Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 79 / 1 / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 79 / 1 / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 79 / 1 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 79 / 2 / iv / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 70 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 68 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 68 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 74 / 1 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 74 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 73 / 1 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 73 / 1 / v / Solution

For an incompressible Newtonian fluid, the nonnegative rate at which viscosity converts mechanical energy into heat is
$$
2\mu\int_{\mathcal D}\mathbf e:\mathbf e\,dV,
\qquad
\mathbf e=\frac12(\nabla\mathbf u+\nabla\mathbf u^T).
$$


Viscous dissipation

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