent of aircraft orientation while also they are shielded from neighboring and/or external heat sources. In firefighting where the temperature of wildfire flames could get beyond 500 °C, dumping large volume of water from aircraft may not be adequate to quench the fire over a reasonable time frame as the liquid water loses its cooling effectiveness above a critical temperature. In chapter 2, after a brief review of existing cooling devices and their corresponding shortcomings commonly used in aircraft and electronic packaging, we develop a unique device for cooling of aircraft which operates independent of aircraft orientation, is durable over time, and can cool down surfaces irrespective of their dimensions. In chapter 3, after highlighting that our proof-of-concept of a new cooling device in chapter 2, was limited to only a finite number of experiments, we theoretically model the operating mechanism of our device to check for the criteria where our device works most efficient. In chapter 4, we discover that by placing an ice disk on a sufficiently hot surface, effective boiling where large amount of heat can be dumped away from the surface to the coolant, is extended to a very large surface temperature. To be specific, liquid water on smooth aluminum loses its cooling efficiency around 150 °C, while cooling the same surface with ice is still effective up to 550 °C. In chapter 5, we report that quenching with ice is twice as fast as quenching with liquid water at low surface temperatures (i.e., 150--300 °C), and at larger surface temperatures (i.e., beyond 300 °C), only ice quenching is successful. Comparing our ice quenching results against current cooling technologies, we note that ice quenching is superior.

Spontaneous expulsion of various forms and types of matter from their solid substrates has always been an integral part of interfacial physics problems. A thorough understanding of such interactions between a solid surface and different soft materials not only expands our theoretical knowledge, but also has applications in self-cleaning, omniphobic surfaces and phase-change heat transfer. Although there is a renewed interest in the design of robust functional surfaces which can passively remove highly viscous liquids or dew, or retard ice accretion or frost formation, the physics of several dewetting and/or deicing mechanisms are yet to be fully understood. Even though we know how jumping-droplet condensation offers significantly better heat transfer performance than regular dropwise condensation and can liberate foreign particles, fundamental questions on the effect of surface orientation on jumping-droplet condensation or how it helps in large-scale fungal disease epidemic in plants are still unanswered. Thus, we first try to fill the knowledge gap in jumping-droplet condensation by characterizing their orientation-dependence and their role in a large-scale pathogenic rust disease dissemination among wheat. Unfortunately, understanding of such dewetting mechanisms does not necessarily translates to prevention or removal of ice and frost on subzero surfaces. Use of superhydrophobic structures or hygroscopic materials to retard the growth of frost was found to be limiting. Therefore the search for an efficient, inexpensive, and environmentally favorable anti-icing or de-icing mechanism is still underway. Here we give a framework for making a novel de-icing construct by analyzing a peculiar jumping frost phenomena where frost particles spontaneously jump off the surface when a polar liquid is brought above. Lastly, we demonstrate a simple and cost-effective technique to design a slippery liquid-infused surface from low-density hydrocarbon-based polymers, which is able to effectively remove a wide variety of soft materials. The main all-encompassing theme of this dissertation is to enhance our understanding of several dewetting phenomena, which might enable better design and/or mitigation strategies to control the expulsion of various forms of matter from a wide variety of surfaces. / Doctor of Philosophy / A few years back, a laundry detergent company in India came up with a famous ad campaign; it showed kids coming home from school with dirt all over their clothes to face the wrath of their parents. Rather than casually disparaging their mischievousness, the ad would make us think with their tagline: "Agar daag (Lit. stain, Fig. mess) lagne se kuch achha hota hain, toh daag achhe hain na? (Fig. If something good comes out of a mess, is it a mess?)". While this presents to us an excellent philosophical conundrum, in reality, we always find ways to get rid of foreign materials from surfaces of everyday use. Using water or dirt-repellent coatings on our shoes/clothes/car windshields or in worst case, spending hours trying to clean frost off our cars is something we are all familiar with. Finding innovative ways to remove unwanted materials from surfaces is not limited to humans, but also exhibited by various natural organisms. The excellent water repellency of lotus leaves, antifogging abilities of mosquito eyes or cicada wings, and slipperiness of pitcher plants are just few examples of natural self-cleaning surfaces designed to keep foreign materials or dew droplets off the surface. Sometimes we take a leaf or two out of these natural designs to help our cause. Surfaces with extreme water repellency are called superhydrophobic (hydro: water, phobos: fear). For a long time, gravity was considered to be the only passive droplet removal mechanism on these surfaces. About ten years ago, researchers found out that when two or more small dew droplets come together on these surfaces, they jump off the surface. Compared to the gravity removal, much smaller droplets can be removed via this method resulting in better anti-fogging qualities and heat transfer performance on the surface. As the jumping droplet event itself is independent of gravity, it was long assumed that the performance of these surfaces would not be dependent on their orientation. These jumped droplets can also take off with contaminating particles by partially or fully engulfing them. A recent study has brilliantly showed how rust spores are liberated from the superhydrophobic wheat leaves via jumping dew droplets. This fundamentally new mode of pathogen transport is yet to be fully understood at the same scale as we know wind or rain-induced fungal spore transport. In this work, we try to fill the knowledge gap by answering questions such as whether the surfaces with the abilities of gravity-independent jumping-induced droplet removal ironically fail to gravity and how far can spore(s) travel engulfed in a jumped droplet. But it is not just water droplets (or particles collected by water droplets) on a surface that we want to get rid off. The solid phase of water, i.e., ice or frost, when formed on regular surfaces, is actually harder to remove. The common ice-preventing surfaces are generally unable to stop complete frost formation and forces us to use salt or other moisture attracting chemicals to remove ice from a surface, knowing very well what is the economic and environmental cost of these chemicals. Here, we have introduced a novel de-icing mechanism by holding only a drop of water over a sheet of frost. The simplicity of our experimental setup may remind you the home physics experiments we all did in our childhood. We finish our discussion by designing a slippery surface from regular polymer films used in food packaging. Although the idea behind these slippery surfaces has been around since 2011, polyethylene films have never been used to make such surfaces before. Here, we show through extensive characterization that by choosing a suitable lubricating oil and a polyethylene-based film, we can finally get all of our ketchup to slide out of their packets, without struggle. If the future design of superhydrophobic condensers, de-icing constructs, or slippery surfaces benefit from the work reported here, may be I can finally say with certainty, "Daag Achhe Hain (Dirt is good.)."

