Accuracy of the finite element solution to steady convection-diffusion heat transport equation in continuous casting problem

Beata Hadała , Zbigniew Malinowski

Department of Heat Engineering and Environment Protection,Faculty of Metals Engineering and Industrial Computer Science,Akademia Górniczo-Hutnicza, Mickiewicza 30, 30-059 Kraków.

DOI:

https://doi.org/10.7494/cmms.2009.2.0246

Abstract:

Steady convection-diffusion equation plays an important role in description of the heat transfer in many technical problems. Finite element method is widely used to solve such problems. However, in convection dominated problems oscillatory solutions to the temperature field have been observed. Several methods have been proposed to overcome these difficulties. Transient solutions give satisfactory results, however the computational time is high and in the case of three dimensional problems difficult to accept. The problem is much more complicated because good looking results may give substantial error in the temperature field determination. In the paper the accuracy of several finite element solutions to the heat transfer in the continues steel casting problem has been discussed. The heat balance in the control volume has been computed in order to assess the solutions accuracy. New variational formulation has been proposed to solve steady convection-diffusion equation. The method uses Hermitian shape function and second order derivatives to the temperature field.

Cite as:

Hadała, B., Malinowski, Z., (2009). Accuracy of the finite element solution to steady convection-diffusion heat transport equation in continuous casting problem. Computer Methods in Materials Science, 9(2), 302 – 308. https://doi.org/10.7494/cmms.2009.2.0246

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