Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing

Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.

Paraffin–CaCl_(2)·6H_(2)O dosage effects on the strength and heat transfer characteristics of cemented tailings backfill

The challenge of high temperatures in deep mining remains harmful to the health of workers and their production efficiency The addition of phase change materials (PCMs) to filling slurry and the use of the cold storage function of these materials to reduce downhole temperatures is an effective approach to alleviate the aforementioned problem.Paraffin–CaCl_(2)·6H_(2)O composite PCM was prepared in the laboratory.The composition,phase change latent heat,thermal conductivity,and cemented tailing backfill (CTB) compressive strength of the new material were studied.The heat transfer characteristics and endothermic effect of the PCM were simulated using Fluent software.The results showed the following:(1) The new paraffin–CaCl_(2)·6H_(2)O composite PCM improved the thermal conductivity of native paraffin while avoiding the water solubility of CaCl_(2)·6H_(2)O.(2) The calculation formula of the thermal conductivity of CaCl_(2)·6H_(2)O combined with paraffin was deduced,and the reasons were explained in principle.(3) The“enthalpy–mass scale model”was applied to calculate the phase change latent heat of nonreactive composite PCMs.(4)The addition of the paraffin–CaCl_(2)·6H_(2)O composite PCM reduced the CTB strength but increased its heat absorption capacity.This research can give a theoretical foundation for the use of heat storage backfill in green mines.

Heat transfer and parametric studies of an encapsulated phase change material based cool thermal energy storage system

This work investigates the transient behaviour of a phase change material based cool thermal energy storage (CTES) system comprised of a cylindrical storage tank filled with encapsulated phase change materials (PCMs) in spherical container integrated with an ethylene glycol chiller plant. A simulation program was developed to evaluate the temperature histories of the heat transfer fluid (HTF) and the phase change material at any axial location during the charging period. The results of the model were validated by comparison with experimental results of temperature profiles of HTF and PCM. The model was also used to investigate the effect of porosity, Stanton number, Stefan number and Peclet number on CTES system performance. The results showed that increase in porosity contributes to a higher rate of energy storage. However, for a given geometry and heat transfer coefficient, the mass of PCM charged in the unit decreases as the increase in porosity. The St number as well as the Ste number is also influential in the performance of the unit. The model is a convenient and more suitable method to determine the heat transfer characteristics of CTES system. The results reported are much useful for designing CTES system.

Effect of different heat transfer fluids on discharging performance of phase change material included cylindrical container during forced convection

In the present work,effects of various heat transfer fluids on the discharging performance of a phase change material(PCM) included cylindrical container are numerically assessed during forced convection.The heat transfer fluid air,hydrogen,water and nanofluid with alumina particles are used and the the geometric variation of the PCM embedded region is also considered.The finite element method is used as the solver.Dynamic features of heat exchange with various phases are explored for different heat transfer fluid types,Reynolds number(between 100 and 300) and PCM embedded region geometric variation(h_(x)between 0.01 d_(1) and 0.65 d_(1),hybetween 0.1 h_(1) and 0.4 h_(1)).It is observed that discharging time is significantly influenced by the heat transfer fluid type while full phase transition time for air is obtained as more than 10 times when hydrogen is utilized as heat transfer fluid.The best performance is achieved with nanofluid.When the PCM integrated region size is reduced,discharging time is generally reduced while due to the form of the geometry,vortex formation is established in the PCM region.This results in performance degeneration at the highest radius and height of the inner cylinder.Discharging time increases by about 12% when radius of the inner cylinder is increased from h_(x)=0.35 d_(1) to h_(x)=0.45 d_(1).Dynamic features of PCM temperature and liquid fraction are affected with Reynolds number while discharging time is reduced by about 48% when configurations with the lowest and highest Reynolds number are compared.

