On the application of the hyperbolic heat equation in transient heat flux estimation during flow film boiling

摘要

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 composite two-dimensional cylindrical body with multiple sensors.The geometry is split into two regions: (i) direct region,where the surface heat flux is to be estimated.In the direct region,solutions are obtained using the parabolic heat conduction equation since initial and boundary conditions (measured temperatures) are known.A hyperbolic heat conduction equation is used to solve the problem in the inverse regtion.The hyperbolic heat equation is mathematically well-posed and closely approximates the parabolic heat equation.Two test problems were designed to test the stability,accuracy and efficiency of the solution procedure.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 indicate that the scheme is 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.