Analytical and numerical model of transient heat transfer in a single tube row heat exchanger

• Autorzy: Taler D.
• Języki publikacji: EN

Abstrakty

EN

Cross-flow tubular heat exchangers are widely applied as condensers and evaporators in air conditioners and heat pumps or as air heaters in heating systems. There are analytical and numerical mathematical models of heat exchangers of that type to determine the steady state temperature distribution of fluids. In this paper the transient response of a single-row tubular cross-flow tube - and - fin heat exchanger is analyzed. Partial differential equations for both hot and cold fluid are solved by the Laplace transform method with numerical inversion and by the finite-difference (finite-volume) method. The transient response of one-row tube - and - fin heat exchanger due to step change of air temperature is calculated using both developed approaches. Good agreement between the analytical predictions (the Laplace transform method and analytical exact steady state solution) and the finite difference solution has been found. After eliminating the time, using the Laplace transform, a simpler system of partial equations is formed, which can be solved analytically. In view of the complex form of the achieved solutions, the inverse Laplace transform is obtained numerically by the method due to Crump improved by de Hoog. The solutions presented in the paper can be used to analyze the operation of heat exchangers in transient conditions and can find application in systems of automatic control or in the operation of heat exchangers.

Słowa kluczowe

EN

cross-flow tube heat exchanger; Laplace transform method; mathematical model; numerical heat transfer; transient response

PL

metoda transformacji Laplace'a; model matematyczny; numeryczna wymiana ciepła; odpowiedź impulsowa; wymiennik ciepła krzyżowy

• Wydawca: Wydawnictwo Instytutu Maszyn Przepływowych PAN ; Komitet Termodynamiki i Spalania PAN
• Czasopismo: Archives of Thermodynamics
• Rocznik: 2007
• Tom: Vol. 28, no. 1
• Strony: 51--64
• Opis fizyczny: Bibliogr. 8 poz.,Wz., rys., wykr., tab.,

Twórcy

autor

Taler D.

• Teoria i pomiary maszyn cieplnych.,

Bibliografia

• [1] TALER D.: Determination of heat transfer correlations for plate-fin-and-tube heat exchangers, Int. J. Heat and Mass Transfer, 40(2004), 809-822.
• [2] WANG C.C., LIN Y.T., LEE C.J.: An airside correlation for plain fin-and-tube heat exchangers in wet conditions, Int. J. Heat Mass Transfer, 43(2000), 1869-1872.
• [3] TAN K.S., SPINNER I.H.: Numerical methods of solution for continuous counter-current processes in the nonsteady state, AIChE J. 30(1984), 770-786.
• [4] LI C.H.: Exact transient solutions of parallel-current transfer processes, ASME J. of Heat and Mass Transfer 108(1986), 365-369.
• [5] ROETZEL W., XUAN Y.: Dynamic behaviour of heat exchangers, Computational Mechanics Publications Vol.3 (1998), WIT Press, Southampton, UK.
• [6] DE HOOG F.R., KNIGHT J.H., STOKES A.N.: An improved method for the numerical inversion of Laplace transforms, SIAM J. on Scientific and Statistical Computing 3(1982), 357-366.
• [7] TUCKER P.G.: Computation of Unsteady Internal Flows, Kluwer Academic Publishers, Norwell 2001.
• [8] PRESS W.H., TEUKOLSKY S.A., VETTERING W.T., FLANNERY B.P.: Numerical Recipes, The Art of Scientific Computing. Second Edition, Cambridge University Press 1996.