References
[1] DL Turcotte and ER Oxburgh. Finite amplitude convective cells and continental drift. Journal of Fluid Mechanics, 28(1):29-42, 1967.
[2] Diana Valencia, Richard J O’Connell, and Dimitar Sasselov. Internal structure of massive terrestrial planets. Icarus, 181(2):545-554, 2006.
[3] Diana Valencia, Richard J O’connell, and Dimitar D Sasselov. Inevitability of plate tectonics on super-earths. The Astrophysical Journal, 670(1):L45, 2007.
[4] Diana Valencia and Richard J O’Connell. Convection scaling and subduction on earth and super-earths. Earth and Planetary Science Letters, 286(3-4):492–502, 2009.
[5] S Morris and D Canright. A boundary-layer analysis of benard convection in a fluid of strongly temperature-dependent viscosity. Physics of the Earth and planetary interiors, 36(3-4):355–373, 1984.
[6] AC Fowler. Fast thermoviscous convection. Studies in Applied Mathematics, 72(3):189-219, 1985.
[7] Viatcheslav S Solomatov and L-N Moresi. Scaling of time-dependent stagnant lid convection: Application to small-scale convection on earth and other terrestrial planets. Journal of Geophysical Research: Solid Earth, 105(B9): 21795-21817, 2000.
[8] VS Solomatov and L-N Moresi. Three regimes of mantle convection with non-newtonian viscosity and stagnant lid convection on the terrestrial planets. Geo-physical Research Letters, 24(15):1907-1910, 1997.
[9] Adrian Lenardic, MA Richards, and Friedrich H Busse. Depth-dependent rheology and the horizontal length scale of mantle convection. Journal of Geophysical Research: Solid Earth, 111(B7), 2006.
[10] Meysam Shahraki and Harro Schmeling. Plume-induced geoid anomalies from 2d axi-symmetric temperature-and pressure-dependent mantle convection models. Journal of Geodynamics, 59:193-206, 2012.
[11] Tania S Khaleque, Andrew C Fowler, PD Howell, and Michael Vynnycky. Numerical studies of thermal convection with tempera-ture-and pressure-dependent viscosity at extreme viscosity contrasts. Physics of Fluids, 27(7):076603, 2015.
[12] Simon Ostrach. Internal viscous flows with body forces. In Grenzschicht- forschung/Boundary Layer Research, pages 185-208. Springer, 1958.
[13] B Gebhart. Effects of viscous dissipation in natural convection. Journal of fluid Mechanics, 14(2):225-232, 1962.
[14] William F McDonough and S-S Sun. The composition of the earth. Chemical geology, 120(3-4):223-253, 1995.
[15] Tanya Lyubetskaya and Jun Korenaga. Chemical composition of earth’s primitive mantle and its variance: 1. method and results. Journal of Geophysical Research: Solid Earth, 112(B3), 2007.
[16] HJ Van Heck and PJ Tackley. Plate tectonics on super-earths: equally or more likely than on earth. Earth and Planetary Science Letters, 310(3-4):252-261, 2011.
[17] Claudia Stein, J¨org Schmalzl, and Ulrich Hansen. The effect of rheological parameters on plate behaviour in a self-consistent model of mantle convection. Physics of the Earth and Planetary Interiors, 142(3-4):225-255, 2004.
[18] C Stein, JP Lowman, and U Hansen. The influence of mantle internal heating on lithospheric mobility: Implications for super-earths. Earth and Planetary Science Letters, 361:448-459, 2013.
[19] Tania S Khaleque and SA Sayeed Motaleb. Effects of temperature-and pressure-dependent viscosity and internal heating on mantle convection. GEM- International Journal on Geomathematics, 12(1):1-22, 2021.
[20] Sumaiya B Islam, Suraiya A Shefa, and Tania S Khaleque. Mathematical modelling of mantle convection at a high Rayleigh number with variable viscosity and viscous dissipation. Journal of the Egyptian Mathematical Society, 30(1): 1-17, 2022.
[21] AC Fowler, PD Howell, and Tania S Khaleque. Convection of a fluid with strongly temperature and pressure dependent viscosity. Geophysical & Astrophysical Fluid Dynamics, 110(2):130-165, 2016.
[22] Gerald Schubert, Donald Lawson Turcotte, and Peter Olson. Mantle convection in the Earth and planets. Cambridge University Press, 2001.
[23] Andrew Fowler. Mathematical geoscience, volume 36. Springer Science & Business Media, 2011.
[24] Gary T Jarvis and WR Peltier. Mantle convection as a boundary layer phenomenon. Geophysical Journal International, 68(2):389-427, 1982.
[25] B Blankenbach, F Busse, U Christensen, L Cserepes, D Gunkel, U Hansen, H Harder, G Jarvis, M Koch, G Marquart, et al. A benchmark comparison for mantle convection codes. Geophysical Journal International, 98(1):23-38, 1989.
[26] Donald E Koglin Jr, Sanaz R Ghias, Scott D King, Gary T Jarvis, and Julian P Lowman. Mantle convection with reversing mobile plates: A benchmark study. Geochemistry, Geophysics, Geosystems, 6(9), 2005.
[27] Gary T Jarvis and Dan P Mckenzie. Convection in a compressible fluid with infinite prandtl number. Journal of Fluid Mechanics, 96(3):515-583, 1980.
[28] Wei Leng and Shijie Zhong. Constraints on viscous dissipation of plate bending from compressible mantle convection. Earth and Planetary Science Letters, 297 (1-2):154-164, 2010.
[29] AM Leitch and David A Yuen. Internal heating and thermal constraints on the mantle. Geophysical Research Letters, 16(12):1407-1410, 1989.