Heat transfer performance testing of a new type of phase change heat sink for high power light emitting diode

In view of the limitations of solid metal heat sink in the heat dissipation of high power light emitting diode （LED）, a kind of miniaturized phase change heat sink is developed for high power LED packaging. First, the fabrication process of miniaturized phase change heat sink is investigated, upon which all parts of the heat sink are fabricated including main-body and end-cover of the heat sink, the formation of three-dimensional boiling structures at the evaporation end, the sintering of the wick, and the encapsulation of high power LED phase change heat sink. Subsequently, with the assistance of the developed testing system, heat transfer performance of the heat sink is tested under the condition of natural convection, upon which the influence of thermal load and working medium on the heat transfer performance is investigated. Finally, the heat transfer performance of the developed miniaturized phase change heat sink is compared with that of metal solid heat sink. Results show that the developed miniaturized phase change heat sink presents much better heat transfer performance over traditional metal solid heat sink, and is suitable for the packaging of high power LED.

Numerical study on freezing-thawing phase change heat transfer in biological tissue embedded with two cryoprobes

A two-dimensional model for freezing and thawing phase change heat transfer in biological tissue embedded with two cryoprobes was established.In this model,the blood vessels were considered as tree-like branched fractal network,and the effective flow rate and effective thermal conductivity of blood were obtained by fractal method.The temperature distribution and ice crystal growth process in biological tissue embedded with two cryoprobes during freezing-thawing process were numerically simulated.The results show that the growth velocity of ice crystal in freezing process from 200 to 400 s is more rapid than that from 400 to 600 s. Thawing process of frozen tissue occurs in the regions around cryoprobes tips and tissue boundary simultaneously,and the phase interfaces are close to each other until ice crystal melts completely.The distance of two cryoprobes has a more profound effect on the temperature distribution in freezing process at 400 s than at 800 s.

Heat Transfer Characteristics of Work Fluid Including Phase Change Material That Flow into Heating Surface from Narrow Path

Use of the low temperature (less than 100°C) energy contributes to effective use of heat resources. The cost recovery by power generation is difficult by using an existing system (the binary cycle or the thermoelectric conversion element), because the initial investment is large. The final purpose of this research is development of the low temperature difference drive engine supposing use in a hot-springs resort as a power source for electric power generation. In order that a traveler may look at and delight a motion of an engine, it is made to drive at low-speed number of rotations. An engine cycle of this study is aimed at the development of Stirling cycle engine which can maintain high efficiency in small size. This kind of engine has simple structure;it brings low cost, and it is easy to perform maintenance. However, it is difficult to obtain enough output by this type of engine, because of its low temperature difference. This paper deals with the heat transfer characteristic that the working fluid including a phase change material flows into the heating surface from the narrow path. In order to increase the amount of the heat transmission, Diethylether is added to the working fluid. Diethylether is selected as a phase change material (PCM) that has the boiling point which exists between the heat source of high temperature and low temperature. The parameters of the experiment are additive amount of PCM, rotational speed of the displacer piston and temperature of heat transfer surface. It is shown that it is possible to make exchange of heat amount increase by adding phase change material. The result of this research shows the optimal condition of the difference in temperature in heat processing, number of revolutions, and addition concentration of PCM.

Lattice Boltzmann simulation of phase change and heat transfer characteristics in the multi-layer deposition

The metal droplets deposition method(MDDM)is a rapid prototyping technology,implemented via metallurgy bonding within droplets.The anisotropy of heat transfer and re-melting is caused by an asymmetric deposition process.A lattice Boltzmann method(LBM)model is established to predict the heat transfer and phase change in the multi-layer deposition.The prediction model is verified by the experimental temperature profiles in existing literature.The monitoring points are set to compare the temperature profiles,and decoupling analyze the heat transfer mechanism in different positions.The negative relationships between the re-molten volume of the temperature difference,as well as the influence of the dispositive position and the relative position of the adjacent component are observed and analyzed under the heat conduction.This work is helpful to choose the appropriate temperature conditions and the optimal dispositive method.

