$k$ - thermal conductivity, $h$ - heat transfer coefficient, $\rho C_p$ - Volumetric heat capacity, $T$ - temperature $T_\infty$ - Temperature of exposed cooling surrounding environment
Consider two spheres (say a and b) having the same geometrical dimensions but made of different materials (such that $k_a > k_b$) and being at the same initial temperature. However, one can assume that they are exposed to the same cooling environment of the same $h$ and $T_\infty$. Also, consider that $Bi_a = Bi_b < 0.1$ (so that lumped body analysis can be assumed).
The equation (of the lumped body analysis) suggests that the temperature profiles of both spheres should decrease exponentially with time and that they must overlap each other (as the equation doesn't care for $k$. It only depends on $h$, area, volume, $\rho C_p$). However, my intuition asks whether the thermal conductivity doesn't play any role in the temperature profile, practically. Don't you believe that the T profile of the one with a higher k should decrease faster?
I am wondering if someone can provide both practical and theoretical insight on the temperature profile.
Thanks
