An analytical study of unsteady heat transfer in the rock surrounding a deep airway

The heat transfer between an airway and the air flowing though it is an unsteady problem. The governing equation of unsteady heat transfer was solved using the method of separation of variables. The solution is an infinite series including Bessel functions. The theoretical solution was analyzed by solving for the positive roots of the transcendental equation by iteration. The dimensionless surface temperature of the sur- rounding rock is only affected by the Bi number but not by the thermo-physical coefficients of the rock. The dimensionless coefficient of heat transfer, k, decreases with the Fo number similarly to the influence of the Bi number on k. A formula for determining the fully developed stage (FDS) suitable for unsteady heat transfer in the airway is proposed. The FDS from theoretical analysis occurs with Fo from 1.6 to 2. The ratio of excess temperature in the surrounding rock is independent of the initial conditions and only dependent on the Bi number and the relative position in the airway, at the FDS. The calculation error is large when using just the first term from the complete series when Fo is from 2 to 12. Five terms give a solution approximately equal to that found using the complete series. The first term could replace the complete series only when Fo is greater than 12. The FDS plays an important role in predication of the temperature field of the surrounding rock and in simplified calculations.

Analysis of Unsteady Heat Transfer Problems with Complex Geometries Using Isogeometric Boundary Element Method

Numerical analysis of unsteady heat transfer problems with complex geometries by the isogeometric boundary element method(IGABEM)is presented.The IGABEM possesses many desirable merits and features,for instance,(a)exactly represented arbitrarily complex geometries,and higher-order continuity due to non-uniform rational B-splines(NURBS)shape functions;(b)using NURBS for both field approximation and geometric description;(c)directly utilizing geometry data from computer-aided design(CAD);and(d)only boundary discretization.The formulation of IGABEM for unsteady heat transfer is derived.The domain discretization in terms of IGABEM for unsteady heat transfer is required as that in traditional BEM.The internal values however are obtained with the analytical formula according to the values on the boundaries,and its computations are therefore mainly dependent on the discretization of the boundaries.The coordinates of internal control points are obtained with the coordinates of control points on the boundaries using Coons body interpolation method.The developed approach is tested with several numerical examples from simple to complicated geometries.Good agreement is gained with reference solutions derived from either analytical or finite element methods.

Numerical Tools for the Control of the Unsteady Heating of an Airfoil

This paper concerns the real time control of the boundary layer on an aircraft wing. This new approach consists in heating the surface in an unsteady regime using electrically resistant strips embedded in the wing skin. The control of the boundary layer＇s separation and transition point will provide a reduction in friction drag, and hence a reduction in fuel consumption. This new method consists in applying the required thermal power in the different strips in order to ensure the desired temperatures on the aircraft wing. We also have to determine the optimum size of these strips （length, width and distance between two strips）. This implies finding the best mathematical model corresponding to the physics enabling us to facilitate the calculation for any type of material used for the wings. Secondly, the heating being unsteady, and, as during a flight the flow conditions or the ambient temperatures vary, the thermal power needed changes and must be chosen as fast as possible in order to ensure optimal operating conditions.

A NEW COMPUTATION METHOD FOR THE UNSTEADY HEAT TRANSFER COEFFICIENT IN A DEEP MINE

In mine geothermal prediction, the unsteady heat transfer coefficient is an important parameter for heat transfer computation between country rock and mine airflow. In this paper, the rock temperature distributions in the geothermal fields have been derived in mathematics, the unsteady heat transfer coefficients that can expound the relation between its nature and influencing factors have been derived also based on this analytic formula. It is shown both by numerical simulations and through in situ measurernents that the new computation method for determining the unsteady heat transfer cofeeicient is accurate, rapid and simple.

Exact Variational Principle For 3-D Unsteady Heat Conduction With Second Sound

The exact variational formulation of the extended unsteady heat conduction equation with finite propagation speed （the 2nd sound speed） of hyperbolic type is derived herein via a systematic and natural way. Moreover, the boundary- and the physically acceptable initial-value conditions are accommodated in the variational principle by a novel method suggested just recently. In this way a perfect justification of the variational theory of transient heat conduction and a rigorous theoretical basis for the finite element analysis of heat conduction are provided.

Mechanism of unsteady aerodynamic heating with sudden change in surface temperature

The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new inflexion near the wall occurs in the profile of the thermal boundary layer. This is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, meaning that, in a long-term aerodynamic heating process considering only unsteady surface temperature, the unsteady characteristics of the flow can be ignored, and the traditional quasi-steady aerodynamic heating prediction methods are still valid.

Study on the Influence of Piloti on Mean Radiant Temperature in Residential Blocks by 3-D Unsteady State Heat Balance Radiation Calculation

Piloti is commonly used in tropical and subtropical climate zones to get high wind velocity and create shadowed areas in order to optimize the living environment of residential blocks,but there are few studies to reveal the influence of piloti on the radiant environment of residential blocks systematically. Taking the city of Guangzhou as an example,using 3-D Unsteady State Heat Balance Radiation Calculation Method,this paper shows that the mean radiant temperature( MRT) under piloti area increases with the increase of piloti ratio,and especially when piloti ratio is equal to 100%,the MRT increase trend becomes sharp. The MRT of exposed area decreases with the increase of piloti ratio,especially when piloti ratio reaches 100%,the decrease trend of MRT becomes sharp,which offers the reference for the study on piloti design in subtropical climate zones and further research on living environment by CFD simulation in residential blocks.

