Enhanced heating surface application in a minichannel flow and the use of the FEM and Trefftz functions for the solution of inverse heat transfer problem Magdalena Piasecka a,⇑ , Beata Maciejewska b a Kielce University of Technology, Faculty of Mechatronics and Machine Building, al. 1000-lecia P.P.7, 25-314 Kielce, Poland b Kielce University of Technology, Faculty of Management and Computer Modelling, al. 1000-lecia P.P.7, 25-314 Kielce, Poland article info Article history: Received 16 December 2011 Received in revised form 26 April 2012 Accepted 27 April 2012 Available online 30 May 2012 Keywords: Flow boiling Rectangular minichannel Enhanced heating wall Liquid crystal thermography Inverse boundary problem Trefftz functions abstract The paper presents results of flow boiling in a rectangular minichannel of 1.0 mm depth and 40 mm width, vertically oriented. The heating element for the working fluid (FC-72) that flows along the mini- channel is a single-sided enhanced alloy foil made from Haynes-230. Micro-recesses were formed on the selected area or entire heating foil by laser technology. The observations of the flow structure were car- ried out through a piece of glass. Simultaneously, owing to the liquid crystal layer placed on the opposite side of the enhanced foil surface, it was possible to measure temperature distribution on the heating wall through another piece of glass. The first objective is to calculate the void fraction for some cross-sections of selected images for increasing heat fluxes supplied to the heating surface. The flow structure photos were processed using Corel graphics software and binarized. The analysis of phase volumes was devel- oped in Techystem Globe software. The second objective of the calculations is to evaluate a heat transfer model and numerical approach to solving the inverse boundary problem, and to calculate the heat trans- fer coefficient at boiling incipience. This problem has been solved by means of the finite element method in combination with Trefftz functions (FEMT). Trefftz functions are used to construct basic functions in Hermite space of the finite element. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction Boiling is a very efficient heat transfer process used in power engineering, as well in chemical and nuclear branches. Mini heat exchangers are used to provide higher cooling capability for new technologies. It means a reduction of their sizes and costs, for an identical power. Owing to the change of the state which accompa- nies flow boiling in minichannels, it is feasible to meet contradic- tory needs simultaneously, i.e. obtain a heat flux as large as possible at small temperature difference between the heating sur- face and the saturated liquid and, at the same time, retain small dimensions of heat transfer systems. The use of enhanced surfaces allows additional intensification of the process. Following the classification by Kandlikar and Grande it has been assumed that channels with hydraulic diameters between 200 lm and 3 mm are referred to as minichannels [1]. Much has been writ- ten on heat transfer experimental studies and analyses of flow boil- ing heat transfer in minichannels of various dimensions. Review of relevant literature and the selected publications covering heat transfer and flow patterns in rectangular minichannels is presented in [2–4]. Literature review leads to the statement that although much has been written recently on flow boiling heat transfer in minichannels, the literature does not offer any generalized, univer- sal criterial equations which would help predict heat transfer for minichannel. They are usually verified experimentally for channel systems heated by smooth heaters. Moreover, the research focused on enhanced structure systems seems interesting due to their the- oretical potential of further heat transfer enhancement. The heat transfer considerations presented in this article focus on heat transfer coefficient identification, which belongs to the group of inverse heat conduction problems [5–7]. The inverse problem and the auxiliary direct problem were solved by means of the finite element method in combination with Trefftz method. The concept of the Trefftz method was presented in [8] and consists in represent- ing the approximate solution to the problem as a linear combination of functions which satisfy the governing equation strictly, while the set boundary conditions are satisfied approximately. Additional information on this method are included in [9–12]. Combinations of Trefftz method and FEM was showed in [13–16]. 2. Main goal The study focuses on two main objectives. The first objective of the experiment is to calculate the void fraction for some cross-sec- tions of selected images for increasing heat fluxes supplied to the 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.04.024 ⇑ Corresponding author. E-mail addresses: tmpmj@tu.kielce.pl (M. Piasecka), beatam@tu.kielce.pl (B. Maciejewska). Experimental Thermal and Fluid Science 44 (2013) 23–33 Contents lists available at SciVerse ScienceDirect Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs