Inverse forced convection problem of simultaneous estimation of two boundary heat fluxes in irregularly shaped channels

This article deals with the use of the conjugate gradient method of functio n estimation for the simultaneous identification of two unknown boundary he at fluxes in channels with laminar flows. Tire irregularly shaped channel i n the physical domain is transformed into a parallel plate channel in the c omputational domain by using an elliptic scheme of numerical grid generatio n, The direct problem, as well as the auxiliary problems and the gradient e quations, required for the solution of the inverse problem with the conjuga te gradient method are formulated in terms of generalized boundary-fitted c oordinates. Therefore, the solution approach presented here can be readily applied to forced convection boundary inverse problems in channels of any s hape. Direct and auxiliary problems are solved with finite volumes. The num erical solution for the direct problem is validated by comparing the result s obtained here with benchmark solutions for smoothly expanding channels. S imulated temperature measurements containing random errors are used in the inverse analysis for strict cases involving functional forms with discontin uities and sharp corners for the unknown functions. The estimation of three different types of inverse problems are addressed in tire paper: (i) time- dependent hear fluxes: (ii) spatially dependent heat fluxes; and (iii) time and spatially dependent heat fluxes.