COMPARISON OF HEAT TRANSFER CALCULATIONS ON A SHIELD USING FINITE ELEMENT METHOD AND FINITE DIFFERENCE METHOD

Abstract

The presented journal concerns calculations of heat transfer in a shield with use of two methods: finite element method and finite difference method. The comparison of heat transfer calculation of the selected problem is performed for a rectangular isotropic shield with the dimensions of 6 m x 4 m, with a rectangular hole with the dimensions of 2 m x 1 m. The shield was divided into 0.25 m x 0.25 m rectangular elements and 0.25 m x 0.25 m triangular elements for calculations in the finite element method and 0.25 m x 0.25 m rectangular elements for calculation in the finite difference method.

The rectangular finite element model has 404 nodes, 352 elements, while the triangular finite element model has 404 nodes, 704 elements; the finite difference model has 445 nodes.

Heat conductivity coefficients for the shield are 1.2 W·m^–1·K^–1 in both x and y directions. Prescribed boundary conditions are: top edge temperature 43 °C, bottom edge temperature 3 °C, left edge convection heat transfer coefficient a = 2.3 W·m^–2 and ambient temperature T_a = 47 °C, right edge radiation heat flux density q = 3.8 W·m^–2, 4 insulated hole edges. The shield has 2 point heat discharges: 5 W located in the point with coordinates (0.5 m, 0.5 m) and 11 W located in the point with coordinates (5.0 m, 1.0 m). The shield thickness is 1 m.

The results of calculations are presented in 3 graphs in the form of contour maps. The comparison shows that the results given by the finite element method with use of the rectangular finite elements and triangular finite elements as well as by the finite difference method are similar which allows to conclude that the calculation results are trustworthy and have been done correctly. It is also confirmed by the energetic balance performed for the finite element method.