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Convection in a spherical shell is widely used to model fluid layers ofplanets and stars. The choice of thermal boundary conditions in such models isnot always straightforward. To understand the implications of this choice, wereport on the effects of the thermal boundary condition on thermal convection,in terms of instability onset, fully developed transport properties and flowstructure. We use the Boussinesq approximation, and impose a Robin boundarycondition at the top. This enforces the temperature anomaly and its radialderivative to be linearly coupled with a proportionality factor $\beta$. Usingthe height H of the fluid layer, we introduce the non-dimensional Biot numberBi* = $\beta$H. Varying Bi* allows us to transition from fixed temperature forBi* = +$\infty$, to fixed thermal flux for Bi* = 0. The bottom boundary of theshell is kept isothermal. We find that the onset of convection is only affectedby Bi* in the non-rotating case. Far from onset, considering an effectiveRayleigh number and a generalized Nusselt number, we show that the Nusselt andP{\'e}clet numbers follow standard universal scaling laws, independent of Bi*in all cases considered. However, the large-scale flow structure keeps thesignature of the boundary condition with more vigorous large scales for smallerBi* , even though the global heat transfer and kinetic energy are the same.Finally, for all practical purposes, the Robin condition can be safely replacedby a fixed flux when Bi* < 0.03 and by a fixed temperature for Bi* > 30.

The Effects of Robin Boundary Condition on Thermal Convection in a Rotating Spherical Shell