A moving boundary solution for solidification of lava lake and magma intrusion in the presence of time-varying contact temperature

During the solidification of a lava lake heat is released convectively from the top surface as well as conductively into the country rock from the base, leading to non-uniform solidification. The upper solidified layer grows at a faster rate than the lower solidified layer. Similarly, solidification of magma intrusion within the crust is also non-uniform due to the presence of thermal gradient in the crust. Available analytical solution for solidification of a melt layer assumes only symmetric cooling about the centre of the layer. In the present work a moving boundary solution for thermal evolution and non-uniform solidification of a melt layer incorporating time-varying contact temperature conditions at both of its boundaries is developed. The solution is obtained by using the Fourier spectral approach in the space domain and a modified finite difference scheme in the time domain, and is validated with available analytical solutions for simple cases and a semi-analytical solution for the case involving temperature gradient in the country rock. This solution can be used to analyse solidification of lava lakes and magma intrusions experiencing time-dependent temperature variation at their contacts with the country rock.