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The extended meniscus and the intermolecular and capillary forces that govern its behavior and connection to change-of-phase heat transfer have been the subject of an increasing body of research over the past 50 years. We have been fortunate to be at the forefront of this effort starting from the development of a capillary feeder, in Earth's gravity, to stabilize film boiling to running a series of transparent heat pipe experiments aboard the International space station hoping to better understand the role of intermolecular forces in microgravity. The use of ellipsometry and interferometry to highlight the location and state of the vapor–liquid interface have been key to these studies and have helped to uncover many new, interesting, and sometimes unexpected phenomena associated with fluid flow and change-of-phase heat transfer.

It was an honor to receive the Max Jakob Memorial Award for 2018. This invited paper is based on the award lecture and is written in an informal style expanding on the lecture and focusing on work in which I have been involved over the past 60 years. Early experimental and theoretical work was published only in conference proceedings when this was regarded an alternative to a journal and not, as seems to be the case nowadays, prior to journal publication or for incomplete work. I welcome this opportunity to clarify and make some of this earlier work more readily accessible. My comments on more recent work of others are also included.

Gas turbines have been extensively used for aircraft engine propulsion, land-based power generation, and industrial applications. Power output and thermal efficiency of gas turbines increase with increasing turbine rotor inlet temperatures (RIT). Currently, advanced gas turbines operate at turbine RIT around 1700 °C far higher than the yielding point of the blade material temperature about 1200 °C. Therefore, turbine rotor blades need to be cooled by 3–5% of high-pressure compressor air around 700 °C. To design an efficient turbine blade cooling system, it is critical to have a thorough understanding of gas turbine heat transfer characteristics within complex three-dimensional (3D) unsteady high-turbulence flow conditions. Moreover, recent research trend focuses on aircraft gas turbines that operate at even higher RIT up to 2000 °C with a limited amount of cooling air, and land-based power generation gas turbines (including 300–400 MW combined cycles with 60% efficiency) burn alternative syngas fuels with higher heat load to turbine components. It is important to understand gas turbine heat transfer problems with efficient cooling strategies under new harsh working environments. Advanced cooling technology and durable thermal barrier coatings (TBCs) play most critical roles for development of new-generation high-efficiency gas turbines with near-zero emissions for safe and long-life operation. This paper reviews basic gas turbine heat transfer issues with advanced cooling technologies and documents important relevant papers for future research references.

Infrared (IR) radiation is used for heating/drying of moist paper in the paper making process owing to its penetration characteristic inside porous media and a high absorptivity of water in the IR wavelength range. However, there is a lack of fundamental understanding of the transport phenomena occurring within moist paper during IR heating/drying. A series of experiments has been conducted along with the development of a theoretical model to fundamentally understand IR heating/drying of moist paper. The experimental results confirm the IR radiation energy penetration into the paper sheet and the theoretical analysis indicates that the penetration depth decreases with increasing sheet moisture content.

This paper traces the evolution of enhanced boiling surfaces. Early work was highly empirical and done in industrial research. The 1968 Milton patent [“Heat Exchange System,” U.S. Patent 3,696,861] described the first porous coated surface, and the 1972 Webb patent [“Heat Transfer Surface Having a High Boiling Heat Transfer Coefficient,” U.S. Patent 3,521,708] described a “structured” tube surface geometry. The first fundamental understanding of the “pore-and-tunnel” geometry was published by Nakayama in 1980 [Nakayama, W., Daikoku, T., Kuwahara, H., and Nakajima, T. 1980, “Dynamic Model of Enhanced Boiling Heat Transfer on Porous Surfaces Part I: Experimental Investigation,” J. Heat Transfer, 102, pp. 445–450]. Webb and Chien’s flow visualization allowed observation of the evaporation in the subsurface tunnels [Chien, L.-H., and Webb, R. L., 1998, “Visualization of Pool Boiling on Enhanced Surfaces,” Exp. Fluid Thermal Sci., 16b, pp. 332–341]. They also performed an experimental parametric study that defines the effect of pore diameter and pitch on the boiling performance. The progression of work on analytical boiling models is also reviewed.

Paper and fiber board are dried by threading a continuous wet web around each of a series of 50 to 70 dryer drums. The cylinders are internally heated by condensing steam. Part of a conventional multicylinder dryer section is shown. The dryer felt is a highly porous material whose main purpose is to hold the paper sheet in close contact with the dryer shell to increase the heat transfer between the paper and dryer shell to increase the heat transfer between the paper and dryer and to help prevent shrinkage and deformation of the paper sheet. The sheet moisture content entering the drying section is 150 to 200% (dry basis) and the final moisture content varies from 2 to 9%. Many attempts have been made to analyze the paper drying process both theoretically and experimentally. Most theoretical models contain critical assumptions that considerably simplify the heat and mass transport phenomena within the sheet during drying. Kirk and Iida provide a review of existing paper drying simulation models. Most of the existing models assume variables such as temperature, moisture content, or thermal conductivity remain uniform through the sheet thickness, and that water fluxes are negligible. Furthermore, a majority of the modelsmore » have been developed for corporate use and the details of the models have remained proprietary. A better understanding of the transport phenomena in the paper sheet is needed to model the heat and mass flow through the paper accurately. A flexible model for the entire drying system could aid in the design and maintenance of dryer systems, overall system efficiency, and improved product quality.« less

An apparatus was constructed for determination of the thermal contact conductance for a paper handsheet/metal interface and for measurement of the effective thermal conductivity of handsheet samples. Bone-dry Bleached Southern Mixed Kraft handsheets with a water retention value of 1.832 were used to study the effect of pressure on thermal contact conductance and to measure the effective thermal conductivity of samples at various sheet density levels. A regression model describing the interface thermal contact conductance as a function of pressure and basis weight was derived. The contact conductance increases with increasing pressure or with decreasing basis weight. At a pressure of 2.3 kPa, the value of the interface contact conductance for the bone-dry samples considered ranges from approximately 97 W/m{sup 2}K for a sheet of 348.7 g/m{sup 2} basis weight to 200 W/m{sup 2}K for a sheet of 68.0 g/m{sup 2} basis weight. For pressures near 300 kPa, these values increase to 146 and 452 W/m{sup 2}K, respectively. The effective thermal conductivity of the handsheet samples was derived from measured values of overall joint conductance and interface contact conductance. The results indicate that the thermal conductivity of the bone-dry samples increases with increasing sheet density, ranging from 0.14 W/mK tomore » 0.70 W/mK for sheet densities of 90 kg/m{sup 3} to 500 kg/m{sup 3}, respectively, for the samples considered.« less

The behavior of downward flame spread over a sheet of filter paper during and after an increase in ambient air velocity was examined. It was shown that the behavior depends not only on the free-stream velocity but also on its rate of change. The extinction mechanisms when the free-stream velocity is instantaneously increased from that for steady flame spread to that above the steady flame spread limit are discussed, and the conditions for continued flame spreading in an air stream with a velocity fluctuation are pointed out.

