Transfer Functions for Efficient Calculation of Multidimensional Transient Heat Transfer

J. E. Seem; S. A. Klein; W. A. Beckman; J. W. Mitchell

doi:10.1115/1.3250659

Transfer Functions for Efficient Calculation of Multidimensional Transient Heat Transfer

Journal of Heat Transfer ◽

10.1115/1.3250659 ◽

1989 ◽

Vol 111 (1) ◽

pp. 5-12 ◽

Cited By ~ 53

Author(s):

J. E. Seem ◽

S. A. Klein ◽

W. A. Beckman ◽

J. W. Mitchell

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Transfer Functions ◽

Piecewise Linear ◽

First Order ◽

Efficient Calculation ◽

Long Time ◽

Transfer Problems ◽

Time Invariant ◽

First Order Differential Equations

Finite difference or finite element methods reduce transient multidimensional heat transfer problems into a set of first-order differential equations when thermal physical properties are time invariant and the heat transfer processes are linear. This paper presents a method for determining the exact solution to a set of first-order differential equations when the inputs are modeled by a continuous, piecewise linear curve. For long-time solutions, the method presented is more efficient than Euler, Crank–Nicolson, or other classical techniques.

Download Full-text

INCREASING OF ACCURACY FOR ENGINEERING CALCULATION OF HEAT TRANSFER PROBLEMS IN TWO LAYER MEDIA

Mathematical Modelling and Analysis ◽

10.3846/13926292.2005.9637280 ◽

2005 ◽

Vol 10 (2) ◽

pp. 173-190 ◽

Cited By ~ 1

Author(s):

H. Kalis ◽

I. Kangro

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Transfer Problem ◽

Engineering Calculation ◽

Radial Symmetry ◽

Initial Model ◽

Initial Value ◽

First Order ◽

Transfer Equations ◽

Transfer Problems

In this paper we study the simple algorithms for modelling the heat transfer problem in two layer media. The initial model which is based on a partial differential equation is reduced to ordinary differential equations (ODEs). The increase of accuracy is shown if instead of first order ODE initial value problem ([4, 5]) the second order differential equations is taken. Such a procedure allows us to obtain a simple engineering algorithm for solving heat transfer equations in two layered domain of Cartesian, cylindrical (with axial symmetry) and spherical coordinates (with radial symmetry). In a stationary case the exact finite difference scheme is obtained. Šiame straipsnyje yra nagrinejami paprasti dvisluoksnes srities šilumos laidumo problemos modeliavimo algoritmai, keičiant diferencialines lygtis dalinemis išvestinemis i paprastas diferencialines lygtis. Parodoma, kad didesnio tikslumo pasiekimui, vietoje pirmos eiles paprastu diferencialiniu lygčiu pradinio uždavinio nagrinejamos antros eiles diferencialines lygtys. Ši proced ura leidžia gauti paprasta inžinerini dvisluoksies srities šilumos laidumo lygties sprendini stačiakampeje, cilindrineje (su ašiu simetrija) ir sferineje (su spinduline simetrija) koordinačiu sistemoje. Tiksli baigtiniu skirtumu schema buvo sudaryta stacionariam atvejui.

Download Full-text

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

Asymptotic Analysis ◽

10.3233/asy-211710 ◽

2021 ◽

pp. 1-19

Author(s):

Calogero Vetro ◽

Dariusz Wardowski

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Order Differential Equation ◽

Nonlinear Differential Equations ◽

Oscillatory Behavior ◽

Third Order ◽

First Order ◽

Third Order Differential Equation ◽

Comparison Technique ◽

First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

Download Full-text