KMM $342$E Mathematical Modeling in Chemical Engineering

$09\mathrm{.}04\mathrm{.}2021$

MIDTERM $1$

Please write your name and student number on your solution and sign it$.$

Question $1.$

Consider a small spherical reactor, where an exothermic reaction is taking place. The reaction generates a constant heat $q_o.$ Suddenly, the reactor is submerged in a water bath of constant temperature $T.$ The initial temperature of the wall is $T_i.$ The temperature of the wall is uniform at all times, which indicates that temperature does not change in the radial direction.

$($a$)$ Derive the temperature profile of the wall at unsteady$-$state conditions.

$($b$)$ What is the temperature of the wall at $t=30$min $?$

$($c$)$ Sketch the temnerature of the wall with resnect to time

$-$GOOD LUCK