The purpose of this study is to investigate the effect of partial liquefaction (due to ageing) of the vitreous humor on the transport of ocular drugs. In our model, the gel part of the vitreous is treated as a Darcy-type porous medium. A spherical region within the porous part of vitreous is in a liquid state which, for computational purposes, is also treated as a porous medium but with a much higher permeability. Using the finite element method, a time-dependent, three-dimensional model has been developed to computationally simulate (using the Petrov–Galerkin method) the transport of intravitreally injected macromolecules where both convection and diffusion are present. From a fluid physics and transport phenomena perspective, the results show many interesting features. For pressure-driven flow across the vitreous, the flow streamlines converge into the liquefied region as the flow seeks the fastest path of travel. Furthermore, as expected, with increased level of liquefaction, the overall flow rate increases for a given pressure drop. We have quantified this effect for various geometrical considerations. The flow convergence into the liquefied region has important implication for convective transport. One effect is the clear diversion of the drug as it reaches the liquefied region. In some instances, the entry point of the drug in the retinal region gets slightly shifted due to liquefaction. While the model has many approximations and assumptions, the focus is illustrating the effect of liquefaction as one of the building blocks toward a fully comprehensive model.

This study explores thermal design aspects of nanowarming-assisted recovery of the heart from indefinite cryogenic storage, where nanowarming is the volumetric heating effect of ferromagnetic nanoparticles excited by a radio frequency electromagnet field. This study uses computational means while focusing on the human heart and the rat heart models. The underlying nanoparticle loading characteristics are adapted from a recent, proof-of-concept experimental study. While uniformly distributed nanoparticles can lead to uniform rewarming, and thereby minimize adverse effects associated with ice crystallization and thermomechanical stress, the combined effects of heart anatomy and nanoparticle loading limitations present practical challenges which this study comes to address. Results of this study demonstrate that under such combined effects, nonuniform nanoparticles warming may lead to a subcritical rewarming rate in some parts of the domain, excessive heating in others, and increased exposure potential to cryoprotective agents (CPAs) toxicity. Nonetheless, the results of this study also demonstrate that computerized planning of the cryopreservation protocol and container design can help mitigate the associated adverse effects, with examples relating to adjusting the CPA and/or nanoparticle concentration, and selecting heart container geometry, and size. In conclusion, nanowarming may provide superior conditions for organ recovery from cryogenic storage under carefully selected conditions, which comes with an elevated complexity of protocol planning and optimization.

Nanoparticles (NPs) are promising agents to absorb external energy and generate heat. Clusters of NPs or NP array heating have found an essential role in several biomedical applications, diagnostic techniques, and chemical catalysis. Various studies have shed light on the heat transfer of nanostructures and greatly advanced our understanding of NP array heating. However, there is a lack of analytical tools and dimensionless parameters to describe the transient heating of NP arrays. Here we demonstrate a comprehensive analysis of the transient NP array heating. Firstly, we develop a set of analytical solutions for the NP array heating and provide a useful mathematical description of the spatial-temporal evolution of temperature for 2D, 3D, and spherical NP array heating. Based on this, we introduce the concept of thermal resolution that quantifies the relationship between minimal heating time, NP array size, energy intensity, and target temperature. Lastly, we define a set of dimensionless parameters that characterize the transition from confined heating to delocalized heating. This study advances the understanding of nanomaterials heating and guides the rational design of innovative approaches for NP array heating.

Thermoregulation is a process that is essential to the maintenance of life for all warm-blooded mammalian and avian species. It sustains a constant core body temperature in the face of a wide array of environmental thermal conditions and intensity of physical activities that generate internal heat. A primary component of thermoregulatory function is the movement of heat between the body core and the surface via the circulation of blood. The peripheral vasculature acts as a forced convection heat exchanger between blood and local peripheral tissues throughout the body enabling heat to be convected to the skin surface where is may be transferred to and from the environment via conduction, convection, radiation, and/or evaporation of water as local conditions dictate. Humans have evolved a particular vascular structure in glabrous (hairless) skin that is especially well suited for heat exchange. These vessels are called arteriovenous anastomoses (AVAs) and can vasodilate to large diameters and accommodate high flow rates. We report herein a new technology based on a physiological principle that enables simple and safe access to the thermoregulatory control system to allow manipulation of thermoregulatory function. The technology operates by applying a small amount of heating local to control tissue on the body surface overlying the cerebral spine that upregulates AVA perfusion. Under this action, heat exchangers can be applied to glabrous skin, preferably on the palms and soles, to alter the temperature of elevated blood flow prior to its return to the core. Therapeutic and prophylactic applications are discussed.

In order to measure the effective diffusion coefficient D of Bevacizumab (Avastin, Genentech) in the vitreous humor, a new technique is developed based on the “contour method” and in vivo optical coherence tomography measurements. After injection of Bevacizumab-fluorescein conjugated compound solution into the rabbit eye, the contours of drug concentration distribution at the subsurface of injection were tracked over time. The 2D contours were extrapolated to 3D contours using reasonable assumptions and a numerically integrated analytical model was developed for the theoretical contours for the irregularly shaped drug distribution in the experimental result. By floating the diffusion coefficient, different theoretical contours were constructed and the least-squares best fit to the experimental contours was performed at each time point to get the best fit solution. The approach generated consistent diffusion coefficient values based on the experiments on four rabbit eyes over a period of 3 h each, which gave D=1.2±0.6×10−6 cm2/s, and the corresponding theoretical contours matched well with the experimental contours. The quantitative measurement of concentration using optical coherence tomography and fluorescein labeling gives a new approach for the “noncontact” in vivo drug distribution measurement within vitreous.

