Question

Heat flows through a composite slab, as shown below. The depth of the slab is 1m. The k values are in W/mK. The overall thermal resistance in K/W is

• A. 17.2
• B. 21.9
• C. 28.6
• D. 39.2

Answer 1

The correct option is C 28.6


$k_1=0.02W/mK$
$k_2=0.10W/mK$
$k_3=0.04W/mK$
${\delta }_1=0.5m$
${\delta }_2={\delta }_3=0.25cm$
Depth: w = 1 m
Total thermal resistance,
$R_t=R_1+\frac{R_2{R}_3}{R_2+R_3}$

where $R_1=\frac{{\delta }_1}{A_1{k}_1}=\frac{0.5}{1\times 1\times 0.02}=25K/W$

$R_2=\frac{{\delta }_2}{A_2{k}_2}=\frac{0.25}{0.5\times 1\times 0.10}=5K/W$

and$R_3=\frac{{\delta }_3}{A_3{k}_3}=\frac{0.25}{0.5\times 0.04}=12.5K/W$

$\therefore R_t=25+\frac{5\times 12.5}{5+12.5}=25+3.57$

$=28.57K/W\simeq 28.6K/W$