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The science
Residence time
Solids tumble down a slightly inclined rotating cylinder. An empirical relation (Sullivan, Maier and Ralston) gives the transit time in minutes as τ = 0.19 (L/D) / (N s), with L/D the length-to-diameter ratio, N the speed in rpm and s the slope (tan of the incline). Slower rotation or lower slope means longer exposure to heat.
Heating, calcination and dead-burning
The bed temperature relaxes towards the gas temperature, dTs/dx = (Tg - Ts)/λ, where λ is a heat-transfer length. Magnesite decomposes, MgCO3 → MgO + CO2, with first-order Arrhenius kinetics dα/dt = k(T)(1 - α), k = A e-E/RT. Above roughly 1500 C the MgO grains sinter; the relative density d approaches its limit as d d/dt = ks(T)(dmax - d), again Arrhenius, so a hotter burning zone or a longer residence gives a denser, lower-porosity product. Bulk density is 3.58 g/cm³ times the relative density.
Honest simplifications: the gas temperature profile is prescribed, not solved; kinetic constants are order-of-magnitude teaching values; the dust, CO2 partial pressure and bed mixing are ignored. It illustrates trends and the strong temperature sensitivity, not a plant design.