Impinging jets are extensively investigated in numerous benchmarks. Such configurations are common in many industrial and engineering applications (e.g., manufacturing, material processing, electronic cooling, paper drying, textiles and tempering of glass). Various comprehensive reviews of jets impingement onto a motionless wall are available in the literature [1–9]. However, a small number of studies were devoted to the effects of the wall motion of impinging jets, on the flow structure and the heat transfer. The first study of a jet impingement on a moving wall was carried out experimentally by Subba Raju and Schlunder [10]. They investigated the heat transfer of a single jet impinging a moving belt. Huang et al. [11] performed numerically the case of a turbulent jet on a rectangular duct with surface motion effects. They have found that, when the plate velocity is great, Nusselt numbers becomes smaller around the area where the surface motion is opposed to that of the flow and augments when the moving wall and the flow evolve in the same direction. Zumbrunnen [12] have developed an analytical study for a single planar laminar impinging slot jet onto a moving plate subjected to a constant heat flux.They show that the heat transfer is more effective when the boundary layer development is slowed down by the plate motion. Chattopadhyay et al. [13] have numerically investigated the turbulent heat transfer of an array of slot jets impinging a moving plate using large Eddy simulation (LES), for jet exit Reynolds numbers ranging between 500 and 3000 and for several surface-jet velocities ratios R sj such as: 0 ≤ R sj ≤ 2. They found that the Nusselt number distribution over the plate becomes more uniform when the total heat transfer and the plate velocity decreases. Later, Chattopadhyay and Saha [14] used large Eddy simulation to investigate both the turbulent flow and the heat transfer resulting from a single slot jet impingement onto a moving hot isothermal plate. They have provided some results for a given jet exit Reynolds number of 5800 on a moving plate corresponding to a velocity ratio between 0 and 2. They were focused on the details of the flow structure, the velocity profiles and the turbulent shear stresses distribution. Similarly, the flow field of a confined turbulent slot air jet impinging perpendicularly a flat surface, was experimentally studied by Senter [15]. The experiments were carried out for a nozzle-to-plate spacing of eight slot nozzle thickness, at three Reynolds number (5300, 8000, and 10,600) and four surface-to-jet velocity ratios (0, 0.25, 0.5 and 1.0). Measurements are performed within the main regions of the jet. It appears that the flow structure patterns corresponding to a given surface-to-jet velocity ratio are independent with the jet exit Reynolds number between 5300 and 10,600. Also, a slight modification of the flow field is observed for a surface-to-jet velocity ratio of 0.25, whereas this effect is more significant for higher ratios of 0.5 and 1. On the other hand, Senter [15], determined the local Nusselt number by means the computation fluid dynamics (CFD) software Fluent using k–e WCP model for jet exit Reynolds number of Re = 10,600 and normalized plate velocities of 0, 0.25, 0.5, and 1.0. This study proves that the local Nusselt number tends to significantly decrease followed by an increasing around the stagnation zone. Sharif and Banerjee [16] have achieved a numerical study by the CFD code Fluent, using the standard k–e turbulence model coupled to the enhanced wall treatment. They showed that the local Nusselt numbers along the moving plate exceed the values in the vicinity of the impinging region for the cases corresponding to lower plate velocities ratios, which can be explained by the thinning of dynamical and thermal boundary layers. These values decrease for greatest plate velocities induced by the parallel dominating shear driven flow. For a given plate velocity, the average Nusselt number close to the plate augments whilst the average skin friction coefficient decreases when jet exit Reynolds number increases. On the other hand, for a given jet exit Reynolds number, these two parameters slightly decrease for small velocity ratio, followed by an increase for greater values In the present paper, the case of a confined slot jet impinging perpendicularly a moving heated wall is numerically investigated (Fig. ​(Fig.1).1). This study complements both the previous work of Senter [15] and Sharif and Banerjee [16] by considering values of jet-plate velocity ratios greater than 1 (0 ≤ R sj ≤ 4). We extend the velocity ratio surface-jet because Zumbrunnen et al. [17] reported that the impingement surface velocity can exceed as much as ten (10) times the jet velocity in some industrial application such as hot rolling process. Open in a separate window Fig. 1 Configuration and parameters

A high thermal conductivity thermal paste can be developed by mixing the oxidized liquid metal alloy (OLMA) with graphene. Four kinds of graphene-OLMA pastes were synthesized at graphene concentrations of 0.25 wt%, 0.75 wt%, 1.5 wt%, and 2.0 wt%, respectively. The paste structures were characterized by MicroXCT-400, which can be used to readily measure the air pocket size, and their thermal conductivities measured by a laser flash analysis method. It is found that the OLMA structure is very different from the liquid metal alloy (LMA), and a small amount of air pockets were formed in the OLMA. The air pocket size significantly affected the thermal conductivity of the graphene-OLMA paste. When the graphene concentration increased, as shown in Fig. 1(c)-(e), the paste's thermal conductivity increased. However, more air pockets were formed around the graphene. In particular, when the graphene concentration increased to 2.0 wt%, clusters of graphene, as shown in Fig. 1(f), were formed resulting in the formation of big air pockets in the thermal paste, which directly affected the thermal conductivity as shown in Fig. 1(g). We thought that when the graphene concentration increases, the thermal conductivity should increases. But the results show that it was not and then we used MicroCT to see the internal structure of the thermal paste and found that the air pockets were formed and significantly affects the thermal performance.

In the spray cooling of a heated surface, variations in the surface texture influence the flow field, altering the maximum liquid film thickness, the bubble diameter, vapor entrapment, bubble departure characteristics, and the ability to transfer heat. A new method for determining and designating the surface texture is proposed, and the effects of surface roughness on evaporation/nucleation in the spray cooling flow field studied. A one-dimensional Fourier analysis is applied to determine experimentally the surface profile of a surface polished with emery paper covering a spectrum of grit sizes between 0.3 to 22 μm. Heat transfer measurements for liquid flow rates between 1 to 5 l/h and air flow rates between 0.1 to 0.4 l/s are presented. Maximum heat fluxes of 1200 W/cm2 for the 0.3 μm surface at very low superheats were obtained.

