An Inverse Thermal Problem for Simultaneous Estimation of Temperature Dependent Thermal Conductivity and Specific Heat
G. Venugopal1, S. P. Venkateshan2,a and C. Balaji2,b
1Asst. Professor in Mechanical Engineering, College of Engineering, Thiruvananthapuram 695 016, India.
gvenucet@gmail.com
2Professor, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India.
aspv@iitm.ac.in
bbalaji@iitm.ac.in
ABSTRACT
An inverse thermal problem is studied for simultaneously estimating the temperature dependent thermal conductivity and specific heat of a solid material. Temperature dependency of thermal conductivity and specific heat is assumed to be linear for the range of temperatures considered in this study. In the present study, a one dimensional transient heat conduction problem is solved using known thermal property data to simulate experimentally measured/known temporal and spatial temperature distribution within the solid. The measured/known temporal and spatial temperature data is compared with a numerically computed temporal and spatial temperature data obtained by solving the transient conduction problem using guessed values of the parameters in the functional form of the temperature dependency of thermal conductivity and specific heat. The sum of the squares of the difference between the measured data and numerically computed data is minimized by using a hybrid numerical optimization technique, i.e. a combination of Genetic Algorithm and the Levenberg Marquardt algorithm to obtain the parameters in the functional form of the temperature dependency of the thermophysical properties. A good agreement between the predicted values of the parameters with those obtained from a regression analysis of the thermal property data indicates the efficacy of the present approach.
Full Text (PDF)
|
