A greedy algorithm for the construction of a reduced model with reduction in both parameter and state is developed for an efficient solution of statistical inverse problems governed by partial differential equations with distributed parameters. Large-scale models are too costly to evaluate repeatedly, as is required in the statistical setting. Furthermore, these models often have high-dimensional parametric input spaces, which compounds the difficulty of effectively exploring the uncertainty space. We simultaneously address both challenges by constructing a projection-based reduced model that accepts low-dimensional parameter inputs and whose model evaluations are inexpensive. The associated parameter and state bases are obtained through a greedy procedure that targets the governing equations, model outputs, and prior information. The methodology and results are presented for groundwater inverse problems in one and two dimensions.

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Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems

Heat transfer—A review of 2003 literature

Applications of ANNs in flow and heat transfer problems in nuclear engineering: A review work

Heat transfer—A review of 2005 literature

Movement of maximum heat flux and wetting front during quenching of hot cylindrical block

An analytical method has been developed for the inverse problem in one- and two-dimensional heat conduction, when the temperatures are known at an appropriate number of the measuring points. On the basis of these known temperatures, a closed form solution is determined for the transient temperatures by using Laplace transform technique. This method first approximates the temperature data with a half polynomial power series of time. The resultant expression for an objective temperature and heat flux are explicitly obtained in the form of power series of time. Numerical results for some representative problems show that the surface temperature and heat flux can be predicted for not only one- but also two-dimensional heat conductions well by the present method.

ANALYTICAL METHOD IN INVERSE HEAT TRANSFER PROBLEM USING LAPLACE TRANSFORM TECHNIQUE Application to one- and two-dimensional cases

An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform

Ted-aj03-294 ultra high critical heat flux during forced flow boiling heat transfer with an impinging jet

An analytical method has been developed for the inverse problem of two-dimensional heat conduction using the Laplace transform technique. The inverse problem is solved for only two unknown surface conditions and the other surfaces are insulated in a finite rectangular body. In actual temperature measurement, the number of points in a solid is usually limited so that the number of temperature measurements required to approximate the temperature change in the solid becomes too small to obtain an approximate function using a half polynomial power series of time and the Fourier series of the eigenfunction. In order to compensate for this lack of measurement points, the third-order Spline method is recommended for interpolating unknown temperatures at locations between measurement points. Eight points are recommended as the minimum number of temperature measurement points. The calculated results for a number of representative cases indicate that the surface temperature and the surface heat flux can be predicted well, as revealed by comparison with the given surface condition. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 618–629, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10116

Analytical method of two‐dimensional inverse heat conduction problem using Laplace transformation: Effect of number of measurement points

Any solution for an inverse heat conduction problem makes the estimation of surface temperature and surface heat flux worsen in the case where these values behave like a triangular shape change with time. In order to compensate for this defect, Monde and colleagues, who succeeded in obtaining analytical inverse solutions using the Laplace transform technique, introduce a new idea where these changes over the entire measurement time can be split into several parts depending on the behavior. Therefore, an approximate equation to trace the measured temperature change can be derived, resulting in good estimation of surface temperature and surface heat flux even in the case of the triangular shape change and sharp change. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 630–638, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10117

Wei Liu

Papers

ANALYTICAL METHOD IN INVERSE HEAT TRANSFER PROBLEM USING LAPLACE TRANSFORM TECHNIQUE Application to one- and two-dimensional cases

An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform

Ted-aj03-294 ultra high critical heat flux during forced flow boiling heat transfer with an impinging jet

Analytical method of two‐dimensional inverse heat conduction problem using Laplace transformation: Effect of number of measurement points

Improvement of inverse heat conduction solution using Laplace transformation: Method of partial division of time