Heat transfer and pressure loss measurements were obtained simultaneously for a range of wood pulp fiber suspensions flowing in a pipeline. Data were obtained over a selected range of flow rates and temperatures from a specially built flow loop. It was found that the magnitude of the heat transfer coefficient was above water at equivalent experimental conditions and at very low fiber concentrations, but progressively decreased until it was below water at slightly higher concentrations. Similar trends were obtained for the pressure drop measurements obtained simultaneously, showing good correspondence between the two sets of data. It was found that both heat and momentum transfer are affected in a closely similar way by varying fiber properties, such as fiber length, fiber flexibility, fiber chemical and mechanical treatment, the variation of fibers from different parts of the tree, as well as the different pulping methods used to liberate the fibers from the wood structure. Drag reduction increased and heat transfer coefficient decreased with increasing fiber flexibility as found by previous workers.

The main motivation of conducting this work is to present a rigorous analysis and investigation of the potential effect of the heat pipe adiabatic region on the flow and heat transfer performance of a heat pipe under varying evaporator and condenser conditions. A two-dimensional steady-state model for a cylindrical heat pipe coupling, for both regions, is presented, where the flow of the fluid in the porous structure is described by Darcy–Brinkman–Forchheimer model which accounts for the boundary and inertial effects. The model is solved numerically by using the finite volumes method, and a fortran code was developed to solve the system of equations obtained. The results show that a phase change can occur in the adiabatic region due to temperature gradient created in the porous structure as the heat input increases and the heat pipe boundary conditions change. A recirculation zone may be created at the condenser end section. The effect of the heat transfer rate on the vapor radial velocities and the performance of the heat pipe are discussed.

Microchannels are being used increasingly in microelectro- mechanical systems (MEMS) where heat transfer constitutes an important process step in many devices. The high heat transfer coefficient and low thermal resistance of these channels also make them attractive in compact heat exchanger applications. In order to design these devices for reliable operation, it is essential to understand the flow and heat transfer characteristics in microchannels. The heat transfer data for gas flow in microchannels reported by earlier researchers were found to deviate considerably from the established heat transfer correlations. Although deviations in the friction factor data for the microchannels are now understood as being attributable to experimental uncertainties, incorrect estimation of boundary conditions, and entrance region effects, the heat transfer data has not yet been clearly reconciled. In general, an effect of Reynolds number (Re) on Nussselt number (Nu) in the laminar flow region has been reported in previous literature. This could stem from a lack of understanding of how heat transfer is affected by parameters that are usually negligible at macroscale, such as roughness, entrance region effect (especially in turbulent flows in tubes with large length to diameter ratio), heat losses, axial heat conduction, viscous heating, and rarefaction effects. The flow characteristics and heat transfer performance in microchannels has been investigated by a few researchers who reported that their experimental data departed from conventional macroscale correlations [1–7]. In the work reported by Yu et al. [1], the friction factor data of water and gas flow in 52–102 μm channels were found to be lower than the predictions from conventional correlations. However, later publications, e.g., Judy et al. [8], have indicated that the data for water flow in microchannels was in good agreement with conventional correlations. Error in channel diameter measurement was noted as one of the main reasons for such deviations in the earlier water data. As to be expected, it has been experimentally verified that there are no microscale effects on friction factors for liquid flow in microchannels [9–12]. Gas flow with nitrogen in microtubes ranging in diameter from 30 to 500 μm and having surface roughness values

Porous capillary wick structures are being employed in two-phase thermal management devices owing to their pumping capabilities and thermal performance enhancement during evaporation of the working fluid. Thin-film evaporation in a porous wick depends primarily on the shape of the liquid–vapor meniscus, especially near the wall. The primary objective of this paper is to study and investigate the thin-film evaporation of the liquid in a unit cell representation (UCR) of a single layer of a metallic wire mesh screen. The volume-of-fluid (VOF) method, which is an interface-capturing technique in multiphase flow modeling, is employed to obtain the steady-state meniscus shape under equilibrium conditions. This paper demonstrates the impact of the equilibrium contact angle (θ) and the initial meniscus height (H) on the steady-state interfacial pressure difference. It outlines a detailed process for estimating 3D interfacial surfaces, obtained from the VOF solution, to generate the final geometry for the thin-film evaporation analysis. A static meniscus heat-transfer model is subsequently solved using the commercial finite volume code, ansysfluent, to obtain the temperature and flow characteristics during evaporation. The relationship of parameters such as the average evaporation mass fluxes and heat transfer coefficients are estimated and presented in this paper. Finally, the relationship between the pressure drop across the liquid–vapor meniscus and the thin-film evaporation rate for screen mesh wicks is discussed.

This paper numerically investigates the optimization of the geometric parameters and the coolant's inflow states of the perforated micropin-fins (MPFs) heat sink using an elitist nondominated sorting genetic algorithm-II (NSGA-II) coupled with a finite volume-based computational fluid dynamics (CFD) solver. Square-shaped MPFs with two circular perforations were considered for the investigations on the fluid flow and conjugate heat transfer using numerical simulations. Five design variables (two perforation diameters, their respective locations, and the inflow velocity) with the essential constrained equations were optimized to search for the optimal solutions. Two objective functions, viz., Nusselt number (Nu) and friction factor (f), were selected to evaluate the hydrothermal performances of the perforated MPFs heat sink. The optimization was performed for 52 generations with a population size of 30. We obtained the Pareto optimal solutions, which gave the design boundary of the important parameters. Some of the cases of the Pareto solutions were also investigated in detail to understand the underlying thermal physics and structural rigidity under thermal and hydraulic stresses. It is observed that the MPF's stiffness was not compromised upon introducing two perforations. This study identified different thermohydraulic features responsible for optimal performance at different inflow velocity regimes. The present paper demonstrates that this optimization technique has led to a better understanding of the underlying thermal physics of complex electronic cooling equipment while systematically exploring the design space.

