Consider a block made of material of high thermal conductivity k and whose density and specific heat capacity is p and c, respectively. Also, its volume and surface area is V and A, respectively. Initially the block and the ambient are kept at same temperature $T_o$. Suddenly, reaction starts within the block, which gives rise to volumetric heat generation $q'''$. The block looses heat from its sides by convection with a heat transfer coefficient h.
(a) Find the variation of the block temperature with time. State your assumptions clearly.
(b) Find the steady-state temperature of the block.
(c) Is it possible to find the steady-state temperature of the block without solving any differential equation?