<Dl> <Dd> ∂ T ∂ t = κ ∇ 2 T + ε (\ displaystyle (\ frac (\ partial T) (\ partial t)) = \ kappa \ nabla ^ (2) T+ \ epsilon) </Dd> </Dl> <Dd> ∂ T ∂ t = κ ∇ 2 T + ε (\ displaystyle (\ frac (\ partial T) (\ partial t)) = \ kappa \ nabla ^ (2) T+ \ epsilon) </Dd> <P> where T is temperature, κ = k / ρ c p (\ displaystyle \ kappa = k / \ rho c_ (p)) is the thermal diffusivity with k thermal conductivity, c p (\ displaystyle c_ (p)) heat capacity, and ρ (\ displaystyle \ rho) density, and ε (\ displaystyle \ epsilon) is an optional heat source . Often the pressure is the dynamic pressure, with the hydrostatic pressure and centripetal potential removed . These equations are then non-dimensionalized, introducing the non-dimensional parameters, </P> <Dl> <Dd> R a = g α T D 3 ν κ, E = ν Ω D 2, P r = ν κ, P m = ν η (\ displaystyle Ra = (\ frac (g \ alpha TD ^ (3)) (\ nu \ kappa)), E = (\ frac (\ nu) (\ Omega D ^ (2))), Pr = (\ frac (\ nu) (\ kappa)), Pm = (\ frac (\ nu) (\ eta))) </Dd> </Dl>

How does the composition of the inner and outer core explain the dynamo theory