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Control of the rate of heat flow in a compact heat exchanger by changing the speed of fan rotation

Taler D.

Archives of Thermodynamics

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2009

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Vol. 30, no. 4

67-80

EN

The aim of the steady-state inverse heat transfer problem for plate-fin and tube heat exchangers is to adjust the number of fan revolutions per minute so that the water temperature at the heat exchanger outlet is equal to a preset value. Since the outlet water temperature is a nonlinear function of the fan revolution number, a nonlinear algebraic equation was solved using the secant or interval searching method. The steady-state outlet water temperature was calculated at every search or iteration step using an analytical mathematical model of the heat exchanger. An analytical model of the plate-fin and tube heat exchanger with two tube rows and two passes allowing for different heat transfer coefficients on each tube row was developed. The procedure developed in the paper was validated by comparing the calculated and measured values of the fan revolutions. The calculated numbers of fan revolutions compare closely with the measured values.

2

Transient inverse heat transfer problem in control of plate fin and tube heat exchangers

Taler D.

Archives of Thermodynamics

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2008

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Vol. 29, no. 4

185-194

EN

A transient inverse heat transfer problem encountered in control of fluid temperature or heat transfer rate in a plate fin and tube heat exchanger was solved. The objective of the process control is to adjust the speed of fan rotation, measured in number of fan revolutions per minute, so that the water temperature at the heat exchanger outlet is equal to a time-dependent target value (setpoint). The least squares method in conjunction with the first order regularization method was used for sequential determining the number of revolutions per minute. Future time steps are used to stabilize the inverse problem for small time steps. The transient temperature of the water at the outlet of the heat exchanger was calculated at every iteration step using a numerical mathematical model of the heat exchanger. The technique developed in the paper was verified by comparing the calculated and measured number of the fan revolutions. The discrepancies between the calculated and measured revolution numbers are small.

3

Estymacja parametrów modelu termicznego elementów półprzewodnikowych

Górecki K., Zarębski J.

Kwartalnik Elektroniki i Telekomunikacji

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2006

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Vol. 52, z. 3

347-360

PL

W pracy przedstawiono opracowaną przez autorów metodę estymacji parametrów modelu termicznego elementów półprzewodnikowych i układów scalonych oraz program komputerowy MASTER2 realizujący tę metodę. Program MASTER2 steruje procesem pomiaru przejściowej impedancji termicznej Z(t) badanych elementów półprzewodnikowych i na podstawie uzyskanego przebiegu Z(t) wyznacza wartości parametrów skupionego modelu termicznego – rezystancji termicznej, termicznych stałych czasowych i odpowiadających im współczynników wagowych, a także wartości elementów biernych występujących w analogu elektrycznym modelu termicznego sformułowanego w postaci sieci Cauera lub Fostera. Poprawność opracowanej metody i programu zweryfikowano doświadczalnie przez porównanie zmierzonych i obliczonych przebiegów przejściowej impedancji termicznej Z(t) tranzystora mocy MOS.

EN

This paper deals with the problem of the estimation of the thermal model parameters of semiconductor devices. A new computer tool – MASTER2 for estimation of these parameters is presented. MASTER2 controlls the method of measuring the transient thermal impedance Z(t) as well as it estimates both the value of Z(t) parameters: Rth, ai, [tau]thi (i = 1, 2, 3,..., N) and the values of RC elements existing in the electrical analogues of a device thermal model of the form of Cauer or Foster network. The procedure of estimation of the parameters of the device thermal model is automatically realised on the authors' special algorithm implemented in MASTER2. In this algorithm, in the first place the values of the parameters: coefficients a i, thermal time constant [tau]thi and the thermal resistance Rth are calculated using the measured Z(t) dependence. Next, the values of RC elements in the Foster and Cauer networks are computed. The considered algorithm is valid in the case when the values of the successive thermal time constants differ from each other at least a few times. Therefore, the dependence Z(t) normalized to Rth is a intervally linear function in the lin-long scale. The value of Rth results directly from Z(t) at the ateady-state. Values of the remaining parameters are calculated by the last-square method used for approximation of any special function with Z(t) as an argument. At first the longest thermal time constant and the coefficient a1 corresponding to them are calculated. The values of RC elements of the Foster network are calculated after analytical dependences containing the considered parameters. In turn, to calculate the values of the Cauer network, the operational thermal impedance Z(s) has to be formulated. Next, division of the values of coefficients corresponding to the highest degree of polynominals representing the numerator and the denominator of Z(s) respectively, have to be performed. The value of such division at the k-th iteration is denoted as Dk. In each iteration step, the product of the denominator value and the value of Dk is substracted from the numerator and the denominator are transformed to each other. The presented computer tool was verified experimentally by comparing the measured and calculated dependence of Z(t) of the VDMOS transistor IRF840. The very well agreement between measurements and simulations have been obtained.