Inverse determination of thermal conductivity using semi-discretization method

Abstract

a b s t r a c tIn this work a semi-discretization method is presented for the inverse determination of spatially-and temperature-dependent thermal conductivity in a one-dimensional heat conduction domain without internal temperature measurements. The temperature distribution is approximated as a polynomial function of position using boundary data. The derivatives of temperature in the differential heat conduction equation are taken derivative of the approximated temperature function, and the derivative of thermal conductivity is obtained by finite difference technique. The heat conduction equation is then converted into a system of discretized linear equations. The unknown thermal conductivity is estimated by directly solving the linear equations. The numerical procedures do not require prior information of functional form of thermal conductivity. The close agreement between estimated results and exact solutions of the illustrated examples shows the applicability of the proposed method in estimating spatially-and temperature-dependent thermal conductivity in inverse heat conduction problem.

Review of the experimental research on the thermal‐hydraulic characteristics in the pebble bed nuclear reactor core and fusion breeder blankets

“…Steady‐state methods and other transient methods are unable to measure multiple parameters simultaneously like ETC and thermal diffusivity while the inverse method characterizes in obtaining such parameters at the same time 111 . In addition, ETC can be obtained in multi‐dimension by the inverse method and the heat loss in some directions is unnecessary to control, compared to other methods, making it proper for large‐scale pebble bed ETC measurement facilities like the one shown in Figure 19 111,112 . However, large amount of experimental data is required for the inverse method, which leads such experiments usually to be in hundreds of hours 96,113 …”

Flux determination using finite elements: global vs. local calculation

“…This example concerns the diffusion coefficient as a function of temperature k=k(T) and is adapted from [11]. There is a linear dependence on the temperature, k(T)=a(T+1), which results in a nonlinear space dependence that, in general, cannot be calculated in advance because it depends on the temperature field.…”