Calculate the heat flux in the radial direction at any time

Question

The transient temperature distribution in an infinitely long cylinder is known to be as follows:

T(r,t) = T_i - [2(q_g/(kr₀))] (r/r₀){exp[-α(λ)²t](J₀[λr])}

Where:  λ satisfies the first zero of J₀[λr₀]

                r₀ = 0.05 m

                q_g = 500 W/m³

                k =0.8 w/(m K)

                T_i = 27 C

                α = 3.(10^-6) m²/s

A) Calculate the heat flux in the radial direction at any time at r= 0.01 m.

B) Calculate the heat flow per length at r=r₀ at a time 0f 0.05 s.