COMPUTATIONAL SOLUTION OF TEMPERATURE DISTRIBUTION IN A THIN ROD OVER A GIVEN INTERVAL I={x├|0

In this paper, two analytical–numerical algorithms are formulated based on homotopy perturbation method and new iterative method to obtain numerical solution for temperature distribution in a thin rod over a given finite interval. The effects of different parameters such as the coefficient which accounts for the heat loss and the diffusivity constant are examined when initial temperature distribution (trigonometry and algebraic functions) are considered. The error in both algorithms approaches to zero as the computational length increases. The proposed algorithms have been demonstrated to be quite flexible, robust and accurate. Thus, the algorithms are established as good numerical tools to solve several problems in applied mathematics and other related field of sciences

Finite element modeling of geothermal source of heat pump in long-term operation

Heat pumps become more and more popular heat source. They can be an alternative choice for obsolete coal fired boilers which are emissive and not ecological. During heat pump installation designing process, especially for heat pumps with higher heating capacity (for example those suppling larger buildings), a simulation of heat balance of ground heat source must be provided. A 3D heat transport model and groundwater flow in the geothermal heat source for heat pump (GSHP) installation was developed in FEFLOW according to Finite Element Modelling Method. The model consists of 25 borehole heat exchangers, arranged with spacing recommended by heat pump branch guidelines. The model consists of both a homogeneous, non-layered domain and a layered domain, which reflected differences in thermal properties of the ground and hydrogeological factors. The initial temperature distribution in the ground was simulating according to conditions typical for Europe in steady state heat flow. Optimal mesh refinement for nodes around borehole heat exchangers were calculated according to Nillert method. The aim of this work is to present influence of geological, hydrogeological factors and borehole arrangement in the energy balance and long term sustainability of the ground source. The thermal changes in the subsurface have been determined for a long term operation (30 years of operation period). Some thermal energy storage applications have also been considered.

Controlling Power Consumption in a Heterogeneous Population Model of TCLs with Diffusion: The Green’s Function Approach

We consider a control problem for a diffusive PDE model of heterogeneous population of thermostatically controlled loads (TCLs) aiming to balance the aggregate power consumption within a given amount of time. Using the Green’s function approach, the problem is formulated as an approximate controllability problem for a residue depending on control parameters nonlinearly. A sufficient condition for approximate controllability is derived in terms of initial temperature distribution, operation time of TCLs and threshold value of the aggregate power consumption. Case studies allow to reveal the advantages of the proposed solution from numerical calculations point of view.

The Green’s Type Matrices for Consumption Reduction in a Heterogeneous Population Model of TCLs with Diffusion

We consider a control problem for a diffusive PDE model of heterogeneous population of thermostatically controlled loads (TCLs) aiming to balance the aggregate power consumption within a given amount of time. Using the Green’s function approach, the problem is formulated as an approximate controllability problem for a residue depending on control parameters nonlinearly. A sufficient condition for approximate controllability is derived in terms of initial temperature distribution, operation time of TCLs and threshold value of the aggregate power consumption. Case studies allow to reveal the advantages of the proposed solution from numerical calculations point of view.

The Green’s Type Matrices for Consumption Reduction in a Heterogeneous Population Model of TCLs with Diffusion

We consider a control problem for a diffusive PDE model of heterogeneous population of thermostatically controlled loads (TCLs) aiming to balance the aggregate power consumption within a given amount of time. Using the Green’s function approach, the problem is formulated as an approximate controllability problem for a residue depending on control parameters nonlinearly. A sufficient condition for approximate controllability is derived in terms of initial temperature distribution, operation time of TCLs and threshold value of the aggregate power consumption. Case studies allow to reveal the advantages of the proposed solution from numerical calculations point of view.

Postcollisional evolution features of the intracontinental structures formed by overthrusting

The investigation of intracontinental collision structures is conducted based on the complex model of the thermal and mechanical evolution of overthrusting process for the rheologically layered lithosphere, which includes brittle upper crust, the lower crust and lithospheric upper mantle with different effective viscosity values. Finite element models with Lagrangian approach were used for the problem simulation. It was shown that thermal evolution of continental orogens essentially results from the geometry and topography due to thrusting and postcollision stage. This work concentrates on the thermal parameters influence on the evolution of collision zones aimed to the study of possibility of granite melt formation. Calculations for mean continental initial temperature distribution lead to the conclusion of possibility of granite melt formation for the case of “wet” granite solidus. The horizon of temperatures higher than “wet” granite solidus appears at the level of 30-40 km, moving upward to the depth 15-20 km at postcollision stage. The early postcollision evolution shows some heat flow increase due to the thickening of the upper crust with maximum heat generation rate. Further history leads to the stable heat flow values because additional loading redistribution resulting from the denudation of surface uplift and corresponding sedimentation is small due to the local erosion in our model. It was shown that surface heat losses after the termination of horizontal shortening depend to a greater extent on radiogenic heat generation rather than thermal conductivity value in the upper crust.

Acoustic Reconstruction for Photothermal Imaging

Pulsed illumination of a sample, e.g., of a biological tissue, causes a sudden temperature increase of light absorbing structures, such as blood vessels, which results in an outgoing acoustic wave, as well as heat diffusion, of the absorbed energy. Both of the signals, pressure and temperature, can be measured at the sample surface and are used to reconstruct the initial temperature or pressure distribution, called photoacoustic or photothermal reconstruction respectively. We have demonstrated that both signals at the same surface pixel are connected by a temporal transformation. This allows for the calculation of a so-called acoustical virtual wave from the surface temperature evolution as measured by an infrared camera. The virtual wave is the solution of a wave equation and can be used to reconstruct the initial temperature distribution immediately after the excitation pulse. This virtual wave reconstruction method was used for the reconstruction of inclined steel rods in an epoxy sample, which were heated by a short pulse. The reconstructed experimental images show clearly the degradation of the spatial resolution with increasing depth, which is theoretically described by a depth-dependent thermographic point-spread-function.

Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient). Some numerical experiments are given.

Thermophysical Property Estimation by Transient Experiments: The Effect of a Biased Initial Temperature Distribution

The identification of thermophysical properties of materials in dynamic experiments can be conveniently performed by the inverse solution of the associated heat conduction problem (IHCP). The inverse technique demands the knowledge of the initial temperature distribution within the material. As only a limited number of temperature sensors (or no sensor at all) are arranged inside the test specimen, the knowledge of the initial temperature distribution is affected by some uncertainty. This uncertainty, together with other possible sources of bias in the experimental procedure, will propagate in the estimation process and the accuracy of the reconstructed thermophysical property values could deteriorate. In this work the effect on the estimated thermophysical properties due to errors in the initial temperature distribution is investigated along with a practical method to quantify this effect. Furthermore, a technique for compensating this kind of bias is proposed. The method consists in including the initial temperature distribution among the unknown functions to be estimated. In this way the effect of the initial bias is removed and the accuracy of the identified thermophysical property values is highly improved.