Rectangular Heat Pulse Research Articles

Dynamic Character of Thermal Analysis Where Thermal Inertia Is a Real and Not Negligible Effect Influencing the Evaluation of Non-Isothermal Kinetics: A Review

The development of instrumentation has allowed thermal analysis to become a widely used method not only in calorimetry but also in the field of non-isothermal kinetics that, however, provides a simplified philosophy of measurements. From the beginning, a methodology is used describing the course of reaction in a simplified temperature regime measured in an inert sample. In a most common case of DTA, the degree of reaction is subtracted from the partial areas of the as-cast peak in the unified mode of the peak linear background. Usually, the effect of thermal inertia, resulting from the reality of heat transfer and changing the peak background to a non-linear s-shaped form, is not incorporated. Therefore, the question of whether or not to include this effect of thermal inertia has become a current underlying problem of thermo-analytical kinetics. The analysis of the rectangular input heat pulses and their DTA responding fundamentally point to the need to include it thus becoming essential and not negligible. In the case of parallel evaluations, the effect of inertia can be partially compensated for each other such as in the Kissinger evaluation method. The study presents a broad overview of the thermo-analytical methodology used and points to the often-neglected literature. However, standard mainstream kinetics procedures need be fixed, and an improved solution found to account for the effect of heat transfer and dissipation, which is becoming the focus of thermal analysis methods of future and also the intention of this review.

The evaluation of nonisothermal thermoanalytical kinetics is simplified without the description of heat transfers, such as thermal inertia, which is not negligible, as indicated by Vyazovkin

AbstractIn the field of thermoanalytical kinetics, which is widely used, basic questions arise regarding a possible description of the effect of heat transfer and subsequent thermal inertia. Current practice still uses a simplified interpretation of directly measured data for an inert sample at a constant temperature rise to describe the studied reaction, which leads to a simplified reaction conversion ratio, which is further used for various mathematical processing. The analysis of the introduced rectangular heat pulses and their indication by DTA clearly shows that the effect of thermal inertia is fundamental and not negligible. This is, after all, known from calorimetry, where the integral constant of inertia has historically been used to calibrate the descending temperature, but it cannot generally be applied to the whole temperature process due to its nonlinearity. In the case of parallel processing, for example by gradually increasing the heating rate, the effect of thermal inertia can be partially compensated for each other which have yet to be confirmed. However, for the kinetic analysis of a single peak, it is necessary to adapt to the effect of the thermal delay due to thermal inertia, which, similarly to the measured enthalpy, is tied to the sample size. Of course, it will be up to the researcher to find a solution that also includes the effect of heat transfer and dissipation, which should become the main principle of thermoanalytical methods of the future, as shown by current examples combining thermal processes with their specific kinetics.

Fast computation approach for parameterized design and simulation of vertical ground heat exchangers and GCHP systems

Vertical ground heat exchanger (GHE) is an expensive part of vertical GCHP systems. Fast and accurate computation of fluid and ground temperatures is desired for the long-term energy performance prediction of GCHP and optimal sizing of bore field. Hourly simulations and iteration of parameterized design in time domain with thermal response factors is quite time-consuming. In this paper, a new thermal response factors, δ-function is proposed for computing fluid and ground temperatures of bore field. δ-function is a non-dimensional ground temperature response and an accurate analytical solution of finite line source model to a unit rectangular heat pulse. Computation of δ-function is quite fast due to its quite small integral range. The validity and accuracy of δ-function are examined by the simulation results of g-function. Through comparing hourly simulation of various periods between g- and δ-functions in both time and spectral domain methods, the combination of δ-function with Fast Fourier Transform spends the least computing time and is suitable to quickly and accurately compute fluid and ground temperatures in parameterized design and long-period hourly simulation of vertical heat exchanger and GCHP systems.

Thermal response factors for fast parameterized design and long-term performance simulation of vertical GCHP systems

Ground-coupled heat pump (GCHP) system is one of the important renewable energy systems. Vertical ground heat exchanger (GHE) is the most expensive part of GCHP systems. Fast and accurate computation of fluid and ground temperatures is desired for the long-term prediction of GCHP performance and the optimal sizing of borehole fields. In this paper, a thermal response factors, δ-function is proposed for computing fluid and ground temperatures of borehole fields. δ-function is a non-dimensional ground temperature response and an accurate analytical solution of finite line source model to a unit rectangular heat pulse. Numerical computation of δ-function is quite fast for its small integral range. The accuracy of δ-function is validated by the simulation results of g-function. The comparative computations are conducted for the hourly simulation of various long periods by combining the g- and δ-functions with both time and spectral domain methods. It is found that the combination of δ-function with fast Fourier transform (FFT) provides dramatically fast computing speed. Therefore, the computation approach of δ-function combined with FFT is the most suitable to quickly and accurately compute the fluid and ground temperatures in parameterized design and long-term simulation of vertical GHE and GCHP systems.

Heat inertia and its role in thermal analysis

The history of the term inertia is mentioned, and the effect of the heat inertia phenomenon is found in equations derived by Newton and Tian as well as in works of Vold and Borchard and Daniels. The mathematical correction of heat inertia consequences can be portrayed using the both differential and/or integral forms. It has been confirmed by the effective rectification applied to DTA (and heat-flux DSC) responses reflecting well the need of heat inertia corrections as to attain the original shape of inserted rectangular heat pulse.

Focusing of heat pulses along nonequilibrium nanowires

As a consequence of the temperature dependence of the speed of heat pulses, rectangular heat pulses will shrink (or extend) spatially, and will increase (or decrease) their temperature when propagating along a temperature gradient. Here, we consider heat pulse propagation along silicon nanowires, because of their interest in nanotechnology. The relative rates of variation per meter may be very high, and variations along relatively short lengths could be experimentally observable.

