Question

A plate of thickness 50 mm is heated upto ${225}^{\circ }C$ in a furnace and then left in open atmosphere at ${25}^{\circ }C$ with convective coefficient of $500{\text{W/m}}^{2}K$. Take thermophysical properties of plate as $k=60\text{W/mK}$
Using shown graph (Heisler chart) the temperature at centerline of wall after 3 minutes from exposure is equal to
$P=7800{\text{kg/m}}^3$
$c=450\text{J/kgK}$
$\alpha =1.5\times {10}^{-5}{\text{m}}^2/\text{s}$

• A. ${106.3}^{\circ }C$
• B. ${118.6}^{\circ }C$
• C. ${187.4}^{\circ }C$
• D. ${199.3}^{\circ }C$

Answer 1

The correct option is B ${118.6}^{\circ }C$


$B_i=\left(\frac{hS}{k}\right)$

$s=\frac{t}{2}$ [characteristic length for plate]

$B_i=\frac{500\times 0.025}{60}=0.2083$

$B_i>0.1$ Lumped analysis is not valid

$\frac{1}{B_i}=4.8$

$F_0=\frac{\alpha \tau }{s^2}=\frac{1.5\times {10}^{-5}\times 180}{(0.025{)}^2}=4.32$

From interpolation:
$R=0.5+\frac{0.5-0.4}{4-5}(4.32-4)$

$R=0.468$

R = centerline temperature ratio

$\frac{T_c-T_{\infty }}{T_i-T_{\infty }}=R$

$\frac{T_c-25}{225-25}=0.468$

$T_c={118.6}^{\circ }C$