ON THE APPLICATION OF THE HYPERBOLIC HEAT EQUATION IN TRANSIENT HEAT FLUX ESTIMATION DURING FLOW FILM BOILING

Abstract

This paper illustrates a numerical solution procedure for the inverse heat conduction problem (IHCP) using the hyperbolic heat equation and its application to the estimation of transient heat flux during flow film boiling. The IHCP geometry of interest consisted of a composite two-dimensional cylindrical body with multiple sensors. The geometry was split into two regions: a direct region, where all temperature measurements were made, and an inverse region, where the surface heat flux was estimated. In the direct region, solutions were obtained using the parabolic heat conduction equation, since initial and boundary conditions (measured temperatures) were known. A hyperbolic heat conduction equation was used to solve the problem in the inverse region. The hyperbolic heat equation is mathematically well posed and closely approximates the parabolic heat equation. The stability, accuracy, and efficiency of the solution procedure were checked using test problems. The effect of the hyperbolic term on the accuracy of the results was also investigated. The solution method was then applied to experimentally obtained flow film boiling data. The results indicated that the scheme was stable and capable of tracking the fast transients that occur during flow film boiling. The IHCP numerical solution method presented here works well for nonlinear (homogeneous or composite) two-dimensional problems with multiple sensors.