Inverse heat conduction problems by using particular solutions

Based on the method of fundamental solutions, we develop in this paper a new computational method to solve two-dimensional transient heat conduction inverse problems. The main idea is to use particular solutions as radial basis functions (PSRBF) for approximation of the solutions to the inverse heat conduction problems. The heat conduction equations are first analyzed in the Laplace transformed domain and the Durbin inversion method is then used to determine the solutions in the time domain. Least-square and singular value decomposition (SVD) techniques are adopted to solve the ill-conditioned linear system of algebraic equations obtained from the proposed PSRBF method. To demonstrate the effectiveness and simplicity of this approach, several numerical examples are given with satisfactory accuracy and stability.Peer reviewe

Properties of a method of fundamental solutions for the parabolic heat equation

We show that a set of fundamental solutions to the parabolic heat equation, with each element in the set corresponding to a point source located on a given surface with the number of source points being dense on this surface, constitute a linearly independent and dense set with respect to the standard inner product of square integrable functions, both on lateral- and time-boundaries. This result leads naturally to a method of numerically approximating solutions to the parabolic heat equation denoted a method of fundamental solutions (MFS). A discussion around convergence of such an approximation is included

A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed

Simultaneous estimation of heat flux and heat transfer coefficient in irregular geometries made of functionally graded materials

A numerical inverse analysis based on explicit sensitivity coefficients is developed for the simultaneous estimation of heat flux and heat transfer coefficient imposed on different parts of boundary of a general irregular heat conducting body made of functionally graded materials with spatially varying thermal conductivity. It is assumed that the thermal conductivity varies exponentially with position in the body. The body considered in this study is an eccentric hollow cylinder. The heat flux is applied on the cylinder inner surface and the heat is dissipated to the surroundings through the outer surface. The numerical method used in this study consists of three steps: 1) to apply a boundary-fitted grid generation (elliptic) method to generate grid over eccentric hollow cylinder (an irregular shape) and then solve for the steady-state heat conduction equation with variable thermal conductivity to compute the temperature values in the cylinder, 2) to propose a new explicit sensitivity analysis scheme used in inverse analysis, and 3) to apply a gradient-based optimization method (in this study, conjugate gradient method) to minimize the mismatch between the computed temperature on the outer surface of the cylinder and simulated measured temperature distribution. The inverse analysis presented here is not involved with an adjoint equation and all the sensitivity coefficients can be computed in only one direct solution, without the need for the solution of the adjoint equation. The accuracy, efficiency, and robustness of the developed inverse analysis are demonstrated through presenting a test case with different initial guesses

Modification of Conventional Sugar Juice Evaporation Process for Increasing Energy Efficiency and Decreasing Sucrose Inversion Loss

The evaporation process, boiler, and turbine are the main components of the cogeneration system of the sugar factory. In the conventional process, the evaporator requires extracted steam from the turbine, and bled vapor from the evaporator is supplied to the juice heater and the pan stage. The evaporation process may be modified by using extracted steam for the heating duty in the pan stage. This paper is aimed at the investigation of the effects of this process modification. Mathematical models of the conventional and modified processes were developed for this purpose. It was found that, under the conditions that the total evaporator area is 13,000 m2, and the inlet juice flow rate is 125 kg/s, the optimum modified evaporation process requires extracted steam at a pressure of 157.0 kPa. Under the condition that the fuel consumption rate is 21 kg/s, the cogeneration system that uses the optimum modified evaporation process yields 2.3% more power output than the cogeneration system that uses a non-optimum conventional cogeneration process. Furthermore, sugar inversion loss of the optimum modified process is found to be 63% lower than that of the non-optimum conventional process

Assessing economic feasibility of retrofitting steam dryer and steam-air preheater to existing biomass power plant

Conventionally, the thermal design a biomass power plant is aimed at maximizing the energy efficiency by using extracted steam to increase feed water temperature in feed water heaters and installing heating surface areas of heat exchangers in boiler to recover flue gas energy. The temperature of flue gas at the boiler outlet must not be so low that a risk of acid corrosion is unacceptable. The energy efficiency can also be improved by reducing fuel moisture content in steam dryer and increasing air temperature in steam-air preheater. However, both devices require extracted steam, which is already used for raising feed water temperature in an existing power plant. In this paper, it is hypothesized that retrofitting steam dryer and steam-air preheater to an existing power plant can improve the energy efficiency. Performances of the existing power plant and the retrofitted power plant integrated with steam dryer and steam-air preheater are compared. Simulation results indicate that, despite lower final feed water temperature in the retrofitted power plant, the retrofitted power plant is more energy efficient than the existing power plant. Economic assessment is carried under the condition that both power plants generate the same power output, which means that the retrofitted power plant consumes less fuel than the existing power plant. The payback period for the retrofitting investment is approximately 7 years

Increased Energy Efficiency of a Backward-Feed Multiple-Effect Evaporator Compared with a Forward-Feed Multiple-Effect Evaporator in the Cogeneration System of a Sugar Factory

The cogeneration system of a sugar factory consists of boiler, steam turbine, and sugar juice evaporation process. The multiple-effect evaporator used for the conventional sugar juice evaporation process is the forward-feed multiple-effect evaporator, in which steam and sugar juice flow in the same direction. The main objective of this paper is to investigate the energy efficiency of the backward-feed multiple-effect evaporator, in which steam and sugar juice flow in opposite directions, compared with that of the forward-feed multiple-effect evaporator. Mathematical models are developed for both multiple-effect evaporators, and used to compare the performances of two cogeneration systems that use the forward-feed and backward-feed multiple-effect evaporators. The forward-feed multiple-effect evaporator requires extracted steam from a turbine at one pressure, whereas the backward-feed multiple-effect evaporator requires steam extraction at two pressures. Both evaporators have the same total heating surface area, process the same amount of sugar juice, and operate at the optimum conditions. It is shown that the cogeneration system that uses the backward-feed multiple-effect is more energy efficient than the cogeneration system that uses the forward-feed multiple-effect because it yields more power output for the same fuel consumption