GLOBAL BLOW-UP FOR A HEAT SYSTEM WITH LOCALIZED SOURCES AND ABSORPTIONS

In this paper there are established the global existence and finite time blow-up results of nonnegative solution for the following parabolic system ut = △u ＋ v^P（x0, t） - au^τ, x ∈ Ω, t 〉 0, △u ＋ v^P（x0, t） - bu^τ, x ∈ Ω, t 〉 0 subject to homogeneous Dirichlet conditions and nonnegative initial data, where x0 ∈ Ω is a fixed point, p, q, r, s ≥ 1 and a, b 〉 0 are constants. In the situation when nonnegative solution （u, v） of the above problem blows up in finite time, it is showed that the blow-up is global and this differs from the local sources case. Moreover, for the special case r = s = 1, lim t→T＊（T＊-t）^p＋1/pq-1u（x,t）=（p＋1）^1/pq-1（q＋1）^p/pq-1（pq-1）^-p＋1/pq-1, lim t→T＊（T＊-t）^q＋1/pq-1u（x,t）=（p＋1）^1/pq-1（q＋1）^p/pq-1（pq-1）^-p＋1/pq-1 are obtained uniformly on compact subsets of/2, where T＊ is the blow-up time.

A Quasilinear Parabolic System with Nonlocal Boundary Conditions and Localized Sources

This paper investigates the properties of solutions to a quasilinear parabolic system with nonlocal boundary conditions and localized sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and blow- up rate estimates are also derived.

Blow-up Sets to a Coupled Heat System

This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtained. In the present paper, we continue to consider the blow-up sets to the system via a complete classification for the nonlinear parameters. That is the discussion on single point versus total blow-up of the solutions. It is mentioned that due to the influence of the localized sources, there is some substantial difficulty to be overcomed there to deal with the single point blow-up of the solutions.

Blow-up of Solutions to Porous Medium Equations with a Nonlocal Boundary Condition and a Moving Localized Source

This paper is devoted to the blow-up properties of solutions to the porous medium equations with a nonlocal boundary condition and a moving localized source. Conditions for the existence of global or blow-up solutions are obtained. Moreover, we prove that the unique solution has global blow-up property whenever blow-up occurs.

Experimental Study on the Performance of ORC System Based on Ultra-Low Temperature Heat Sources

This paper discussed the experimental results of the performance of an organic Rankine cycle(ORC)system with an ultra-low temperature heat source.The low boiling point working medium R134a was adopted in the system.The simulated heat source temperature(SHST)in this work was set from 39.51°C to 48.60°C by the simulated heat source module.The influence of load percentage of simulated heat source(LPSHS)between 50%and 70%,the rotary valve opening(RVO)between 20%and 100%,the resistive load between 36Ωand 180Ωor the no-load of the generator,as well as the autumn and winter ambient temperature on the system performance were studied.The results showed that the stability of the system was promoted when the generator had a resistive load.The power generation(PG)and generator speed(GS)of the system in autumn were better than in winter,but the expander pressure ratio(EPR)was lower than in winter.Keep RVO unchanged,the SHST,the mass flow rate(MFR)of the working medium,GS,and the PG of the system increased with the increasing of LPSHS for different generator resistance load values.When the RVO was 60%,LPSHS was 70%,the SHST was 44.15°C and the resistive load was 72Ω,the highest PG reached 15.11 W.Finally,a simulation formula was obtained for LPSHS,resistance load,and PG,and its correlation coefficient was between 0.9818 and 0.9901.The formula can accurately predict the PG.The experimental results showed that the standard deviation between the experimental and simulated values was below 0.0792,and the relative error was within±5%.

Chemically Radiative MHD Flow of a Micropolar Nanofluid over a Stretching/ Shrinking Sheet with a Heat Source or Sink

This study examines the behavior of a micropolar nanofluidflowing over a sheet in the presence of a transverse magneticfield and thermal effects.In addition,chemical(first-order homogeneous)reactions are taken into account.A similarity transformation is used to reduce the system of governing coupled non-linear partial differ-ential equations(PDEs),which account for the transport of mass,momentum,angular momentum,energy and species,to a set of non-linear ordinary differential equations(ODEs).The Runge-Kutta method along with shoot-ing method is used to solve them.The impact of several parameters is evaluated.It is shown that the micro-rota-tional velocity of thefluid rises with the micropolar factor.Moreover,the radiation parameter can have a remarkable influence on theflow and temperature profiles and on the angular momentum distribution.

