Many features of the behaviour of mantle convection are dependent on the relative ratio of the core and planet surface area, f. Terrestrial planets attain a range of thermal viscosity contrasts and internal heating rates which influence convective vigour throughout their evolution. In previous studies implementing Cartesian geometry models, convection in strongly temperature-dependent viscosity fluids was investigated for a range of viscosity contrasts, internal heating rate and Rayleigh numbers. The viscosity contrasts give rise to convective regimes widely described as mobile-lid, transitional (or sluggish)-lid, and stagnant-lid. In our solar system, the Earth is an example of a planet with mobile surface plates. Mars by comparison is a planet with an immobile solid surface plate. Since the surface velocity boundary conditions are different, behaviour of mantle convection at present must be different in these two planets. Thus for numerical models, the ratio of surface velocity to root-mean-squared internal velocity, known as the mobility, M, is useful in mapping transitions between regimes. Plate-like surface motion is different from mobile-lid surface motion due to surface yielding effects in the rheology law used. For this reason, a Frank-Kamenetskii (exponential in temperature) viscosity law was employed. Transitions to stagnant-lid regime (M < 0.01) for variable core-size planets with increasing viscosity contrasts and internal heating rates were the main focus of the study. In this talk I will discuss the critical internal parameters which lead to transitions in convective regime and their associated global features.