This is the second part of a two-paper series that presents the results of liquid nitrogen spray quenching of a stainless steel (SS) disk plate. The first paper focuses on the heat transfer characteristics of the liquid nitrogen spray quenching, whereas the second paper emphasizes the overall chilldown performance and efficiency. Serving as the baseline information for evaluating the effects of disk surface coating and pulse flow, the results of continuous-flow spray chilldown of a bare surface SS disk are summarized first. We found that for continuous-flow spray chilldown of a bare surface disk, the chilldown efficiency is mainly a function of the average spray mass flow rate with the trend of decreasing efficiency with increasing average mass flow rate. Additional experiments were performed to evaluate the enhancement of cryogenic spray quenching by three techniques: (1) using intermittent pulse sprays on SS bare surface, (2) coating the SS surface with a layer of low thermal conductivity Teflon film, and (3) spraying liquid nitrogen intermittently on the coated SS surface. In general, the results indicate that all three methods effectively produced higher spray efficiencies. However, it was also found that the Teflon coating was more effective than the flow pulsing. The coating produced a quick transition from film boiling to transition boiling. This quick transition shortens the poor heat transfer film boiling period and thus facilitates the switch to much higher heat transfer transition boiling and nucleate boiling periods earlier to expedite the chilldown process and enhance the heat transfer.

This is the first part of a two-paper series that reports the design, experimentation, and results of a spray quenching experiment of a circular metal disk in terrestrial gravity condition. The objective of this experiment is to provide experimental data and corresponding analysis on the heat transfer characteristics and chilldown performance of the cryogenic spray quenching process. In this paper, the presented continuous-flow spray quenching results include the spray-cone angle visualization, spray cooling heat transfer characteristics represented by chilldown curves and boiling curves, gravity effects, and Leidenfrost rewet point temperatures. Additionally, detailed discussion is given on the film boiling heat transfer and rewet temperature in terms of various contributing factors such as gravitational acceleration, spray mass flux, and radial position on the plate. Based on the experimental data, empirical correlations for film boiling heat transfer coefficient, and rewet temperatures are provided. We expect that the current terrestrial study would offer invaluable information for the design of a robust in-space cryogenic propellant storage tank spray chilldown system.

Since their introduction in the early 1990s, pulsating heat pipes (PHPs) have received a lot of attention due to their obvious advantages such as their geometrical simplicity, and their potential for high-heat flux applications even without power consumption. Although numerous investigators have studied PHPs over the last three decades, there still exist a few controversial issues on fundamental characteristics and several technical problems in practical applications. To put the finishing touches to the controversial issues and to shed light on the technical problems, recent advances in PHPs are critically reviewed in this paper. The results of this critical review are classified into two categories: (i) fundamental aspects of PHPs and (ii) practical aspects of PHPs. The first category focuses on reviewing the current state-of-the-art fundamental characteristics of PHPs. The second category summarizes the technical problems that are resolved for utilizing PHPs in practical applications. This review paper would help researchers or engineers who are working on or utilizing PHPs.

Couplings connect the spinning shafts of driving and driven machines in the industry. A coupling guard encloses the coupling to protect personnel from the high-speed rotating coupling. The American Petroleum Institute API publishes standards that restrict the overheating of the coupling guards due to windage caused by the spinning shaft. Based on the most recent version of API 671, the peak temperature for the coupling guard should not exceed 60 °C. This paper proposes a machine learning (ML) model and an empirical formula to predict the maximum guard temperature and power loss. The ML models use a database obtained from simulated computational fluid dynamics (CFD) cases for different coupling guards under various conditions. Also, the paper provides validation for the CFD models with experimental tests for different cases. The proposed ML model uses eight different input parameters to predict temperature and power loss. The model shows an accurate prediction for a varied number of CFD cases. The performance of the generated model has been verified with the experimental results. Also, an empirical formula has been created using the same database from CFD results. The results show that the ML model has better prediction accuracy than the empirical formula for predicting peak temperature and power loss for all cases.

Synthetic jets, often abbreviated as 'SJs' or 'Synjets' are a type of Zero Net Mass Flux (ZNMF) jets which have gained popularity due to their ability to transfer momentum without transferring mass. This property distinguishes SJs from their counterpart traditional continuous jets. Over a stretch of time, SJs have been employed extensively in applications such as active flow control, impingement heat transfer, miniature electronics cooling, etc. However, researchers are now slowly extending the frontiers of SJ research and making efforts to utilize excellent properties of SJs in novel applications such as AUVs, marine systems, bio-inspired propulsion systems, etc. This paper strives to identify the gaps in the current research and the areas which have remained unexplored yet. The article begins with a discussion of the origin of SJs i.e. 'acoustic streaming'. The resulting segments talk about the formation criteria and the recent works employing various configurations of orifices and cavities. The paper discusses critical concepts such as JIF, volumetric efficiency, and propulsive efficiency of synthetic jets. It is followed by the introduction of novel flow control systems employing SJs such as gurney flaps, bumps, and electroactive synthetic jets. Finally, the most innovative applications of SJs such as AUVs, UAVs, jetting cavities. Pulsatile jet flows found in jellyfish, cephalopod, squid and salp have been discussed in great detail. The exhaustive discussion on future prospects strives not only to provide reader with comprehensive insights into SJs, but also to motivate future researchers to overcome the gaps identified in this paper.

This paper presents thin-loop heat pipes (tLHPs) with evaporator thickness of 1 mm and a one-way transport length of 200 mm. Grooves and liquid cores are mounted on the evaporator case in the design of a flat evaporator. Liquid cores play a critical role in reducing the pressure drop in the wick and in increasing the path length for heat transfer. A one-dimensional steady model was applied to the design of the tLHP. New tLHPs with thin evaporator (26 × 24 × t1 mm3) were fabricated by a three-dimensional printer. First, two kinds of tLHP systems were (type-1) fabricated with different wick materials—microglass paper (MGP) and Shirasu porous glass (SPG). Ethanol was selected as a working fluid. The experimental results showed the both LHPs can transport heat up to 12 W. Second, the evaporator structure was modified based on the experimental results with the type-1 tLHP, and the tLHP with SPG wick (type-2) was fabricated. The experimental results demonstrated the stable operation. The operation temperature was 83 °C, and the thermal resistance became 1.98 °C/W. The power cycle test at the range of a heat load from 5 to 10 W was also conducted. No temperature hysteresis was observed during three cycles.

This is the second paper in a set that defines the discrete Green's function (DGF). This paper focuses first on the turbulent boundary layer and presents two different methods to estimate the DGF. The long-element formulation defines the DGF with just two simple algebraic equations, but it is not quantitatively accurate for short element lengths. A short element correction is derived, but must be recalculated for each selection of flow parameters and element lengths. A similarity solution is derived that allows accurate estimates of the DGF diagonal elements for laminar boundary layers and for turbulent boundary layers discretized with short element lengths. To illustrate other methods to derive DGFs in more complex flows, a low-resolution DGF for laminar stagnation line boundary layers is determined using the skin-friction formulation combined with similarity solutions for two different thermal boundary conditions. Stagnation line flow is shown to be highly sensitive to the thermal boundary condition, and this can be analyzed effectively using the DGF.

