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.     

A modified genetic algorithm for solving the inverse heat transfer problem of estimating plan heat source

This work considers a new approach for solving the inverse heat conduction problem of estimating unknown plan heat source. It is shown that the physical heat transfer problem can be formulated as an optimization problem with differential equation constraints. A modified genetic algorithm is developed for solving the resulting optimization problem. The proposed algorithm provides a global optimum instead of a local optimum of the inverse heat transfer problem with highly-improved convergence performance. Some numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.     

Two-dimensional inverse problem in estimating heat flux of pin fins

The two-dimensional inverse problem of estimating the unknown heat flux of a pin fin base has been solved using the conjugate gradient method. The advantage of the conjugate gradient method is that no information on the functional form of the unknown quantity is required beforehand. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements of temperature in an interior location of a pin fin. Numerical results show that good estimations on the heat flux can be obtained for all the test cases considered here. Furthermore, such a technique can be applied to determine the heat flux acting on an internal wall surface, where direct measurements are difficult to make.     

A two-dimensional inverse heat conduction problem in estimating the fluid temperature in a pipeline

An inverse heat conduction problem (IHCP) was investigated in the two-dimensional section of a pipe elbow with thermal stratification to estimate the unknown transient fluid temperatures near the inner wall of the pipeline. An inverse algorithm based on the conjugate gradient method (CGM) was proposed to solve the IHCP using temperature measurements on the outer wall. In order to examine the accuracy of estimations, some comparisons have been made in this case. The temperatures obtained from the solution of the direct heat conduction problem (DHCP) using the finite element method (FEM) were pseudo-experimental input data on the outer wall for the IHCP. Comparisons of the estimated fluid temperatures with experimental fluid temperatures near the inner wall showed that the IHCP could accurately capture the actual temperature in form of the frequency of the temperature fluctuations. The analysis also showed that the IHCP needed at least 13 measurement points for the average absolute error to be dramatically reduced for the present IHCP with 37 nodes on each half of the pipe wall.     

An inverse heat transfer problem for restoring the temperature field in a polymer melt flow through a narrow channel

An important problem in polymer processing is to provide suitable thermal conditions for polymer melt flows through narrow channels during extrusion or injection. Due to various thermal effects (e.g., viscous dissipation, chemical reactions) the temperature profile of the melt could be quite sharp. In order to numerically simulate polymer flows and heat transfer through a narrow channel, the inlet boundary conditions, which are generally unknown, have to be specified. For such a creeping flow, the area where the velocity field develops is very short. In contrast, the inlet temperature profile develops quite slowly and affects the temperature field far downstream. An approach is suggested for restoring the inlet temperature profile by solving an inverse heat transfer problem using Cauchy data at the channel wall. The polymer flow is assumed to be a steady, laminar and incompressible flow of a non-Newtonian pseudo-plastic fluid, which is governed by the Navier–Stokes equations and a constitutive “power law” model for viscosity. This non-linear inverse problem is solved by a sequential approximation method combined with Tikhonov's regularization method. Notably, this approach has been found to be efficient for field observation problems, when the magnitude of non-linearity is not too large. The results of numerical simulation are presented and questions regarding accuracy are discussed.     

The theory of heat and moisture transfer in porous media revisited

In this paper a review is presented of the present status of the theory of combined heat and moisture transfer in porous media, developed by J. R. Philip and the author in the mid-1950s. First, attention is drawn to the limitations of the theory and the assumptions underlying it. Next, attempts to test the theory by laboratory and field experiments are briefly discussed, leading to the conclusion that the usefulness of the theory in describing and analysing the experiments was proven, but that doubts remain about its predictive value. These doubts are a consequence of: (a) the limitations of the theory; (b) uncertainty about the quality of the experimental procedures and data. Remarks are made on hysteresis and its possible influence. It is concluded that experiments aimed at a study of the behaviour of nonisothermal systems subjected to hysteresis are needed. Finally, the problem of the definition and use of an apparent thermal conductivity is analysed. In the original papers two alternatives were presented. An expression for the phase average of the vapour flux density is derived. A numerical example is presented and suggestions are made concerning the proper choice between the alternatives.     

