Combined Parameter and Function Estimation With Application to Thermal Conductivity and Surface Heat Flux

This is a numerical and experimental study on the combined parameter and function estimation. The determination of thermal conductivity and the surface heat flux is an illustration of combined estimation of one parameter and one function by means of the conjugate gradient method with vectorial descent parameter. The experimental example developed herein uses one set of good data obtained by Beck and Arnold (1977, Parameter Estimation in Engineering and Science, Wiley, New York). For this case, two measured temperatures in the solid are used to illustrate combined estimation. The unknown boundary condition and thermal conductivity of this solid were satisfactorily reconstructed and a good enough comparison is demonstrated between the known and estimated unknowns. The temperature data of Beck and Arnold are found to be excellent. Also, it is shown that the developed approach is general, stable, powerful, and able to process a wide variety of heat transfer problems where a simultaneous estimation is unavoidable.