Local heat flux estimation inside tubes through conjugate gradient method with adjoint operator: application to the pulsating heat pipes case

PurposeThe purpose of this paper is to apply the conjugate gradient (CG) method, together with the adjoint operator (AO) to the pulsating heat pipe problem, including some quite interesting experimental results. The CG method, together with the AO, was able to estimate the unknown functions more efficiently than the other techniques presented in this paper. The estimation of local heat transfer coefficients, rather than the global ones, in pulsating heat pipes is a relatively new subject and presenting a robust, efficient and self-regularized inverse tool to estimate it, supported also by some experimental results, is the main purpose of this paper. To also increase the visibility and the general use of the paper to the heat transfer community, the authors include, as supplemental material, all numerical and experimental data used in this paper. Design/methodology/approachThe approach was established on the solution of the inverse heat conduction problem in the wall by using as starting data the temperature measurements on the outer surface. The procedure is based on the CG method with AO. The here proposed approach was first verified adopting synthetic data and then it was validated with real cases regarding pulsating heat pipes. FindingsAn original fast methodology to estimate local convective heat flux is proposed. The procedure has been validated both numerically and experimentally. The procedure has been compared to other classical methods presenting some peculiar benefits. Practical implicationsThe approach is suitable for pulsating heat pipes performance evaluation because these devices present a local heat flux distribution characterized by an important variation both in time and in space as a result of the complex flow patterns that are generated in this type of devices. Originality/valueThe procedure here proposed shows these benefits: it affords a general model of the heat conduction problem that is effortlessly customized for the particular case, it can be applied also to large datasets and it presents reduced computational expense.