Modeling and Optimization of Solar Collector Design for the Improvement of Solar-Air Source Heat Pump Building Heating System

To enhance system stability,solar collectors have been integrated with air-source heat pumps.This integration facilitates the concurrent utilization of solar and air as energy sources for the system,leading to an improvement in the system’s heat generation coefficient,overall efficiency,and stability.In this study,we focus on a residential building located in Lhasa as the target for heating purposes.Initially,we simulate and analyze a solar-air source heat pump combined heating system.Subsequently,while ensuring the system meets user requirements,we examine the influence of solar collector installation angles and collector area on the performance of the solar-air source heat pump dual heating system.Through this analysis,we determine the optimal installation angle and collector area to optimize system performance.

Research on Operation Optimization of Heating System Based on Electric Storage Coupled Solar Energy and Air Source Heat Pump

For heating systems based on electricity storage coupled with solar energy and an air source heat pump(ECSA),choosing the appropriate combination of heat sources according to local conditions is the key to improving economic efficiency.In this paper,four cities in three climatic regions in China were selected,namely Nanjing in the hot summer and cold winter region,Tianjin in the cold region,Shenyang and Harbin in the severe cold winter region.The levelized cost of heat(LCOH)was used as the economic evaluation index,and the energy consumption and emissions of different pollutants were analyzed.TRNSYS software was used to simulate and analyze the system performance.The Hooke-Jeeves optimization algorithm and GenOpt software were used to optimize the system parameters.The results showed that ECSA systemhad an excellent operation effect in cold region and hot summer and cold winter region.Compared with ECS system,the systemenergy consumption,and the emission of different pollutants of ECSA system can be reduced by a maximum of 1.37 times.In cold region,the initial investment in an air source heat pump is higher due to the lower ambient temperature,resulting in an increase in the LOCH value of ECSA system.After the LOCH value of ECSA system in each region was optimized,the heating cost of the system was reduced,but also resulted in an increase in energy consumption and the emission of different pollutant gases.

Study of energy-efficient heat resistance and cooling technology for high temperature working face with multiple heat sources in deep mine

In the present research,we proposed a scheme to address the issues of severe heat damage,high energy consumption,low cooling system efficiency,and wastage of cold capacity in mines.To elucidate the seasonal variations of environmental temperature through field measurements,we selected a high-temperature working face in a deep mine as our engineering background.To enhance the heat damage control cability of the working face and minimize unnecessary cooling capac-ity loss,we introduced the multi-dimensional heat hazard prevention and control method called"Heat source barrier and cooling equipment".First,we utilize shotcrete and liquid nitrogen injection to eliminate the heat source and implemented pressure equalization ventilation to disrupt the heat transfer path,thereby creating a heat barrier.Second,we establish divi-sional prediction models for airflow temperature based on the variation patterns obtained through numerical simulation.Third,we devise the location and dynamic control strategy for the cooling equipment based on the prediction models.The results of field application show that the heat resistance and cooling linkage method comply with the safety requirement throughout the entire mining cycle while effectively reducing energy consumption.The ambient temperature is maintained below 30℃,resulting in the energy saving of 10%during the high-temperature period and over 50%during the low-temperature period.These findings serve as a valuable reference for managing heat damage in high-temperature working faces.

Interdecadal Variations of the March Atmospheric Heat Source over the Southeast Asian Low-Latitude Highlands

Based on the fifth-generation reanalysis dataset from the European Centre for Medium-Range Weather Forecasts for 1979–2019,we investigated the effects of the circumglobal teleconnection(CGT)on the interdecadal variation of the March atmospheric heat source(AHS)over the Southeast Asian low-latitude highlands(SEALLH).The dominant mode of the March AHS over the SEALLH features a monopole structure with an 8–11-year period.Decadal variations in the AHS make an important contribution to the 11-year low-pass filtered component of the AHS index,whichexplains 54.3%of the total variance.The CGT shows a clear interdecadal variation,which explains 59.3%of the total variance.The March AHS over the SEALLH is significantly related to the CGT on interdecadal timescales.When the CGT is optimally excited by a significant cyclonic vorticity source near northern Africa(i.e.,in its positive phase),the SEALLH is dominated by anomalous southerly winds and ascending motions on the east of the anomalous cyclone.The enhanced advection and upward transfer result in a high-enthalpy air mass that converges into and condenses over the SEALLH,leading to a largerthan-average March AHS over this region.The key physical processes revealed by this diagnostic analysis are supported by numerical experiments.

