A spherical, stainless steel (AISI 302) canister is used to store reacting chemicals that provide for a uniform heat flux q”_i to its inner surface. The canister is suddenly submerged in a liquid bath of temperature T_∞i, where T_i is the initial temperature of the canister wall.

(a) Assuming negligible temperature gradients in the canister wall and a constant heat flux q”_i, develop an equation that governs the variation of the wall temperature with time during the transient process. What is the initial rate of change of the wall temperature if q”_i = 10⁵ W/m²?

(b) What is the steady-state temperature of the wall?

(c) The convection coefficient depends on the velocity associated with fluid flow over the canister and whether or not the wall temperature is large enough to induce boiling in the liquid. Compute and plot the steady-state temperature as a function of h for the range 100 ≤ h ≤ 10,000 W/m². K. Is there a value of h below which operation would be unacceptable?

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Reacting chemicals = 0.6 m Canister 0.6 m T= 500 K p= 8055 kg/m T= 300 K h = 500 W/m?-K Bath = 510 J/kg-K = 0.5 m