A method of fundamental solutions for the radially symmetric inverse heat conduction problem

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric inverse heat conduction problem (IHCP). In the radially symmetric IHCP data on an inner fixed boundary is determined from Cauchy data given on an outer boundary. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach of Johansson et al. (2008) for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.     

Application of the homotopy perturbation method for the solution of inverse heat conduction problem

This paper deals with an application of the homotopy perturbation method for the solution of inverse heat conduction problem. This problem consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of functions describing the temperature and heat flux on the boundary, when the temperature measurements in the domain are known. Examples illustrating discussed application and confirming utility of this method in such a type of problem was also presented.     

The method of fundamental solutions for solving free boundary saturated seepage problem

The problem of seepage flow through a dam is free boundary problem that is more conveniently solved by a meshless method than a mesh-based method such as finite element method (FEM) and finite difference method (FDM). This paper presents method of fundamental solutions, which is one kind of meshless methods, to solve a dam problem using the fundamental solution to the Laplace's equation. Solutions on free boundary are determined by iteration and cubic spline interpolation. The numerical solutions then are compared with the boundary element method (BEM), FDM and FEM to display the performance of present method.     

The application of the homotopy perturbation method to one-phase inverse Stefan problem

In this paper, the application of the homotopy perturbation method for solving the inverse Stefan problem is presented. This problem consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of the functions describing temperature and heat flux on the boundary, when the position of the moving interface is known.     

Solution of inverse heat conduction problem using the lattice Boltzmann method

In this paper the D2Q9 lattice Boltzmann method (LBM) was utilized for the solution of a two-dimensional inverse heat conduction (IHCP) problem. The accuracy of the LBM results was validated against those obtained from prevalent numerical methods using a common benchmark problem. The conjugate gradient method was used in order to estimate the heat flux test case. A complete error analysis was performed. As the LBM is attuned to parallel computations, its use is recommended in conjugation with IHCP solution methods.     

Using genetic algorithms for the determination of an heat transfer coefficient in three-phase inverse Stefan problem

In the paper, an example is presented of the application of a genetic algorithm to a design inverse Stefan problem. The problem consists in the reconstruction of the function which describes the heat transfer coefficient, where the positions of phase change moving interfaces are well-known. In numerical calculations, the Tikhonov regularization, a genetic algorithm and a generalized alternating phase truncation method were used. The featured examples of calculations show a very good approximation of the exact solution.     

Design of inverse multiquadric radial basis neural networks for the dynamical analysis of MHD casson nanofluid flow along a nonlinear stretchable porous surface with multiple slip conditions

The present research, a numerical approach to examine magnetohydrodynamics (MHD) Casson nanofluid flow in a porous medium along a stretchable surface with different slips using artificial neural networks (ANNs) by taking inverse multiquadric (IMQ) radial basis function (RBF) as an activation function. i.e. ANNs-IMQ-RBF. The hybridization of genetic algorithms (GAs) and sequential quadratic programming (SQP) is used for learning in ANNs-IMQ-RBF. The PDEs representing the fluid flow are converted into a nonlinear system of dimensionless form of ODEs through an appropriate transformation while effects of variation in the values of Casson parameter (β), Brownian motion parameter (Nb), Prandtl number (Pr), stretching parameter (n), porosity parameter (P), Lewis number (Le) along with temperature slip parameter (λ₂) on velocity, temperature and nanofluid concentration are depicted through graphs. The effectiveness, convergence and accuracy of the proposed solver are validated evidently through boxplot analysis, histograms and cumulative distribution function (CDF) plots.     

Approximate polynomial solutions for nonlinear heat transfer problems using the squared remainder minimization method

In the present paper we introduce a new approximation method, called the squared remainder minimization method (SRMM), which allows us to compute analytical approximate polynomial solutions for several nonlinear heat transfer problems. The applications illustrate the validity of the method and a comparison with previous results emphasizes the accuracy of the method.     

An inverse problem of parameter estimation for heat and mass transfer in capillary porous media

This work deals with the solution of an inverse problem of parameter estimation involving heat and mass transfer in capillary porous media, as described by the dimensionless linear Luikov’s equations. The physical problem under picture involves the drying of a moist porous one-dimensional medium. The main objective of this paper is to simultaneously estimate the dimensionless parameters appearing in the formulation of the physical problem by using transient temperature and moisture content measurements taken inside the medium. The inverse problem is solved by using the Levenberg-Marquardt method of minimization of the least-squares norm with simulated measurements.     

