Consider a pool reactor whose core is constructed from a number of vertical fuel plates of thickness T$.$ Initially the system has the uniform temperature T; then assume that the constant nuclear internal energy q$"\text{'}$ is uniformly generated in these plates. The heat transfer coefficient between the plates and the coolant is h$.$ The temperature of the coolant remains constant, and the thickness of the plates is small compared with other dimensions. Thus, if the end effects are neglected, the heat transfer may be taken to be one$-$dimensional. We wish to formulate the unsteady temperature problem of the reactor. Assume lumped system. Consider a pool reactor whose core is constructed from a number of vertical fuel plates of thickness $\backslash (\backslash$left$($T$\_\{\backslash$infty$\}\backslash$right$)\backslash ).$ Initially the system has the uniform temperature $\backslash (\backslash$left$(\backslash$mathrm$\{$T$\}\_\{\backslash$infty$\}\backslash$right$)\backslash )$; then assumes that the constant nuclear internal energy $\backslash ($ q$^\{\backslash$prime $\backslash$prime$\}\backslash )$ is uniformly generated in these plates. The H$.$T$.$ coefficient between the plates and the coolant is $($h$).$ The temperature of the coolant remains constant, and the thickness of the plates is small compared with other dimensions. Thus, if the end effects are neglected, the H$.$T$.$ may be taken to be $1-$D$,$ we wish to formulate the unsteady temperature problem of the reactor. Assume lumped system.