Convection driven by a nonuniform radiative internal heat source in a cavity

While most studies of convection driven by an internal heat source in a fluid layer have been focused on a uniform heating of the fluid, the nonuniformity in the heat source has important implications for the temperature and flow fields, and the boundary heat fluxes.

Here, using direct numerical simulations we examine convection in a square cavity subject to a highly nonuniform internal heating generated by the energy deposition of a proton beam, motivated by applications in medical isotope production.  The internal heat source has a gaussian distribution in the direction of gravity (vertical) with a maximum at the center of the cavity. Two convective cells are formed in the horizontal direction, separated at the location where the internal heating stops. Interestingly, the scaling of the maximum and averaged temperatures with the Rayleigh number compare similarly to previously found power laws for uniformly heated fluid layers. At higher levels of internal heating, the layer of fluid near the top cold boundary becomes convectively unstable via Rayleigh–Taylor (RT) instabilities. The critical Rayleigh number for the onset of these instabilities was also close to uniform internal heating. The size of the convective cells plays a crucial role in controlling the maximum temperature and the growth of RT instabilities. By comparing the rate of growth of the RT instabilities from the linear stability analysis of self-similar temperature profiles to the rate of advection of the instabilities to the boundaries of the cavity, we develop a model for predicting the occurrence of RT instabilities.