Irreversible electroporation has recently emerged as an effective focal ablation technique. When performed clinically, the procedure involves placing electrodes into, or around, a target tissue and applying a series of short, but intense, pulsed electric fields. Oftentimes, patient specific treatment plans are employed to guide procedures by merging medical imaging with algorithms for determining the electric field distribution in the tissue. The electric field dictates treatment outcomes by increasing a cell's transmembrane potential to levels where it becomes energetically favorable for the membrane to shift to a state of enhanced permeability. If the membrane remains permeabilized long enough to disrupt homeostasis, cells eventually die. By utilizing this phenomenon, irreversible electroporation has had success in killing cancer cells and treating localized tumors. Additionally, if the pulse parameters are chosen to limit Joule heating, irreversible electroporation can be performed safely on surgically inoperable tumors located next to major blood vessels and nerves. As with all technologies, there is room for improvement. One drawback associated with therapeutic irreversible electroporation is that patients must be temporarily paralyzed and maintained under general anesthesia to prevent intense muscle contractions occurring in response to pulsing. The muscle contractions may be painful and can dislodge the electrodes. To overcome this limitation, we have developed a system capable of achieving non-thermal irreversible electroporation without causing muscle contractions. This progress is the main focus of this dissertation. We describe the theoretical basis for how this new system utilizes alterations in pulse polarity and duration to induce electroporation with little associated excitation of muscle and nerves. Additionally, the system is shown to have the theoretical potential to improve lesion predictability, especially in regions containing multiple tissue types. We perform experiments on three-dimensional in vitro tumor constructs and in vivo on healthy rat brain tissue and implanted tumors in mice. The tumor constructs offer a new way to rapidly characterize the cellular response and optimize pulse parameters, and the tests conducted on live tissue confirm the ability of this new ablation system to be used without general anesthesia and a neuromuscular blockade. Situations can arise in which it is challenging to design an electroporation protocol that simultaneously covers the targeted tissue with a sufficient electric field and avoids unwanted thermal effects. For instance, thermal damage can occur unintentionally if the applied voltage or number of pulses are raised to ablate a large volume in a single treatment. Additionally, the new system for inducing ablation without muscle contractions actually requires an elevated electric field. To ensure that these procedures can continue to be performed safely next to major blood vessels and nerves, we have developed new electrode devices that absorb heat out of the tissue during treatment. These devices incorporate phase change materials that, in the past, have been reserved for industrial applications. We describe an experimentally validated numerical model of tissue electroporation with phase change electrodes that illustrates their ability to reduce the probability for thermal damage. Additionally, a parametric study is conducted on various electrode properties to narrow in on the ideal design. / Ph. D.

