Multiple choice

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

  1. 17.2

  2. 21.9

  3. 28.6

  4. 39.2
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C Correct answer
Explanation

$\hspace{3cm}\frac{1}{R_{eq}}=\frac{1}{R_2}+\frac{1}{R_3}\\ \hspace{3cm}\frac{1}{R_{eq}}=\frac{R_3+R_2}{R_2R_3}\\ \hspace{3cm}R_{eq}=\frac{R_2R_3}{R_2+R_3}=\frac{5\times12.5}{5+12.5}=3.6K/W\\ \text{Resistance $R_1$ & $R_{eq}$ are in series .So total Resistance will be}\\ \hspace{3.5cm}R=R_1+R_{eq}=25+3.6=28.6K/W$ 

AI explanation

For a composite slab, thermal resistances of layers in series add up just like electrical resistances in a series circuit, with each layer's resistance being R = L/(kA) (thickness divided by conductivity times area). Any layers in parallel (side-by-side paths for heat flow) combine like parallel resistors, 1/R_total = ΣΣ(1/R_i). Working through the specific layer thicknesses, conductivities, and areas shown in the diagram yields an overall resistance of 28.6 K/W.

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