Consider a quadrilateral element shown in the figure below. The nodal temperatures of the element are given as \(\left\{T_{1}, T_{2}, T_{3}, T_{4}\right\}=\{80,40,40,80\}\).

a. Compute the expression of the temperature \(T\) along the line \(\xi\) that connects nodes 3 and 1. For example, \(T=3+5 \xi+3 \xi^{2}+\cdots\). You can assume that \(\xi=0\) at node 3 and \(\xi=1\) at node 1 . Plot the graph of \(T(\xi)\) with respect to \(\xi\).

b. Compute the temperature gradient \(\partial T / \partial x\) at the center of the element.

Transcribed Image Text:

(0,4) (4,4) 3 (0,0) (4) (6,0)