Recently, buildings have been receiving more serious attention to help reduce global energy consumption. At the same time, thermal comfort has become an increasing concern for building occupants. Phase Change Materials (PCMs), which are capable of storing and releasing significant amounts of energy by melting and solidifying at a given temperature, are perceived as a promising opportunity for improving the thermal performance of buildings. This is because they use their thermophysical properties and latent heat while transforming state (or phase) as a feature for thermal energy storage systems to reduce overall energy demand, specifically during peaks hours, as well as to improve thermal comfort in buildings. This research aims to provide an overview of opportunities and challenges for the utilization of PCMs in the Architecture, Engineering, and Construction (AEC) sector, a broader understanding of specifically promising technologies, and a clarification of the effectiveness of different applications in building enclosures design especially in exterior walls. The research discusses how PCMs can be incorporated within building enclosures effectively to enhance building performance and improve thermal comfort while reducing heating and cooling energy consumption in buildings. The major objectives of the research include studying the properties of PCMs and their potential impact on building construction, clarifying PCMs selection criteria for building application, identifying the effectiveness of utilizing PCMs on saving energy, and evaluating the contribution of utilizing PCMs in building enclosures to thermal comfort. The research uses an exploratory quantitative approach that contains three main stages: 1) a systematic literature review, 2) laboratory experiments, and 3) validation to meet the goal of the research. Finally, by extrapolating results, the research ends with a practical assessment of application opportunities and how to effectively utilize PCMs in exterior walls of buildings. / PHD

Seafood transportation/distribution has become an important activity in the seafood industry due to increasing global demand for fresh seafood. Providing good quality seafood to consumers requires appropriate handling and packaging technology. The purpose of this research is to study the effect of various combinations of insulation and coolant quantities on temperature distribution within a seafood shipping container and packaging cost. A three-dimensional transient heat transfer model was developed to predict the temperature distribution in a fish shipping container. The finite element method was used to develop the model. An eight-noded isoparametric hexahedron element was selected. The geometric configuration of the fish shipping container and the physical and thermal properties of the materials used for packaging were the input parameters of the model. The model validation was performed in two stages to ensure component-wise validation. The first stage was for the case with no ice. The second stage was for the case with ice. The results from the model were compared to those obtained through experiments. Predicted and observed temperatures showed good agreement. The temperature predictions were within 2 °C for the case with no ice and 3 °C for the case with ice. The effect of a polyethylene/aluminum foil laminated bag on the temperature distribution in the shipping container was studied for the case with no ice. The temperatures of high density polyethylene, which simulated fish, were reduced by approximately 3 °C (maximum) due to the low emissivity of aluminum foil. The model was applied to study the effect of various combinations of insulation and coolant quantities on the temperature distribution and the packaging cost. It was found that the fish container with 1.70 cm thick polystyrene and 10 kg of ice can be used for a required shipping time of 24 hours whereas the fish container with 2.54 cm thick polystyrene and 10 kg of ice can be used for a required shipping time of 48 hours under the simulated transport conditions used in this study. / Ph. D.

Convection in a layer of fluid with a free surface due to a combination of thermocapillary stresses and buoyancy is a classic problem of fluid mechanics. It has attracted increasing attentions recently due to its relevance for two-phase cooling. Many of the modern thermal management technologies exploit the large latent heats associated with phase change at the interface of volatile liquids, allowing compact devices to handle very high heat fluxes. To enhance phase change, such cooling devices usually employ a sealed cavity from which almost all noncondensable gases, such as air, have been evacuated. Heating one end of the cavity, and cooling the other, establishes a horizontal temperature gradient that drives the flow of the coolant. Although such flows have been studied extensively at atmospheric conditions, our fundamental understanding of the heat and mass transport for volatile fluids at reduced pressures remains limited. A comprehensive and quantitative numerical model of two-phase buoyancy-thermocapillary convection of confined volatile fluids subject to a horizontal temperature gradient has been developed, implemented, and validated against experiments as a part of this thesis research. Unlike previous simplified models used in the field, this new model incorporates a complete description of the momentum, mass, and heat transport in both the liquid and the gas phase, as well as phase change across the entire liquid-gas interface. Numerical simulations were used to improve our fundamental understanding of the importance of various physical effects (buoyancy, thermocapillary stresses, wetting properties of the liquid, etc.) on confined two-phase flows. In particular, the effect of noncondensables (air) was investigated by varying their average concentration from that corresponding to ambient conditions to zero, in which case the gas phase becomes a pure vapor. It was found that the composition of the gas phase has a crucial impact on heat and mass transport as well as on the flow stability. A simplified theoretical description of the flow and its stability was developed and used to explain many features of the numerical solutions and experimental observations that were not well understood previously. In particular, an analytical solution for the base return flow in the liquid layer was extended to the gas phase, justifying the previous ad-hoc assumption of the linear interfacial temperature profile. Linear stability analysis of this two-layer solution was also performed. It was found that as the concentration of noncondensables decreases, the instability responsible for the emergence of a convective pattern is delayed, which is mainly due to the enhancement of phase change. Finally, a simplified transport model was developed for heat pipes with wicks or microchannels that gives a closed-form analytical prediction for the heat transfer coefficient and the optimal size of the pores of the wick (or the width of the microchannels).