Class Example $1\mathrm{.}4$

$($Unsteady State heat transfer, Variable volume system$)$

Problem Statement

Consider a well agitated cylindrical tank, D $m$ in diameter and $L[m]$ high.

The tank content is heated by a steam jacket $($around the side of the tank only$).$

The tank itself is completely insulated. Liquid $($water$)$ is introduced at a uniform rate, $G[k\frac{g}{h}],$ starting with no water in the tank, and the steam is turned on at the instant that liquid flows into the tank. The steam temperature, $T_S[C],$ and the overall heat transfer coefficient, Ut $[$:$[\frac{W}{m^2}$@$C)\},$ from steam to water, are constant..

List of Variables

$\backslash$table$[[D=,4[m],$diameter of the tank$],[L=,4[m],$height of the tank$],[T_o=,5[C],$inlet temperature of the water$],[T_s=,105[C],$steam temperature$],[T=,C,$temperature of the water in the tank$],[C_{pw}=,4180,\frac{J}{kgC}$ specific heat of water$],[{}_w=,1000,\frac{kg}{m^3}$ density of water$],[h=,m,$liquid level in the tank$],[U_t=,418[\frac{J}{s*m^{2\text{@}}C}],\backslash$table$[[$overall heat transfer coefficient $($from steam to$],[$water$)]]],[G=,1800[k\frac{g}{h}],$rate of water input to the tank$],[A=,m^2,$total area for heat transfer$],[a=,m^2,\backslash$table$[[$area of heat transfer at any time $t$