Consider heat transfer over a flat plate again but now include an additional term due to viscous heating. Show that the similarity method is applicable to this problem as well, and derive the resulting equation for \(\theta\). Solve the problem for various values of \(\operatorname{Pr}\) and the additional dimensionless group resulting from the viscous heating term. This group is known as the Eckert number,

\[E c=\frac{v_{\infty}^{2}}{c_{p} T_{\infty}}\]

What is the physical meaning of this group? Show that \(\operatorname{PrEc}\) is a dimensionless group similar to the Brinkman number.