An inverse problem in estimating the base heat flux of an annular fin based on the hyperbolic model of heat conduction

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent base heat flux of an annular fin from the knowledge of temperature measurements taken within the fin. The inverse solutions will be justified based on the numerical experiments in which two specific cases to determine the unknown base heat flux are examined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent base heat flux can be obtained for the test cases considered in this study.     

On the problem of heat transfer in phase-change materials for small Stefan numbers

The problem of solidification of an infinite liquid slab by linear convection cooling from the adjacent air is considered. It is assumed that at the initial moment the slab has a critical temperature and that on one side the air temperature has diurnal fluctuations of relatively small amplitude. The solution is found in the form of power series of small parameters. The first three terms of each series are obtained. This permits construction of a simple formula for the total solidification time. Evaluation of the accuracy of the solution based on the integral heat balance equation is suggested. Some particular cases of the problem are considered on the assumption that one side of the slab is insulated. One of these cases is the simplest Stefan problem which has an exact solution. Comparison with this solution is made.     

Macroscopic continuum analysis of simultaneous heat and mass transfer in unsaturated porous materials containing a heat source

The paper briefly outlines a development of the transport equations which describes simultaneous heat and mass transfer in unsaturated porous materials when a heat source is embedded in the medium. A macroscopic continuum mechanics approach is adopted to derive the coupled continuity, momentum and energy equations. Hydrodynamic laws such as Darcy's law and the Darcy-Buckingham theorem are utilized to simplify the continuity and momentum equations of fluid flow. Migration of liquid due to surface tension effects is modeled in the analysis. The effects of phase change on the heat transfer are also included in the energy equation. The resulting equations reported in this paper are found to agree with equations obtained by other researchers who used volume averaging techniques to study similar phenomena in unsaturated porous materials.     

A three-dimensional inverse problem in imaging the local heat transfer coefficients for plate finned-tube heat exchangers

A three-dimensional inverse heat conduction problem in imaging the local heat transfer coefficients for plate finned-tube heat exchangers utilizing the steepest descent method and a general purpose commercial code CFX4.4 is applied successfully in the present study based on the simulated measured temperature distributions on fin surface by infrared thermography.It is assumed that no prior information is available on the functional form of the unknown local heat transfer coefficients in the present study. Thus, it can be classified as function estimation for the inverse calculations.Two different heat transfer coefficients for in-line tube arrangements with different measurement errors are to be estimated. Results show that the present algorithm can obtain the reliable estimated heat transfer coefficients.     

Periodic homogenization for heat,air, and moisture transfer of porous building materials

ABSTRACT

In this work, a macroscopic model of hygrothermal transfers in porous building materials was developed, using periodic homogenization, where the air infiltration was added to the classical mass and energy balance equations written at the microscopic scale. The corresponding infiltration, hygric, and thermal input parameters were carefully identified. Numerical calculations of thermal and diffusion tensors were performed on a representative concrete elementary cell. Further, the diffusion tensor was compared to the equivalent experimental results available in the literature, and its sensitivity to the water content variations and porosity has been evaluated on the concerned elementary cell.     

An inverse problem in estimating the reaction functions and solute concentration simultaneously in a reversible process

An inverse algorithm basing on the Iterative Regularization Method (IRM) is applied in this study in determining the unknown time-dependent reaction functions and solute concentration in the solution, i.e. three unknown time-dependent functions, simultaneously in a reversible process by using measurements of concentration components. It is assumed that no prior information is available on the functional form of the unknown functions in the present study, it can thus be classified as function estimation for the inverse calculations. The accuracy of this inverse problem is examined by using the simulated exact and inexact concentration measurements in the numerical experiments. Results show that the estimation of the time-dependent reaction functions and solute concentration in the solution can be obtained in a very short CPU time on a HP d2000 2.66 GHz personal computer. Moreover, the sensors should be placed as close to the boundary as possible to obtain better estimations.     

Network numerical simulation of coupled heat and moisture transfer in capillary porous media

In this paper we present the numerical solution of the problem of coupled heat and moisture transfer in porous materials. A network model introducing an analogy based in the equivalence mass transfer-electrical current is proposed to obtain the numerical solutions. An algorithm based on a finite-difference scheme for the spatial variable (as in the lines method because the time remains as a continuous variable) is formally equivalent to those derived from the mathematical model. An implementation of the Network Simulation Method is used to derive a solution to the heat and mass conservation coupled equations in porous media for the cases of distributed and lumped models. The obtained values by the theoretical model are compared with other author data to demonstrate the efficiency of the method used, moreover all the cases the convergence is always quickly reached.     

