A 2D inverse problem of predicting boiling heat transfer in a long fin

A method for the determination of local values of the heat transfer coefficient on non-isothermal surfaces was analyzed on the example of a long smooth-surfaced fin made of aluminium. On the basis of the experimental data, two cases were taken into consideration: one-dimensional model for Bi < 0.1 and two-dimensional model for thicker elements. In the case when the drop in temperature over the thickness could be omitted, the rejected local values of heat fluxes were calculated from the integral of the equation describing temperature distribution on the fin. The corresponding boiling curve was plotted on the basis of temperature gradient distribution as a function of superheat. For thicker specimens, where Bi > 0.1, the problem was modelled using a 2-D heat conduction equation, for which the boundary conditions were posed on the surface observed with a thermovision camera. The ill-conditioned inverse problem was solved using a method of heat polynomials, which required validation.