The approximations of the nonlinear heat transport problem are based on the finite volume (FM) and averaging (AM) methods [1,2]. This procedures allows reduce the nonlinear 2‐D problem for partial differential equation (PDE) to a initial‐value problem for a system of 2 nonlinear ordinary differential equations(ODE) of first order in the time t or to a initial‐value problem for one nonlinear ODE of first order with two nonlinear algebraic equations.
Netiesinio šilumos pernešimo plonose plokštelėse matematinis modeliaivimas
Santrauka. Darbe sprendžiamas netiesinis šilumos pernešimo uždavinys. Uždavinio specifika yra ta, kad šilumos pernešimas vyksta labai plonose plokštelėse, todėl nagrinėjamas vienmatis apibendrintas modelis. Ši redukcija atliekama baigtinių tūrių ir vidurkinimo metodais. Gautoji dviejų netiesinių paprastųjų diferencialinių lygčių sistema yra sprendžiama skaitiškai. Išnagrinėtas ir alternatyvus variantas, kai po redukcijos gaunama viena netiesinė paprastoji diferencialinė lygtis bei dvi papildomos algebrinės lygtys.
Buikis, A., & Kalis, H. (1999). The mathematical modelling of the nonlinear heat transport in thin plate. Mathematical Modelling and Analysis, 4(1), 44-50. https://doi.org/10.3846/13926292.1999.9637109
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