Catalog of Enhanced Geothermal Systems based on Heat Sources

It is common sense that a deeper well implies higher temperature in the exploration of deep geothermal resources, especially with hot dry rock(HDR) geothermal resources, which are generally exploited in terms of enhanced geothermal systems(EGS). However, temperature is always different even at the same depth in the upper crust due to different heat sources. This paper summarizes the heat sources and classifies them into two types and five sub-types: crustorigin(partial melting, non-magma-generated tectonic events and radiogenic heat production), and mantle-origin(magma and heat conducted from the mantle). A review of global EGS sites is presented related to the five sub-types of heat sources. According to our new catalog, 71% of EGS sites host mantle-origin heat sources. The temperature logging curves indicate that EGS sites which host mantle-origin magma heat sources have the highest temperature. Therefore, high heat flow(>100 m W/m^(2)) regions with mantle-origin magma heat sources should be highlighted for the future exploration of EGS. The principle to identify the heat source is elucidated by applying geophysical and geochemical methods including noble gas isotope geochemistry and lithospheric thermal structure analysis. This analytical work will be helpful for the future exploration and assessment of HDR geothermal resources.

Discussion on heat source mechanism and geothermal system of Qinghai Gonghe-Guide Basin

The Qinghai Gonghe-Guide Basin together with the alternatively distributed mountainous region shows characteristics that the conductive geothermal resource of the basin has high geothermal gradient, the granite occurs in the bottom of borehole for geothermal exploration, and the convective hot springs in the basin-edge uplift fracture are in zonal distribution and with high-temperature geothermal water. There are still some divergences about the heat source mechanism of the basin. In this paper, queries to the view of mantle-derived heat source have been put forward, coming up with geochemical evidences to prove that the radiogenic heat of granite is the heat source within the mantle. Additionally, temperature curve is drawn based on the geothermal boring and geochemical geothermometer has been adopted for an estimation of the temperature and depth of the geothermal reservoir, it has been found that the surrounding mountains belong to the medium-temperature geothermal system while the area within the basin belongs to the high-temperature geothermal system with the temperature of borehole bottom reaching up to 175-180 ℃. In this paper, discussions on the problems existing in the calculation of geothermal gradient and the differences generated by the geothermal system have been carried out.

Simulation of embedded heat exchangers of solar aided ground source heat pump system

Aimed at unbalance of soil temperature field of ground source heat pump system, solar aided energy storage system was established. In solar assisted ground-source heat pump (SAGSHP) system with soil storage, solar energy collected in three seasons was stored in the soil by vertical U type soil exchangers. The heat abstracted by the ground-source heat pump and collected by the solar collector was employed to heating. Some of the soil heat exchangers were used to store solar energy in the soil so as to be used in next winter after this heating period; and the others were used to extract cooling energy directly in the soil by circulation pump for air conditioning in summer. After that solar energy began to be stored in the soil and ended before heating period. Three dimensional dynamic numerical simulations were built for soil and soil heat exchanger through finite element method. Simulation was done in different strata month by month. Variation and restoration of soil temperature were studied. Economy and reliability of long term SAGSHP system were revealed. It can be seen that soil temperature is about 3 ℃ higher than the original one after one year's running. It is beneficial for the system to operate for long period.

