A long hollow plastic cylinder (λ = 0.23W/K m, c = 1045 J/kg K, = 2200 kg/m 3 ) with diameters di = 60 mm and da = 100 mm initially has a temperature of ϑ0 = 20 ◦C, which is the same as that of the...

A long hollow plastic cylinder (λ = 0.23W/K m, c = 1045 J/kg K, = 2200 kg/m³
) with diameters di = 60 mm and da = 100 mm initially has a temperature of ϑ0 = 20 ◦C, which is the same as that of the surroundings (air). At time t = 0 the hollow cylinder is filled with a hot liquid and is heated such that the inner wall assumes a temperature of ϑi = 80 ◦C for t ≥ 0. At the outer wall, heat is transferred to the air with a heat transfer coefficient of α = 12.0W/m²
K.

a) Using the explicit difference method with Δr = 4.0 mm, show that the step size Δt = 60 s is permissible and go on to calculate the temperature profile at time t∗ = 15 min.

b) How large is the difference between the steady temperature profile and the temperatures calculated for time t ∗?