Engineering innovations—including those in heat and mass transfer—are needed to provide food, water, and power to a growing population (i.e., projected to be 9.8 × 109 by 2050) with limited resources. The interweaving of these resources is embodied in the food, energy, and water (FEW) nexus. This review paper focuses on heat and mass transfer applications which involve at least two aspects of the FEW nexus. Energy and water topics include energy extraction of natural gas hydrates and shale gas; power production (e.g., nuclear and solar); power plant cooling (e.g., wet, dry, and hybrid cooling); water desalination and purification; and building energy/water use, including heating, ventilation, air conditioning, and refrigeration technology. Subsequently, this review considers agricultural thermal fluids applications, such as the food and water nexus (e.g., evapotranspiration and evaporation) and the FEW nexus (e.g., greenhouses and food storage, including granaries and freezing/drying). As part of this review, over 100 review papers on thermal and fluid topics relevant to the FEW nexus were tabulated and over 350 research journal articles were discussed. Each section discusses previous research and highlights future opportunities regarding heat and mass transfer research. Several cross-cutting themes emerged from the literature and represent future directions for thermal fluids research: the need for fundamental, thermal fluids knowledge; scaling up from the laboratory to large-scale, integrated systems; increasing economic viability; and increasing efficiency when utilizing resources, especially using waste products.

To estimate the thermal properties from transient data, a model is needed to produce numerical values with sufficient precision. Iterative regression or other estimation procedures must be applied to evaluate the model again and again. From this perspective, infinite or semi-infinite heat conduction problems are a challenge. Since the analytical solution usually contains improper integrals that need to be computed numerically, computer-evaluation speed is a serious issue. To improve the computation speed with precision maintained, an analytical method has been applied to three-dimensional (3D) cylindrical geometries. In this method, the numerical evaluation time is improved by replacing the integral-containing solution by a suitable finite body series solution. The precision of the series solution may be controlled to a high level and the required computer time may be minimized by a suitable choice of the extent of the finite body. The practical applications for 3D geometries include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. This paper is an extension of earlier works on one-dimensional (1D) and two-dimensional (2D) cylindrical geometries. In this paper, the computer-evaluation time for the finite geometry 3D solutions is shown to be hundreds of times faster than the infinite or semi-infinite solution with the precision maintained.

For many industrial applications, heat flow through composites relates directly to energy usage and thus is of highest interest. For multilayer composites, the heat flow is a result of multiple variables, such as the temperature gradient over the surface boundaries and each material's thermal conductivity, specific heat, and thickness. In addition, the transient heat flux also depends on how the materials are aligned together. The heat flow through composites can be estimated using advanced computer simulations for applied heat transfer. Although these tools are powerful, they are also time consuming. Therefore, approximations that allow the estimation of heat flow through composites can be very useful. This paper presents approximations to solve transient heat transfer in multilayer composites, with and without an interior surface resistance. Since the energy use for various applications relates to the heat transferred at the surface boundary, the main focus of this paper is to define approximate solutions for interior heat flow. In other words, these approximations are found by applying a unit step change in temperature on one side of a composite and then in real-time emulating the surface heat flux on the opposite side from which the step change occurs. The approximations are presented based on lumped analyses and Laplace network solutions and are validated against analytical and numerical solutions.

This paper presents an experimental investigation of heat transfer in direct contact membrane distillation (DCMD) flow channels with and without the spacer. In this experiment, the usual hydrophobic membrane of DCMD is replaced by a copper plate to eliminate mass transfer. The study shows the most appropriate heat transfer correlations for empty channel cases with different channel heights and flow rates. For the case with the spacer in the flow channels, two spacer materials are investigated: nonwoven plastic and woven stainless steel. The paper presents the most appropriate heat transfer correlation for both these spacer materials. Further, the paper presents finding with two more spacer materials, woven fiberglass and aluminum spacer. It is found that the most appropriate heat transfer correlation for these materials is in the turbulent flow regime although the experimentally estimated Reynolds number suggests laminar flow is presented.

This paper presents the results of a numerical study for using a simple insertion to reduce the heat transfer through an air-filled square cavity when subjected to a temperature gradient. The insertion is a rectangular sheet folded in a special way to produce the shape of a rotated letter G. The insertion is thermally conductive, and in perfect contact with the walls of the cavity. The cavity has thick conductive walls. The two outer vertical sides of the cavity are isothermal, and the two horizontal sides are adiabatic. The solution of continuity, momentum, and energy equations for this system yields the isotherms, streamlines, and heat flux transported across the cavity. The insertion suppresses the convection currents inside the cavity and hence reduces the heat transfer rate across them. The analysis shows the effect of the insertion dimensions and thermal properties on the heat transfer rate through the cavity. This paper also presents the results of using this insertion inside the holes of an ordinary building brick. The insertion is an easy tool to manufacture and a simple device to use for reducing the heat transfer through the blocks. The G insertion reduces the heat flux by 27–42%.

The energy pile technology has been widely used, and the solid cylindrical heat source (SCS) model is usually adopted to describe the heat transfer process between the energy pile and the surrounding soil. This paper investigates the SCS model with a convective boundary condition (SCS-3 model), and realistic conditions such as transversely isotropic ground and groundwater flow are all included in the model. An analytical solution for the problem is established using Green's function method and the theory of moving heat sources. Solutions for the SCS model with a boundary condition of the first kind (SCS-1 model) and for the line source (LS) model with a convective boundary condition (LS-3 model) are recovered as special cases of the solution in this paper. Computational examples are presented, and comparisons between different models are made. First, the SCS-1 model is compared with the SCS-3 model, showing the error caused by neglecting the surface convective effect. Second, the LS-3 model is compared with the SCS-3 model, showing the error associated with neglecting the size of heat source. The effects of groundwater flow velocity and convective heat transfer coefficient on the temporal and spatial variations of these errors are also investigated.