Evaluation of Characteristics of Phase Change Heat Transfer in Ultrafine Cryoprobe

To reduce the invasiveness of cryosurgery, a miniaturized cryoprobe is necessary. The authors have developed an ultrafine cryoprobe for realizing low-invasive cryosurgery by local freezing. The objectives of this study are to estimate the heat transfer coefficient and investigate the characteristics of the phase change heat transfer in the ultrafine cryoprobe. This cryoprobe has a double-tube structure consisting of two stainless steel microtubes. The outer diameter of the cryoprobe was 550 μm. The alternative Freon HFC-23, which has a boiling point of ?82?C at 0.1 MPa, was used as a refrigerant. To evaluate the characteristics of boiling flow in the cryoprobe, the heat transfer coefficient was estimated. The derived heat transfer coefficient was higher than that obtained from the conventional correlation. Additionally, a bubble expansion model was introduced to evaluate the heat transfer mode of the phase change flow in the ultrafine cryoprobe. This model can estimate the liquid film thickness during the expansion of a single bubble in a microchannel. The experimentally measured wall superheat was much lower than that obtained from the model. Therefore, this result also implied that the heat transfer mode in the ultrafine cryoprobe should be nucleate boiling.

Comparative Heat Transfer Data for Solid-Liquid Phase Change of D-Mannitol and Adipic Acid

The goal of this work was to measure the heat transfer rates from thermofluid, Therminol 66, to two phase change materials, D-mannitol and adipic acid. It concerns the determination of heat transfer coefficients for the design of a concentrated solar energy plant requiring PCM thermal energy storage and is part of a wider set of experiments, where several PCMs were tested. An experimental installation was used with a cylindrical vessel with three tubes disposed almost horizontally (5°inclination), containing the phase change material, around which the thermal fluid flowed almost perpendicular to the tubes. The experimental installation allowed to recreate heating and cooling cycles. In order to evaluate the influence of the flow on the rate at which the heating and cooling processes took place, tests were performed at different thermofluid mass flow rates, concluding that there is no great influence, since the thermal resistance inside the tubes is much higher than on the outside. D-mannitol and adipic acid, present different phase change temperatures, 164°C for D-mannitol and 152°C for adipic acid. The average heat transfer coefficient, during the phase change process, was of 340 W/(m2K) for D-mannitol and 1320 W/(m2K) for adipic acid.

Simplified Correlation Equations of Heat Transfer Coefficient during Phase Change for Flow inside Tubes

In this work, the easy to use, simple and direct equations were formulated and tested. These equations can be used to calculate the mean values of the heat transfer coefficients of inside tube flow during phase change. Analytical and experimental methods were used to correlate these equations. Two different forms were used, one for evaporation case and the other for condensation case. Carbon dioxide, CO2, was used as case study. Correlated values of the mean heat transfer coefficients （hcor,.） were compared with the experimental results （he^e） and with other published result, a good agreement was noticed. The resulted correlations can be used to simplify the design and performance studies of both condensers and evaporators.

Fabrication and testing of phase change heat sink for high power LED

A novel phase change heat sink was fabricated for packaging cooling of high power light emitting diode （LED）. 3D structures as enhanced boiling structure in the evaporation surface were composed of a spiral micro-groove along circumferential direction and radial micro-grooves which were processed by ploughing-extrusion （P-E） and stamping, respectively. Meanwhile, the cycle power of refrigerant was supplied by wick of sintered copper powder on internal surface of phase change heat sink. Operational characteristics were tested under different heat loads and refrigerants. The experimental results show that phase change heat sink is provided with a good heat transfer capability and the temperature of phase change heat sink reaches 86.8 ℃ under input power of 10 W LED at ambient temperature of 20 ℃.

A Two-dimensional Heat Transfer Model for Atmosphere-land System in the Lake-dominated Alaskan Arctic

Understanding lake ice growth and its sensitivity to climate change is vital to understand the thermal regime of thaw lake systems and predict their response to climate change. In this paper, a physically-based, two-dimensional, non-steady mathematical model is developed for studying the role of shallow tundra lakes in the Alaskan Arctic. Both the radiation absorption in lake water and the phase change in permafrost are considerd in the model. The materials the model includes are snow, ice, water, unfrozen and frozen soil (peat, silt, sand and gravel). The basic inputs to the model observed mean daily air temperature and snow depth. The ability of this model to simulate lake ice growth and thickness variation, lake water temperature distribution, the thermal regime of permafrost and talik dynamics beneath lakes, and thawing rate of permafrost below and adjacent to shallow thaw lakes offers the potential to describe the effects of climate change in the Alaskan Arctic.