Dynamic Calibration of the Cutting Temperature Sensor of NiCr/NiSi Thin-film Thermocouple

In high-speed cutting, natural thermocouple, artificial thermocouple and infrared radiation temperature measurement are usually adopted for measuring cutting temperature, but these methods have difficulty in measuring transient temperature accurately of cutting area on account of low response speed and limited cutting condition. In this paper, NiCr/NiSi thin-film thermocouples（TFTCs） are fabricated according to temperature characteristic of cutting area in high-speed cutting by means of advanced twinned microwave electro cyclotron resonance（MW-ECR） plasma source enhanced radio frequency（RF） reaction non-balance magnetron sputtering technique, and can be used for transient cutting temperature measurement. The time constants of the TFTCs with different thermo-junction film width are measured at four kinds of sampling frequency by using Ultra-CFR short pulsed laser system that established. One-dimensional unsteady heat conduction model is constructed and the dynamic performance is analyzed theoretically. It can be seen from the analysis results that the NiCr/NiSi TFTCs are suitable for measuring transient temperature which varies quickly, the response speed of TFTCs can be obviously improved by reducing the thickness of thin-film, and the area of thermo-junction has little influence on dynamic response time. The dynamic calibration experiments are made on the constructed dynamic calibration system, and the experimental results confirm that sampling frequency should be larger than 50 kHz in dynamic measurement for stable response time, and the shortest response time is 0.042 ms. Measurement methods and devices of cutting heat and cutting temperature measurement are developed and improved by this research, which provide practical methods and instruments in monitoring cutting heat and cutting temperature for research and production in high-speed machining.

Numerical Simulation of an Airfoil Electrothermal-Deicing-System in the Framework of a Coupled Moving-Boundary Method

A numerical method for the analysis of the electrothermal deicing system for an airfoil is developed taking into account mass and heat exchange at the moving boundary that separates the water film created due to droplet impingement and the ice accretion region.The method relies on a Eulerian approach(used to capture droplet dynamics)and an unsteady heat transfer model(specifically conceived for a multilayer electrothermal problem on the basis of the enthalpy theory and a phase-change correction approach).Through application of the continuous boundary condition for temperature and heat flux at the coupled movingboundary,several simulations of ice accretion,melting and shedding,runback water flow and refreezing phenomena during the electrothermal deicing process are conducted.Finally,the results are verified via comparison with experimental data.A rich set of data concerning the dynamic evolution of the distribution of surface temperature,water film height and ice shape is presented and critically discussed.

Calculation of Temperature Fields of Electric Locomotive Wheels during Emergency Braking on Tangent Track at a Speed of 200 km/h

According to the heat transfer theory, an unsteady state heat transfer model of electric locomotive wheels during emergency braking on tangent track at a speed of 200 km/h has been established in this paper. The explicit finite difference method is used in the numerical calculation of temperature fields of wheels. From the calculation results, the determination of braking distance and the material choice of brake shoes are discussed.

Numerical analysis on phase change material melting process of a conical spiral tube energy storage tank

Spiral tube heat exchangers have been widely used in phase change energy storage due to the compact structure and large heat transfer area.Therefore,this study numerically analyzes the effects of spiral tube diameter,number of rotations,and unsteady heat source on the melting process in conical spiral tube energy storage tanks using Fluent software.The results indicate that when the tube diameter is increased from 8 to 11 mm and the number of rotations is increased from 5 to 8,the melting time is extended by 15.74%and 17.83%,respectively.The energy storage capacity increases by 0.64%and 1.83%,respectively.The average energy storage rate decreases by 13.05%and 13.58%,respectively.Furthermore,the sinusoidal wave heat source with small heat source periods has little effect on the melting process,while large heat source periods can significantly accelerate the melting.And the influence of amplitudes on the thermal storage performance under large heat source periods is more obvious.When the heat source period is increased from 2 to 160 min and the amplitude is increased from 5 to 20 K,the melting time is reduced by 24.50%and 17.20%,respectively.The total energy storage capacity decreases by 6.36%and increases by 1.62%,respectively.The average energy storage rate increases by 24.03%and 22.74%,respectively.The study provides guidance for the performance optimization of spiral tube phase change systems.

A machine learning-assisted multifunctional tactile sensor for smart prosthetics

The absence of tactile perception limits the dexterity of a prosthetic hand and its acceptance by amputees.Recreating the sensing properties of the skin using a flexible tactile sensor could have profound implications for prosthetics,whereas existing tactile sensors often have limited functionality with cross-interference.In this study,we propose a machine-learning-assisted multifunctional tactile sensor for smart prosthetics,providing a human-like tactile sensing approach for amputations.This flexible sensor is based on a poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)(PEDOT:PSS)-melamine sponge,which enables the detection of force and temperature with low cross-coupling owing to two separate sensing mechanisms:the open-circuit voltage of the sensor as a force-insensitive intrinsic variable to measure the absolute temperature and the resistance as a temperature-insensitive extrinsic variable to measure force.Furthermore,by analyzing the unsteady heat conduction and characterizing it using real-time thermal imaging,we demonstrated that the process of open-circuit voltage variation resulting from the unsteady heat conduction is closely correlated with the heatconducting capabilities of materials,which can be utilized to discriminate between substances.Assisted by the decision tree algorithm,the device is endowed with thermal conductivity sensing ability,which allows it to identify 10 types of substances with an accuracy of 94.7%.Furthermore,an individual wearing an advanced myoelectric prosthesis equipped with the above sensor can sense pressure,temperature,and recognize different materials.We demonstrated that our multifunctional tactile sensor provides a new strategy to help amputees feel force,temperature and identify the material of objects without the aid of vision.