Page 141 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

STEADY STATE HEAT CONDUCTION IN MULTI-DIMENSIONS

Figure 5.7 Fine structured mesh 133

3(0, 50) 2(50, 50)

4(40, 40)

1 (50, 0)
Figure 5.8 Interpolation into a triangular element

coordinates of these points are (50, 0), (50, 50) and (0, 50), respectively. All dimensions
are in cm. Also, calculate the heat flux in both the x and y directions. Assume a thermal
conductivity value of 10 W/m C.
◦
The following expression can be used to describe the linear variation of temperature
within the element

(5.21)
T = N 1 T 1 + N 2 T 2 + N 3 T 3
In order to calculate the temperature at node 4, the shape functions N 1 , N 2 and N 3 have
to be calculated at node 4.