Coupled models of heat transfer and phase transformation for the run-out table in hot rolling

Mathematical models are been proposed to simulate the thermal and metallurgical behaviors of the strip occtLrring on the run-out table （ROT） in a hot strip mill. A variational method is utilized for the discretization of the governing transient conduction-convection equation, with heat transfer coefficients adaptively determined by the actual mill data. To consider the thermal effect of phase transformation during cooling, a constitutive equation for describing austenite decomposition kinetics of steel in air and water cooling zones is coupled with the heat transfer model. As the basic required inputs in the numerical simulations, thermal material properties are experimentally measured for three carbon steels and the least squares method is used to statistically derive regression models for the properties, including specific heat and thermal conductivity. The numerical simulation and experimental results show that the setup accuracy of the temperature prediction system of ROT is effectively improved.

Impact of Fin Arrangement on Heat Transfer and Melting Characteristics of Phase Change Material

Present work investigates the heat transfer and melting behaviour of phase change material(PCM) in six enclosures(enclosure-1 to 6) filled with paraffin wax.Proposed enclosures are equipped with distinct arrangements of the fins while keeping the fin's surface area equal in each case.Comparative analysis has been presented to recognize the suitable fin arrangements that facilitate improved heat transfer and melting rate of the PCM.Left wall of the enclosure is maintained isothermal for the temperature values 335 K,350 K and 365 K.Dimensionless length of the enclosure including fins is ranging between 0 and 1.Results have been illustrated through the estimation of important performance parameters such as energy absorbing capacity,melting rate,enhancement ratio,and Nusselt number.It has been found that melting time(to melt 100% of the PCM) is 60.5%less in enclosure-2(with two fins of equal length) as compared to the enclosure-1,having no fins.Keeping the fin surface area equal,if the longer fin is placed below the shorter fin(enclosure-3),melting time is further decreased by 14.1% as compared to enclosure-2.However,among all the configurations,enclosure-6 with wire-mesh fin structure exhibits minimum melting time which is 68.4% less as compared to the enclosure-1.Based on the findings,it may be concluded that fins are the main driving agent in the enclosure to transfer the heat from heated wall to the PCM.Proper design and positioning of the fins improve the heat transfer rate followed by melting of the PCM in the entire area of the enclosure.Evolution of the favourable vortices and natural convection current in the enclosure accelerate the melting phenomenon and help to reduce charging time.

A Mathematical Model of Heat Transfer in Problems of Pipeline Plugging Agent Freezing Induced by Liquid Nitrogen

A mathematical model for one-dimensional heat transfer in pipelines undergoing freezing induced by liquid nitrogen is elaborated.The basic premise of this technology is that the content within a pipeline is frozen to form a plug or two plugs at a position upstream and downstream from a location where work a modification or a repair must be executed.Based on the variable separation method,the present model aims to solve the related coupled heat conduction and moving-boundary phase change problem.An experiment with a 219 mm long pipe,where water was taken as the plugging agent,is presented to demonstrate the relevance and reliability of the proposed model(results show that the error is within 18%).Thereafter,the model is applied to predict the cooling and freezing process of pipelines with different inner diameters at different liquid nitrogen refrigeration temperatures when water is used as the plugging agent.

Experimental Investigation of the Operating Characteristics of a Pulsating Heat Pipe with Ultra-Pure Water and Micro Encapsulated Phase Change Material Suspension

