Solving nonlinear direct and inverse problems of stationary heat transfer by using Trefftz functions

Grysa, Krzysztof; Maciąg, A.; Pawińska, Anna

doi:10.1016/j.ijheatmasstransfer.2012.07.072

Cited by 51 publications

(34 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More information on inverse differential operators can be found in [15,16]. The boundary conditions assumed for equation (6) , one has to modify the boundary conditions any time we pass to the next iteration.…”

Section: Homotopy Perturbation Methods (Hpm)mentioning

confidence: 99%

Two dimensional heat transfer problem in flow boiling in a rectangular minichannel

Hożejowska

Piasecka

Hożejowski

2015

EPJ Web of Conferences

View full text Add to dashboard Cite

Abstract. The paper presents mathematical modelling of flow boiling heat transfer in a rectangular minichannel asymmetrically heated by a thin and one-sided enhanced foil. Both surfaces are available for observations due to the openings covered with glass sheets. Thus, changes in the colour of the plain foil surface can be registered and then processed. Plain side of the heating foil is covered with a base coat and liquid crystal paint. Observation of the opposite, enhanced surface of the minichannel allows for identification of the gasliquid two-phase flow patterns and vapour quality. A two-dimensional mathematical model of heat transfer in three subsequent layers (sheet glass, heating foil, liquid) was proposed. Heat transfer in all these layers was described with the respective equations: Laplace equation, Poisson equation and energy equation, subject to boundary conditions corresponding to the observed physical process. The solutions (temperature distributions) in all three layers were obtained by Trefftz method. Additionally, the temperature of the boiling liquid was obtained by homotopy perturbation method (HPM) combined with Trefftz method. The heat transfer coefficient, derived from Robin boundary condition, was estimated in both approaches. In comparison, the results by both methods show very good agreement especially when restricted to the thermal sublayer.

show abstract

Section: Homotopy Perturbation Methods (Hpm)mentioning

confidence: 99%

Two dimensional heat transfer problem in flow boiling in a rectangular minichannel

Hożejowska

Piasecka

Hożejowski

2015

EPJ Web of Conferences

View full text Add to dashboard Cite

show abstract

“…Data necessary for the heat transfer coefficient evaluation were obtained from numerical computations in which two approaches were used: a calculation procedure based on the Trefftz functions [5][6][7][8][9][10][11][12][13][14][15][16] and FEM simulations by ADINA software…”

Section: Main Aimmentioning

confidence: 99%

Comparison of FEM calculated heat transfer coefficient in a minichannel using two approaches: Trefftz base functions and ADINA software

Maciejewska¹,

Łabędzki²,

Piasecki³

et al. 2017

EPJ Web Conf.

View full text Add to dashboard Cite

Abstract. The paper presents the methods of heat transfer coefficient determination for boiling research during FC-72 flow in a minichannel. The boundary condition in the form of distributions of temperature on the outer side of the minichannel heated wall was obtained using infrared thermography. It was assumed two-dimensional steady-state heat flow. The local values of the heat transfer coefficients on the surface between the heated foil and boiling liquid, were determined from the Robin boundary condition. Data necessary for the heat transfer coefficient evaluation were obtained from numerical computations using two approaches: calculation procedure based on the Trefftz functions and FEM simulations by ADINA software. The shape functions were linear combinations of the Trefftz functions. Combinations of the Trefftz functions exactly satisfy the differential equation. Coefficients of the linear combination of the shape function in the approximate solution were chosen to minimize residuals on domain boundary and along common edges of adjacent elements. Temperature measurement points were located in boundary nodes. During FEM simulations 4-node FCBI elements were used, fluid flow was assumed to be laminar, incompressible and material constants of the fluid and of the foil were independent on temperature. The results of the comparative analysis were presented and discussed.

show abstract

“…Results obtained by using the Levenberge-Marquardt method to solve 3-D inverse problem were based on the numerical experiments. Estimation of unknown parameters in a rectangular fin satisfying a predefined temperature are discussed by Das et al [25]. The study is useful for selecting various unknowns in a conductive-convective and radiative fin for required temperature and efficiency.…”

Section: List Of Symbols a B Matrices A I Coefficients Bimentioning

confidence: 99%

A 2D inverse problem of predicting boiling heat transfer in a long fin

Orzechowski

2015

Heat Mass Transfer

View full text Add to dashboard Cite

Solving nonlinear direct and inverse problems of stationary heat transfer by using Trefftz functions

Cited by 51 publications

References 7 publications

Two dimensional heat transfer problem in flow boiling in a rectangular minichannel

Two dimensional heat transfer problem in flow boiling in a rectangular minichannel

Comparison of FEM calculated heat transfer coefficient in a minichannel using two approaches: Trefftz base functions and ADINA software

A 2D inverse problem of predicting boiling heat transfer in a long fin

Contact Info

Product

Resources

About