Question

A thin walled metal tank of surface area $5m^2$ is filled with water tank and contains an immersion heater dissipating $1kW$. The tank is covered with $4cm$ thick layer of insulation whose thermal conductivity is $0.2W/m/K$. The outer face of the insulation is ${25}^{\circ }C$. Find the temperature(in ${}^{o}C$) of the tank in the steady state.

Answer 1

$\frac{dQ}{dt}=KA\frac{dT}{dx}$ ....(1)
Given,
$A=5m^2$
$\frac{dQ}{dt}=1kW={10}^{3}W$
$dx=4cm=4\ast {10}^{-2}m$
$K=0.2W{m}^{-1}{K}^{-1}$
$dT=T_2-T_1=T_2-25$
Substituting the values in (1)
${10}^3=\frac{0.2\times 5\times (T_2-25)}{4\times {10}^{-2}}$
$\therefore 40=T_2-25$
$\therefore T_2={65}^{0}C$