SOLUTION OF INVERSE PROBLEM FOR DETERMINING MEAN CONVECTIVE HEAT-TRANSFER COEFFICIENT BY MEANS OF GRAM-SCHMIDT AND NELDER-MEADE METHODS

Abstract

In the paper an experimental-numerical method of determining mean values of convective heat-transfer coefficients in shell and tube exchangers has been presented. The method is based on relatively cheap and fast measurements without any special measuring apparatus. The experimental part of the method covers the measurement of mean values of convective heat-transfer coefficients. Such measurement can be based on the definition of the heat exchanger mean rate, using balance equation, (on both sides of heat exchange surfaces z — outer, w — inner) and determination of mean logarithmic difference of temperatures following the measurement of media temperatures at inlet and outlet of the exchanger together with the calculation, using Peclet equation, of heat-transfer coefficient as referred to surface A0. The above measurements should cover the data on temperatures and mass flux for the media between which the heat is transferred. This allows the determination of Reynolds and Prandtl numbers for each measurement point and each medium, the functions of these numbers in case of forced convection being Nusselt (Nu) number. Thus, the determination of mean values of convective heat-transfer coefficients means the assumption of formulae for calculating the coefficients of heat transfer (from the inner and outer sides of the heat surface). It also means selection of the coefficients' constants in the formulae in such a way that the deviation between the measured and the calculated values of coefficients for measurements series m were minimal. The solution of the problem can be reduced to minimization of the sum square of the measured and calculated values k. The minimization problem posed in such a way can be solved by one of optimization methods. In the example of determining mean convective heat-transfer coefficients for finned air coolers presented in the paper the Gram-Schmidt and Nelder-Meade methods have been compared.