Solidification dynamics are crucial for determining microstructure development in additively manufactured parts. Multiphysics models based on finite element or finite volume methods may help gain insight for complicated phenomena such as fluid flow, keyholing, and porosity but are too computationally expensive to use for simulating actual builds. Recent analytic and semi-analytic solutions for moving heat sources in a semi-infinite three-dimensional space provide a way to accurately estimate the solidification conditions for entire builds. The downside to these methods is that, unlike finite element or finite volume methods, they cannot use the temperature distribution of the previous timesteps to march the solution forward in time. This paper provides the mathematical formulation and implementation of a forward time stepping (FTS) approach to an existing semi-analytic solution. The speed and accuracy of the two methods are then compared for various scan patterns. The result is that, for spot melts, the forward time-stepping model provides improvements in both speed and accuracy. This is especially true for longer simulations, where the simulation can be orders of magnitude faster. The longest simulation analyzed in this paper was roughly 30× faster when using the forward time-stepping model versus the straightforward implementation of the semi-analytic solution.

This paper presents a visualization of condensation droplet distribution affected by the electrowetting-on-dielectric (EWOD) approach. A single-side double-layer-electrode design (grid wire, thin wire, and thick wire) and coplanar-electrode design (zigzag) are discussed. Side-by-side experiments with applied 40 V DC electric potential are carried out to compare droplet distribution between identically designed charged and uncharged devices. The uncharged devices show a random droplet distribution, whereas charged devices have a regulated distribution based on the designed patterns. As droplets on the electrode boundaries become larger, they are likely to slide away and stay in electrode-free regions. The droplets “sit” inside the grid wires and distribute vertically along thin and thick wires. On the coplanar-electrode zigzag device, droplets are distributed vertically. The charged surfaces lead to a faster droplet growth rate and more dispersed droplet distribution. This phenomenon accelerates the shedding frequency of the droplets and frees up more areas for small droplets to nucleate and grow. The first shedding moment of the charged surfaces occurs earlier than the uncharged ones for all types of EWOD devices. The detected droplet shedding diameter ranges from 1.2 mm to 2.5 mm in this study. The number of large droplets is found greater on the charged devices compared with the uncharged devices and theoretical model. The work presented in this paper introduces a novel approach to actively influence droplet distribution on microfabricated condensing surfaces and indicates great potential for improving the condensation heat transfer rate via EWOD.

The numerical simulation was carried out to investigate mechanism of the heat transfer enhancement in the fin-and-tube heat exchangers. As known, the vortex generators (VGs) were widely used to improve the thermal performance with bad flow resistance characteristics and led to bad comprehensive performance. This paper aims to expound the mechanism of thermal hydraulic characteristics and explore the effect of VGs position on the comprehensive performance. Three types of fins (type 1, type 2, and type 3) were discussed in this paper. The j factor, f factor, and performance evaluation (PEC) of three types of VGs in different positions were discussed and compared. Based on the numerical results, a detailed description of the effect of three types of VGs on the heat transfer performance and flow resistance characteristics was presented at different Reynolds number in the range between 1300 and 2000. In addition, local velocity distribution, local temperature distribution, and local pressure drop distribution were analyzed and discussed. And the effect of VG angle on the thermal performance and flow resistance was presented. It can be concluded that the main heat transfer occurred in the region before the tube, and the wake region behind the tube was harmful to improve the thermal performance and reduce the flow resistance. Besides, VG in the wake region was obviously beneficial to the enhancement of the thermal performance with less energy loss.

In this paper is described the development and the experimental study of a flat plate pulsating heat pipe (FPPHP) built by means of metal additive manufacturing (AM). In the recent years, small/medium aerospace companies have gained interest in the development of small satellites. The small dimensions, coupled with the need for high-power devices for science and communications, increase the interest in thermally functional structures. The space business is characterized by a very small production lot, and custom designs from project to project. The AM exactly fits these needs and, in the past years, the use of this technology in aerospace projects has grown significantly. This paper, after a brief review of the pulsating heat pipe (PHP), focuses on the development and testing of a panel with an embedded closed-loop FPPHP built by means of metal AM technique. The article presents a trade-off analysis between the metal AM technologies available on the market; by means of the trade-off analysis, a design strategy is proposed by the authors. A comparison between available FPPHP results in literature and the three-dimensional (3D) printed structure will show the differences between the common subtractive technology and the innovative AM technique.

Theoretical understanding of phase change heat transfer problems is of much interest for multiple engineering applications. Exact solutions for phase change heat transfer problems are often not available, and approximate analytical methods are needed to be used. This paper presents a solution for a one-dimensional (1D) phase change problem with time-dependent heat flux boundary condition using the perturbation method. Two different expressions for propagation of the phase change front are derived. For the special case of constant heat flux, the present solution is shown to offer key advantages over past papers. Specifically, the present solution results in greater accuracy and does not diverge at large times unlike past results. The theoretical result is used for understanding the nature of phase change propagation for linear and periodic heat flux boundary conditions. In addition to improving the theoretical understanding of phase change heat transfer problems, these results may contribute toward design of phase change based thermal management for a variety of engineering applications, such as cooling of Li-ion batteries.

Saturation of the water vapor is essential to form frost inside a permeable membrane. The main goal of this paper is to develop a numerical model that can predict temperature and humidity inside a membrane in order to show the location and time of saturation. This numerical model for heat and mass transfer is developed to show that frost formation may be prevented or delayed by controlling the moisture transfer through the membrane, which is the new approach in this paper. The idea is to simultaneously dry and cool air to avoid saturation conditions and thereby eliminate condensation and frosting in the membrane. Results show that saturation usually occurs on side of the membrane with the highest temperature and humidity. The numerical model is verified with experimental data and used to show that moisture transfer through the membrane can delay or prevent frost formation.

This paper presents corrections for existing hydrodynamic instability-based critical heat flux (CHF) models in pool boiling by taking into account the effect of the viscosity, geometry and size of the liquid–vapor interface. Based on the existing literature, the Kelvin–Helmholtz (KH) theory, used by the most commonly adopted CHF models, can lead to noticeable errors when predicting the instability conditions. The errors are mainly due to the inaccuracy of the inviscid flow assumptions and the oversimplification of the interface geometry. In addition, the literature suggests the most unstable condition predicted by the viscous correction for viscous potential flow (VCVPF) theory for the cylindrical interfaces best match the observed air column breakup conditions in water. In this paper, the most unstable instability conditions predicted by the VCVPF theory are used to correct the existing CHF models. The comparison between the existing and corrected CHF models suggests that the corrected models always predict a higher CHF value. In addition, the corrected Zuber model predicts similar CHF value to the Lienhard and Dhir model. The comparison with experimental data suggests that the correction to the Zuber model can increase its prediction accuracy in most cases, but not necessary for the Lienhard and Dhir model. When compared to experimental CHF data for boiling cryogens at different pressures, the corrected CHF models are consistently more accurate than the original CHF models.

