The critical Rayleigh number for convective flow of pore water through a permeable spherical body is derived. The result affords constraints on carbonaceous chondrite planetesimal sizes and rates of heat production. If the chemical compositions of carbonaceous chondrites are taken as evidence against flow of pore water, then the present calculations suggest that the parent bodies were less than ~80 km in diameter. Pore water would have flowed through bodies larger than ~120 km. Convective flow and isochemical alteration are not compatible and our calculations can be used to identify the combinations of parent body size and heat generation consistent with one or the other.