An inverse biotechnology problem in estimating the optical diffusion and absorption coefficients of tissue

An inverse algorithm for biotechnology problem utilizing the conjugate gradient method is applied in the present study in determining the unknown spatial-dependent optical diffusion and absorption coefficients of the biological tissue based on irradiance and temperature measurements. The accuracy of this inverse problem is examined by using the simulated exact and inexact irradiance and temperature measurements in the numerical experiments. Results show that the estimation on the spatial-dependent diffusion and absorption coefficients can be obtained with any arbitrary initial guesses on a Pentium IV 1.4 GHz personal computer for the test cases considered in the present study.     

Transient model for coupled heat,air and moisture transfer through multilayered porous media

Most building materials are porous, composed of solid matrix and pores. The time varying indoor and outdoor climatic conditions result heat, air and moisture (HAM) transfer across building enclosures. In this paper, a transient model that solves the coupled heat, air and moisture transfer through multilayered porous media is developed and benchmarked using internationally published analytical, numerical and experimental test cases. The good agreements obtained with the respective test cases suggest that the model can be used to assess the hygrothermal performance of building envelope components as well as to simulate the dynamic moisture absorption and release of moisture buffering materials.     

A three-dimensional inverse problem in estimating the applied heat flux of a titanium drilling – Theoretical and experimental studies

The applied heat flux on the drilling surface of drilling tool is estimated in the present three-dimensional inverse heat conduction problem. The inverse algorithm utilizing the Steepest Descent Method (SDM) and a general purpose commercial code CFX4.4 is applied successfully in this study based on the simulated and measured temperature distributions with time at four sensors embedded on the drilling surfaces. The numerical experiments are considered at the first stage to illustrate the validity of inverse determination of the unknown heat flux using exact and error measurements. Experimental data are then used to estimate the actual heat flux along the drilling edge at two different drill peripheral cutting speeds. Results of both the numerical and experimental examinations show that the reliable estimated heat flux can be obtained by using the present inverse algorithm.     

Optimal operation of alloy material in solidification processes with inverse heat transfer

A transient nonlinear inverse heat transfer problem arising from alloy solidification processes is considered. In practice, the solidus and liquidus interface motions and thus the mushy zone thicknesses are pre-given to control the material quality. To achieve the desired front motions, the required time-dependent boundary conditions have to be predicted on both mold sides simultaneously. In this study, the enthalpy method is used for the derivation of governing equations. Hence, the inverse problem will be solved only in a single spatial and temporal domain. The conjugate gradient method with adjoint equation is applied for the resulting minimization problem. The method is applied as comparison for pure material with other previous studies. Then, alloy material with different front velocities is set up to investigate the solidification process. The obtained results show a close agreement between the desired and computed front motions and mushy zone thickness.     

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.     

Three dimensional numerical modeling of simultaneous heat and moisture transfer in a moist object subjected to convective drying

The drying behavior of a moist object subjected to convective drying is analyzed numerically by solving heat and moisture transfer equations. A 3-D numerical model is developed for the prediction of transient temperature and moisture distribution in a rectangular shaped moist object during the convective drying process. The heat transfer coefficients at the surfaces of the moist object are calculated with an in-house computational fluid dynamics (CFD) code. The mass transfer coefficients are then obtained from the analogy between the thermal and concentration boundary layer. Both these transfer coefficients are used for the convective boundary conditions while solving the simultaneous heat and mass transfer governing equations for the moist object. The finite volume method (FVM) with fully implicit scheme is used for discretization of the transient heat and moisture transfer governing equations. The coupling between the CFD and simultaneous heat and moisture transfer model is assumed to be one way. The effect of velocity and temperature of the drying air on the moist object are analyzed. The optimized drying time is predicted for different air inlet velocity, temperature and moisture content. The drying rate can be increased by increasing the air flow velocity. Approximately, 40% of drying time is saved while increasing the air temperature from 313 to 353 K. The importance of the inclusion of variable surface transfer coefficients with the heat and mass transfer model is justified.