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

The heat fluxes across the turbine tip gap are characterized by large unsteady pressure gradients and shear from the viscous effects. The classical Newton heat convection equation, based on the turbine inlet total temperature, is inadequate. Previous research from our team relied on the use of the adiabatic wall temperature. In this paper, we propose an alternative approach to predict the convective heat transfer problem across the turbine rotor tip using discrete Green's functions (DGF). The linearity of the energy equation in the solid domain with constant thermal properties can be applied with a superposition technique to measure the data extracted from flow simulations to determine the Green's function distribution. The DGF is a matrix of coefficients that relate the temperature spatial (GF) distribution with the heat flux. This methodology is first applied to a backward facing step, validated using experimental data. The final aim of this paper is to demonstrate the method in the rotor turbine tip. A turbine stage at engine-like conditions was assessed using cfd software. The heat flux pulses were applied at different locations in the rotor tip geometry, and the increment of temperature in this zone was evaluated for different clearances, with a consequent variation of the DGF coefficients. Ultimately, a detailed uncertainty analysis of the methodology was included based on the magnitude of the heat flux pulses used in the DGF coefficients calculation and the uncertainty in the experimental measurements of the wall temperature.

This paper presents a novel transient method for calibrating heat transfer gauges for convective wall heat flux measurements in high enthalpy flows. The new method relies on the transient heating of sensor substrates under rapid exposure to a hot flow in order to obtain the necessary reference heat flux. Compared to previous calibration facilities, the new facility is simple, inexpensive, easy to adapt for different flow configurations and sensor geometries, and quick to run across a wide range of conditions. In this paper, the design of the new calibration facility is described and the transient calibration method explained. The method is demonstrated by calibrating a Gardon gauge at convective heat transfer coefficients between 300 and 600 W/m2 K. Typical facility data and calibration results are presented in terms of voltage-heat flux sensitivity and calibration correction ratio. These results are shown to agree with theoretical estimates within the estimated calibration uncertainty.

Estimation of thermal properties or diffusion properties from transient data requires that a model is available that is physically meaningful and suitably precise. The model must also produce numerical values rapidly enough to accommodate iterative regression, inverse methods, or other estimation procedures during which the model is evaluated again and again. Bodies of infinite extent are a particular challenge from this perspective. Even for exact analytical solutions, because the solution often has the form of an improper integral that must be evaluated numerically, lengthy computer-evaluation time is a challenge. The subject of this paper is improving the computer evaluation time for exact solutions for infinite and semi-infinite bodies in the cylindrical coordinate system. The motivating applications for the present work include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. In this paper, the computer evaluation time is improved by replacing the integral-containing solution by a suitable finite-body series solution. The precision of the series solution may be controlled to a high level and the required computer time may be minimized, by a suitable choice of the extent of the finite body. The key finding of this paper is that the resulting series may be accurately evaluated with a fixed number of terms at any value of time, which removes a long-standing difficulty with series solution in general. The method is demonstrated for the one-dimensional case of a large body with a cylindrical hole and is extended to two-dimensional geometries of practical interest. The computer-evaluation time for the finite-body solutions are shown to be hundreds or thousands of time faster than the infinite-body solutions, depending on the geometry.

A relatively simple theory of annular laminar film condensation in microchannels, based on the Nusselt approximations for the condensate film and a theoretically based approximation for the vapor shear stress, has no empirical input and gives the local heat transfer coefficient and local quality for given vapor mass flux and vapor–surface temperature difference distribution along the channel. As well as streamwise vapor shear stress and gravity, the theory includes transverse (to the flow direction) surface tension-driven motion of the condensate film and gives a differential equation for the local (transverse and streamwise) condensate film thickness. As well as four transverse direction boundary conditions due to condensate surface curvature, a streamwise boundary condition is required as in the Nusselt theory. When the vapor is saturated or superheated at inlet, this is provided by the fact that the film thickness is zero around the channel perimeter at the position of onset on condensation. Most experimental investigations have been conducted with quality less than one at inlet and only approximate comparisons, discussed in earlier papers, can be made. The present paper is devoted to comparisons between theory and measurements in investigations where local heat flux and channel surface temperature were measured and the vapor at inlet was superheated. Measured and calculated heat transfer coefficients and their dependence on distance along the channel and on local quality are in surprisingly good agreement and suggest that the mode of condensation is, in fact, annular and laminar, at least where the quality is high.

In this study, a three-layered skin tissue has been modeled to assess the heat transfer characteristics in laser skin tumor–tissue interaction. A finite-volume-based two-dimensional numerical bioheat transfer model has been put together to study the damage prediction of healthy tissues by considering both Fourier and non-Fourier laws. The combination of the bioheat transfer equation with Fourier law forms the parabolic equation (Pennes model) and with the non-Fourier equation forms the hyperbolic equation (thermal wave model). In this paper, the laser source is provided on the outer layer of the skin to dismantle the undesired tumor region exemplified as inhomogeneity (tumor) present in the intermediate layer. Heat input through the laser source is on until it reaches the tumor-killing criteria. The heat transport equation has been discretized by the finite volume method (FVM). The finite-volume-based numerical model is developed in such a way that the non-Fourier model predictions can be obtained through conventional Fourier-based solver. The central difference scheme is adopted for discretizing the spatial derivative terms. An implicit scheme is applied to treat the transient terms in the model. For few cases of the hyperbolic problems, certain limitation for a chosen implicit scheme has also been addressed in this paper. The results are validated with the existing literatures. The evaluated results are based on both the Fourier and the non-Fourier model, to investigate the temperature distribution and thermal damage by ensuring irreversible thermal damage in the whole tumor region placed in the dermis layer. Thermal damage of the healthy tissue is found to be more in the time scale of the thermal wave model.