Mixtures of Euler’s fluids and second sound propagation in superfluid helium

We study the second sound propagation in superfluid helium using the theoretical background developed in a recent paper [1], through which this phenomenon, both in crystals and in Helium II, can be inserted in a unique framework. In particular, considering an initial rectangular heat pulse and exploiting the selection rules of the physical shocks, a wide phenomenology of travelling shock waves, including the very special case of double shocks, is explained.

A method to measure thermal conductivity and thermal diffusivity under pore and confining pressure

A measuring equipment was developed for the determination of thermal conductivity and thermal diffusivity of rocks under pore and confining pressure up to 90 MPa and 300 MPa, respectively. A quadratic heater placed between two cubic samples generates a rectangular heat pulse of 5 s length. In one of the cubes the pulse response at a known distance from the heater is measured by a thermocouple. The sample holder is mounted on the upper plug of the used high pressure vessel. The whole sample arrangement is sealed against the pressure medium by an elastic polyurethene jacket. Pore fluid is introduced into the pore space of the rock sample by a perforated back plate. A numerical modelling of the pulse propagation is used to determine thermal conductivity and thermal diffusivity from the measured pulse amplitude and half value time. First results are given for a 16 % porosity sandstone from Obernkirchen, Germany.

Criterion for quantum turbulence onset after rectangular heat pulse in superfluid helium

On the basis of transient heat transfer measurements of the film boiling onset time in a He II bath, a criterion correlated to the bath temperature and pressure for quantum turbulence onset after a rectangular heat pulse in superfluid helium is shown. Using the criterion parameter α it is possible to determine the time τ needed to initiate quantum turbulence in the He II bath after a rectangular heat pulse. It is found that the criterion value in a He II bath is much smaller than that for He II confined in small channels. A strong pressure effect is also exhibited.

Pressure drop and transient heat transport in forced flow single phase helium II at high Reynoldsnumbers

Pressure drop and transient heat transport measurements had been performed in the superfluid helium test loop at CEA/CEN-Grenoble, France. Single phase helium II was circulated through a 28 mm I.D. tube, over a length of 200 m for mass flow rates between 0.02 and 0.1 kg/s. Steady-state pressure drop measurements allow us to estimate the friction factor for Reynolds numbers in the 10 6 range. Rectangular heat pulses were applied at mid-length, and the fluid temperature was measured at several locations along the flow, upstream and downstream. A code has been developed which uses the two-fluid model to simulate time-dependent heat transport helium 11 flow. Simulation results are in good agreement with experimental measurements.

Interaction of second sound acoustic waves with a counterflow-induced turbulent field

The evolution of the flow and temperature fields produced by rectangular heat pulses on the background of a steady velocity and vortex line density (VLD) field is considered. This flow is described by a simplified linearised theoretical model exhibiting the dynamics of the VLD evolution. The Gorter-Mellink coefficient A is obtained from experiments on the decay of weak temperature pulses with distance from the heater. A comparison of experimental and theoretical temperature-time slopes yields a correction factor to the growth and decay coefficients of Vinen's VLD evolution equation.

The evolution of axisymmetric rectangular second-sound (heat) pulses in superfluid helium

Very little attention has been given, so far, to the problem of the propagation of axisymmetric second-sound shock waves, although they may occur in practical applications. In this paper, research on the propagation of moderate cylindrical heat pulses in superfluid helium is reported. A theoretical model is built based on the experimental observation of the evolution of the structure of rectangular heat pulses. The agreement between the experimental measurements and the theoretical calculations of the evolution of the main parameters is very satisfactory.

Stability of superconductors for poloidal field coil application

Experiments were performed on a Cu/CuNi/NbTi mixed-matrix conductor which was supplied with a transport current and exposed to magnetic-field pulses of typically ten milliseconds length and with a dB/dt up to a few hundred tesla per second. Various cooling regimes were employed: bath cooling, supercritical helium, and liquid helium in a closed, small volume (the case of a cable in conduit conductor). The stability limit was found to be determined mainly by the transient heat transfer during the pulse. A stability model is developed which compares the energy coupled into the conductor by the field pulse with the energy which can be absorbed by the near-surface helium layer due to the transient heat transfer. The model assumes that the stability for a short heat pulse is determined by the transient heat transfer during the pulse. The description of transient heat transfer is based on diffusion models; no convective effects are considered. The relevant quantity describing the disturbance is energy input per unit cooled conductor surface. The model is derived for a uniform heat input during a pulse time (rectangular heat pulse), for different cooling conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Two-dimensional unsteady temperature field on the surface of a semiinfinite body subject to heating by an annular pulse

The development of an unsteady temperature field on the surface of a semiinfinite body is studied in the case where the body is heated by rectangular heat pulse through an annular region.

Determining the thermophysical characteristics of materials on a model of a semiinfinite body with heat supplied by means of a thin annular heater

Methods of complex calculation of the thermophysical characteristics of materials without destroying their integrity are proposed, on the basis of a model of a semiinfinite body on heating with a rectangular heat pulse through a specified annular region.

Thermogenesis: Relative kinetic limits

This work presents kinetic limits for conduction calorimeters taken from experimental data and given in reduced units (ν τ 1). Two different criteria are proposed concerning either a full reconstruction of a rectangular heat pulse (used in calibration procedures) or a complete separation of elementary pulses to provide a fair reconstruction of the thermogenesis. These upper limits are given for several signal to noise ratios.