Abstract
Explicit expressions are obtained for sensitivity coefficients to separately estimate temperature-dependent thermophysical properties, such as specific heat and thermal conductivity, in two-dimensional inverse transient heat conduction problems for bodies with irregular shape from temperature measurement readings of a single sensor inside the body. The proposed sensitivity analysis scheme allows for the computation of all sensitivity coefficients in only one direct problem solution at each iteration with no need to solve the sensitivity and adjoint problems. In this method, a boundary-fitted grid generation (elliptic) method is used to mesh the irregular shape of the heat conducting body. Explicit expressions are obtained to calculate the sensitivity coefficients efficiently and the conjugate gradient method as an iterative gradient-based optimization method is used to minimize the objective function and reach the solution. A test case with different initial guesses and sensor locations is presented to investigate the proposed inverse analysis.
Highlights
The accuracy of the numerical simulation of heat transfer problems relies significantly on the accuracy of data, including, among others, the thermophysical properties such as the thermal conductivity and the specific heat of heat-conducting body
Novel explicit expressions were derived for the sensitivity coefficients to estimate the temperature-dependent thermal conductivity and the temperature-dependent specific heat in general two-dimensional heat-conducting bodies using an inverse transient heat conduction analysis
Due to inability of the traditional finite-difference method to effectively handle the solution of heat transfer problems involving the irregular shapes, the irregular heat-conducting body was transformed into a regular computational domain to perform all computations related to the direct and inverse transient heat conduction solution using the finite-difference method, a method chosen for its widespread use in numerical heat transfer and ease of implementation
Summary
The accuracy of the numerical simulation of heat transfer problems relies significantly on the accuracy of data, including, among others, the thermophysical properties such as the thermal conductivity and the specific heat of heat-conducting body. The inverse heat transfer problems are mathematically challenging problems due to their ill-posed nature They are inherently unstable and very sensitive to noise and special methods are required to treat them. As this study is concerned with a parameter estimation problem, the gradient of the objective function with respect to the unknown parameters (as needed in gradient-based minimization methods) can be computed by using the finite-difference method (by additional direct problem solutions and forming the sensitivity matrix) or adjoint method. Both methods involve an increase in computational cost. In this study using the obtained explicit sensitivity coefficients, the gradient of the objective function can be computed in only one direct problem solution at each iteration, thereby decreasing the computational cost significantly
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