The specific heat capacity of working fluid is an important influence factor on heat transfer characteristic of the pulsating heat pipe(PHP).Due to the relatively large specific heat capacity of micro encapsulated phase change material(MEPCM) suspension,a heat transfer performance experimental facility of the PHP was established.The heat transfer characteristic with MEPCM suspension of different mass concentrations(0.5% and 1.0%) and ultra-pure water were compared experimentally.It was found that when the PHP uses MEPCM suspension as its working fluid,operating stability is impoverished under lower heating power and the operating stability is better under higher heating power.At the inclination angle of 90°,the temperature at heating side decreases compared to ultra-pure water and the temperature at heating side decreases with the raising of MEPCM suspension mass concentration.The heat transfer characteristic of the PHP is positively correlated with the inclination angle and the 90° is optimum.The unfavorable effect of the inclination angle decreases with heating power increasing.When the inclination angle is 90°,the PHP with MEPCM suspension at 1.0% of mass concentration has the lowest thermal transfer resistance and followed by ultra-pure water and MEPCM suspension at 0.5% of mass concentration has the highest thermal transfer resistance.When the inclination angles are 60° and30°,the effect of gravity on the flow direction is reduced to 86.6% and 50% of that on the inclination angle of 90°,respectively,and the promoting effect of gravity on the working fluid is further weakened as the inclination angle further decreases.Due to the high viscosity of MEPCM suspension,the PHP with ultra-pure water has the lowest heat transfer resistance.When the inclination angles is 60°,the thermal resistance with MEPCM suspension at0.5% of the mass concentration is lower than that at 1.0% at the heating power below 230 W.The thermal resistance of MEPCM suspension tends to be similar for heating power of 230-250 W.At the heating power above 270 W,the thermal resistance with MEPCM suspension at 1.0% of the mass concentration is lower than that at 0.5%.

Phase change analysis of an underwater glider propelled by the ocean's thermal energy

The phase change characteristic of the power source of an underwater glider propelled by the ocean＇s thermal energy is the key factor in glider attitude control. A numerical model has been established based on the enthalpy method to analyze the phase change heat transfer process under convective boundary conditions. Phase change is not an isothermal process, but one that occurs at a range of temperature. The total melting time of the material is very sensitive to the surrounding temperature. When the temperature of the surroundings decreases 8 degrees, the total melting time increases 1.8 times. But variations in surrounding temperature have little effect on the initial temperature of phase change, and the slope of the temperature time history curve remains the same. However, the temperature at which phase change is completed decreases significantly. Our research shows that the phase change process is also affected by container size, boundary conditions, and the power source＇s cross sectional area. Materials stored in 3 cylindrical containers with a diameter of 38ram needed the shortest phase change time. Our conclusions should be helpful in effective design of underwater glider power systems.

Thermal energy storage inside the chamber with a brick wall using the phase change process of paraffinic materials:A numerical simulation

Phase change materials are one of the potential resources to replace fossil fuels in regards of supplying the energy of buildings.Basically,these materials absorb or release heat energy with the help of their latent heat.Phase change materials have low thermal conductivity and this makes it possible to use the physical properties of these materials in the tropical regions where the solar radiation is more direct and concentrated over a smaller area.In this theoretical work,an attempt has been made to study the melting process of these materials by applying constant heat flux and temperature.It was found that by increasing the thickness of phase change materials’layers,due to the melting,more thermal energy is stored.Simultaneously it reduces the penetration of excessive heat into the chamber,so that by increasing the thickness of paraffin materials up to 20 mm,the rate of temperature reduction reaches more than 18%.It was also recognized that increasing the values of constant input heat flux increases buoyancy effects.Increasing the Stefan number from 0.1 to 0.3,increases the temperature by 6%.

Phase change microcapsules in thermal Energy applications:A critical review

Phase change microcapsules can carry large amounts of heat and be dispersed into other mediums either as a solid composite or as slurry fluids without changes to their appearance or fluidity. These two standout features make phase change microcapsules ideal for use in thermal energy applications to enhance the efficiency of energy utilisation. This review paper includes methods used for the encapsulation of phase change materials, especially the method suitable for large scale productions, the trends of phase change microcapsule development and their use in thermal energy applications in static and dynamic conditions. The effect of phase change microcapsules on convective heat transfer through addition to thermal fluids as slurries is critically reviewed. The review highlighted that so far the phase change microcapsules used mainly have polymeric shells, which has very low thermal conductivities. Their enhancement in convective heat transfer was demonstrated in locations where the phase change material experiences phase change. The phase change results in the slurries having higher apparent local specific heat capacities and thus higher local heat transfer coefficients. Out of the phase change region, no enhancement is observed from the solid microcapsule particles due to the low specific heat capacity and thermal conductivity of the phase change microcapsules compared to that of water, which is normally used as slurry media in the test. To further the research in this area, phase change microcapsules with higher specific heat capacity, higher thermal conductivity and better shape stability need to be applied.