Nonlinear heat conduction in solidH2

On the basis of recent empirical data, the temperature distribution in solid crystalline hydrogen is shown to be governed by the essentially nonlinear diffusion equation $\frac{\partial \theta }{\partial t}=D{\theta }^2{\nabla }^2\theta$ in which there appears the dimensionless variable $\theta \equiv {[1+{\left(\frac{T}{T_c}\right)}^4]}^{-1\mathrm{}}$ with the constants $D$ and $T_c$ dependent on the ortho-${\mathrm{H}}_2$ percentile. It is observed that this governing equation can be transformed to an equivalent linear diffusion equation for situations with one-dimensional spatial symmetry. By utilizing this remarkable linear-theoretic correspondence, exact solutions to initial-value boundary-value problems of current experimental interest are derived and reported here.