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Basis approximating functions selection to maximize heat transfer coefficient of water-propylene glycol electrolyte coolant

DOI: 10.21047/1606-4313-2016-15-2-76-80
UDC 621.564.3

Basis approximating functions selection to maximize heat transfer coefficient of water-propylene glycol electrolyte coolant

Kirillov V. V., Chashnikov M .V.

Abstract
The article deals with the task of finding optimum parameters for electrolyte coolant (salt concentration and water-propylene glycol weight ratio) maximizing heat transfer coefficient from tube walls. The coefficient dependence on coolant viscosity, density, thermal capacity, and specific heat capacity is known. Function data are given in the table on the basis of which approximation by least square method is made. Heat transfer coefficient is calculated for every pair of arguments from the table, and then it is approximated. The result is more exact than when approximating each of the functions. Two variants of approximation are considered: by second order polynomial and by a combination of linear functions with hyperbolas. Second order polynomial approximation has been chosen as it shows less error. Necessary extremum conditions are verified. They being met beyond the range of argument values in question, we do not to check their sufficiency, and transfer maximum is reached at the boundary of the range. The sought argument values are calculated by Lagrange method of multipliers. The graph for approximating polynomial contour line and calculation results of optimum parameters are shown.

Keywords: water-propylene glycol electrolyte coolant, approximation, estimation, maximization

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