The low Reynolds number limit of flow past a blowing reactant sphere serves to illustrate a powerful theoretical approximation for the conservation equations of combustion. For this approximation to work, the crossflow rate measured by the Reynolds number must be at least one order of magnitude smaller than the blowing Stefan flow rate from the porous sphere (droplet). This approximation, which retains in the equations only the irrotational component of the velocity field, enables analytical solutions to be derived for the mixture fraction and all other scalar variables. The mixture fraction solution permits predictions to be made for the flame including its shape and its position, and their dependence on both crossflow and radial sphere blowing. The porous sphere can also be treated as a transient, decaying fuel droplet in aquasi-steady gas. Using this simplification, an analytical droplet burning rate formula is derived and compared with an empirical correlation formula. Diffusion flame hole development is examined as a function of the crossflow.