A review of soldering by localized heating

In recent years,the rapid development of the new energy industry has driven continuous upgrading of high-density and high-power devices.In the packaging and assembly process,the problem of differentiation of the thermal needs of different modules has become increasingly prominent,especially for small-size solder joints with high heat dissipation in high-power devices.Localized soldering is con-sidered a suitable choice to selectively heat the desired target while not affecting other heat-sensitive chips.This paper reviews several local-ized soldering processes,focusing on the size of solder joints,soldering materials,and current state of the technique.Each localized solder-ing process was discovered to have unique characteristics.The requirements for small-size solder joints are met by laser soldering,microres-istance soldering,and self-propagating soldering;however,laser soldering has difficulty meeting the requirements for large heat dissipation,microresistance soldering requires the application of pressure to joints,and self-propagating soldering requires ignition materials.However,for small-size solder junctions,selective wave soldering,microwave soldering,and ultrasonic soldering are not appropriate.Because the magnetic field can be focused on a tiny area and the output energy of induction heating is large,induction soldering can be employed as a significant trend in future research.

A degenerate parabolic system with localized sources and nonlocal boundary condition

This paper deals with the blow-up properties of the positive solutions to a degenerate parabolic system with localized sources and nonlocal boundary conditions. We investigate the influence of the reaction terms, the weight functions, local terms and localized source on the blow-up properties. We will show that the weight functions play the substantial roles in determining whether the solutions will blow-up or not, and obtain the blow-up conditions and its blow-up rate estimate.

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by a finite difference scheme,and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation.Secondly,the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution.And then,the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation,respectively.The LKM is a recently proposed local radial basis function collocationmethod with themerits of being simple,accurate,and free ofmesh and integration.Compared with the traditional domain-type and boundary-type schemes,the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains.Numerical experiments,including two-and three-dimensional heat transfer models,demonstrated the effectiveness and accuracy of the new methodology.

Research on single hole heat transfer power of ground source heat pump system

In this paper,the single hole heat transfer power of the ground source heat pump system in Hengshui is compared with data gained from thermal response test.The results show that maximum monitoring data of heat transfer power per meter in summer is 97.1% of the test data,and the average value accounts for 81.8%.The per meter heat power data through on-site thermal response test can provide references for designing engineering project and optimizing ground source heat pump system as these data do not vary greatly from the actual monitoring data.

Study on ground source heat pump system zoning and methods in the Northwest of Shandong Province

Based on the basic geology, hydrogeology, engineering geology, geothermal geology and ground source heat pump(GSHP) engineering of the work space, the thesis studies the local shallow geothermal energy. Three conditions of the attribute index for the suitability zoning of the northwest of Shandong are determined, namely, hydrodynamic condition, geological and hydrogeological condition and geological environment condition. The assessment result is that the total area of the suitable zone is 205.88 km^2, that of relative suitable zone, 1 407.76 km^2, and that of unsuitable zone, 286.8 km^2. The result conforms to the real development situation and provides experience for similar regions needed for selecting and assigning a value to suitability zoning of GSHP.

Experimental Investigation on System with Combination of Ground-Source Heat Pump and Solar Collector

This paper presents the heating performance and energy distribution of a system with the combination of ground-source heat pump and solar collector or a solar-assisted ground-source heat pump system (SAGSHPS) by calculation and experiment.The results show that the average absolute error is less than 0.6 ℃ and the relative error is less than 5% under the pulse load when the analytical solution to the 2-D solid cylindrical source model is used for the SAGSHPS.The coefficient of performance (COP) of the SAGSHPS is 2.95-4.70.The average fluid temperature in the borehole heat exchanger can increase by 3 ℃ with the assistance of solar collector,which will improve the COP of the heat pump by approximately 10% from the experimental data.The energy contributions to the total heating load of soil,electricity and solar are 56.30%,36.87% and 6.83%,respectively.

Heat balance of solar-soil source heat pump compound system

Based on the state-of-the-art studies of solar-soil source heat pump compound system,operation patterns of solar-soil compound system were analyzed,particularly the advantages of parallel operation pattern.It is found that parallel operation pattern is better for solar-soil compound system.Furthermore,the heat balance issue of solar-soil compound system was emphatically analyzed from four aspects,which were annual analysis of heating and cooling load,the heat exchange of ground heat exchanger,capacity determination of solar-assisted heat source and heat balance calculation of solar-soil compound system.Moreover,annual rate of heat balance in a solar-soil source heat pump compound system was calculated with a case study.It is shown that the annual heat unbalance ratio is 19%,which is less than 20%.As a result,the practical solar-soil compound system can basically maintain the heat balance of soil.