Sylwia Hożejowska

Application of adjustment calculus to the Trefftz method for calculating temperature field of the boiling liquid flowing in a minichannel

Purpose – The purpose of this paper is to focus on the application of the Trefftz method to the calculation of the two-dimensional (2D) temperature field in the boiling refrigerant flow through an asymmetrically heated vertical minichannel with a rectangular cross-section. The considerations were limited to determining the temperature of the continuous phase – liquid for bubbly and bubbly-slug flow. The numerical solution found with the Trefftz methods was compared with the simplified solution. For nucleate boiling, heat transfer coefficient at the heating foil – liquid contact was determined. Design/methodology/approach – The Trefftz method was used to determine 2D temperature distributions for the glass pane, the heating foil and the boiling liquid. The temperature fields were approximated by the sum of the particular solution and the linear combination of suitable Trefftz functions. Coefficients of linear combination were computed using experimental data, including heating foil temperature measurements...

Experimental Error Analysis and Heat Polynomial Method Improvement for Boiling Heat Transfer Numerical Calculations in Minichannels

The paper continues the discussion of experimental and numerical investigations of forced convection boiling heat transfer in vertical minichannels covered by two former editions of this conference and our previous papers. Liquid crystal thermography technique was used for measuring the two-dimensional heating surface temperature distribution and boiling front detection. Influence of selected parameters on boiling heat transfer and nucleation hysteresis was observed and discussed. The two-dimensional heat transfer model and the analytic-numerical heat polynomial method were applied to solve the inverse boundary value problem and determine the temperature distributions in the heating foil and protecting glass and the boiling heat transfer coefficient as well. This paper shows how to modify and improve the heat polynomial method if we know the measurement errors and implement them into the numerical procedure. The accuracy of temperature measurements on the heating surface with liquid crystal method was estimated and the analysis of experimental results was given. The functions sought in numerical calculations describe temperature distribution in the protecting glass and the heating foil of the minichannel. They are presented in the form of linear combination of heat polynomials. The adopted boundary conditions and temperature measurements are used to construct error functionals. The latter express the root-mean-square errors, with which computed solutions satisfy relevant boundary conditions. On the basis of functional minimalisation unknown coefficients of linear combinations are determined. The solutions obtained satisfy the differential equations in the exact manner whereas the adopted boundary conditions are met in the approximate fashion. The unknown boiling heat transfer coefficient is the function computed from the boundary condition of the third kind. In the modified method, measurement errors are weights for individual temperature measurements. The more accurate is the measurement, i.e. has a smaller error, the greater is the weight put to it in further calculations. Therefore, it is possible to heighten the accuracy with which glass and foil temperature distributions, determined experimentally, fulfil the assumed equality conditions on the contact surface. Temperature distributions in the glass and the foil, computed on the basis of the modified method, are closer to real values than those obtained with the basic one. Local heat transfer coefficients obtained for two-dimensional boiling heat transfer model with both the basic and the modified heat polynomial methods are also compared.Copyright