Inverse problem and variation method to optimize cascade heat exchange network in central heating system

Urban heating in northern China accounts for 40％ of total building energy usage.In central heating systems,heat is often transfened from heat source to users by the heat network where several heat exchangers arc installed at heat source,substations and terminals respectively.For given overall heating capacity and heat source temperarure,increasing the terminal fluid temperature is an effective way to improve the thermal performance of such cascade heat exchange network for energy saving.In this paper,the mathematical optimization model of the cascade heat exchange network with three-stage heat exchangers in series is established.Aim at maximizing the cold fluid temperature for given hot fluid temperature and overall heating capacity,the optimal heat exchange area distribution and the medium fluids' flow rates are determined through inverse problem and variation method.The preliminary results show that the heat exchange areas should be distributed equally for each heat exchanger.It also indicates that in order to improve the thernmal performance of the whole system,more heat exchange areas should be allocated to the heat exchanger where flow rate difference between two fluids is relatively small.This work is important for guiding the optimization design of practical cascade heating systems.     

Inverse problem of estimating time-dependent heat generation in a frictional heated strip and foundation

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent frictional heat generation for the tribosystem consisting of a semi-infinite foundation and a plane-parallel strip sliding over its surface, from the knowledge of temperature measurements taken within the foundation. It is assumed that no prior information is available on the functional form of the unknown heat generation; hence the procedure is classified as the function estimation in inverse calculation. Results show that an excellent estimation on the time-dependent heat generation can be obtained for the test case considered in this study. The current methodology can be applied to the prediction of heat generation in engineering problems involving sliding-contact elements.     

An inverse geometry design problem in optimizing the shape of the gas channel for a proton exchange membrane fuel cell

The inverse design problem technique presented in this paper is intended for optimizing the shape of the gas channel at the cathode side in a proton exchange membrane fuel cell (PEMFC). The technique uses the desired current densities located on a carbon plate near the outlet of the channel at the cathode side as a starting point. The desired current density distributions can be obtained by modifying the current density distributions of the existing PEMFC with rectangular gas channels. The geometry of the redesigned gas channel is generated using a B-spline curve method, which enables the shape of the fuel channel to be completely specified using only a small number of control points, thus applying the technique of parameter estimation for the inverse design problem. Results show that by utilizing the redesigned optimal gas channel, the total current of the PEMFC can be increased, and at the same time the phenomenon of saturated water accumulation in the channel can be greatly reduced.     

An analytical method for solving exact solutions of the convective heat transfer in fully developed laminar flow through a circular tube

This paper proposes an exact solution to the classical Graetz problem in terms of an infinite series represented by a nonlinear partial differential equation considering two space variables, two boundary conditions, and one initial condition. The mathematical derivation utilized the separation of variables method where several stages were completed to reach the solution to the Graetz problem.     

Analytical approach with Laplace transform to the inverse problem of one‐dimensional heat conduction transfer: Application to second and third boundary conditions

An analytical method using Laplace transformation has been developed for one‐dimensional heat conduction. This method succeeded in explicitly deriving the analytical solution by which the surface temperature for the first kind of boundary condition can be well predicted. The analytical solutions for the surface temperature and heat flux are applied to the second and third of the boundary conditions. These solutions are also found to estimate the corresponding surface conditions with a high degree of accuracy when the surface conditions smoothly change. On the other hand, when these conditions erratically change such as the first derivative of temperature with time, the accuracy of the estimation becomes slightly less than that for a smooth condition. This trend in the estimation is similar irrespective of any kind of boundary condition. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 29–41, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10069     

Fundamental solution for a line source of heat in the fractional order theory of thermoelasticity using the new Caputo definition

Abstract

The new Caputo Fabrizio fractional differential operator is used to investigate a problem in the fractional order theory of thermoelasticity. The problem concerns an infinite elastic space under the effect of a continuous line source of heat. The problem is solved using asymptotic expansions valid for short times. Laplace and Hankel transforms are used to solve the problem. A brief study to the nature of propagation of waves is introduced. Graphical results are presented and discussed.     

Modeling the impact of integrating solar thermal systems and heat pumps for domestic hot water in electric systems – The case study of Corvo Island

The use of solar thermal systems with electricity backup and heat pumps as hot water suppliers in residential buildings seems to be a very promising way to increase energy efficiency. Nevertheless, the massive adoption of such solutions in small networks (neighborhood, village) may induce problems in the electric grid management. This study explores the impact of such systems in small electric grids, using an hourly electricity backup load model. To test and validate the model, we used the island of Corvo (Azores), a small isolated community where it is being implemented a project of electrification of domestic hot water systems (DHW). We consider different load scenarios to manage the backup of DHW systems and analyze its consequences on the peak load and overall energy demand. For Corvo, for the best case where the backup is limited and distributed along off-peak hours, we observed an increase of 24% in the peak load and 7.5% in the annual energy demand. Critical values of peak load are found in winter, when daily solar irradiation is lower than 2000 Wh/m²/day. We conclude that the solar thermal systems are responsible for most of the peak load increase, but since they have the flexibility to adjust the electric backup hours due to the thermal storage capacity, the use of these systems can minimize the impact on the grid. Heat pumps on the other hand, albeit being more efficient in terms electric backup, are less flexible to contribute to the grid management as they operate continuously.