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Ten identical rods of length L, area A made of same material with conductivity K are joined as shown in the figure. Ends A and E are maintained at constant temperatures of $100^{0} C$ and $0^{0} C$ . Assuming no radiative and convective heat loss. Choose the correct option.

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Total thermal resistance of combination is $\frac{12}{11} (\frac{L}{K A})$

Total thermal resistance of combination is $\frac{38}{15} (\frac{L}{K A})$

Heat flow rate is $\frac{750}{19} (\frac{K A}{L})$

Heat flow rate is $\frac{225}{19} (\frac{K A}{L})$

answer is B.

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Detailed Solution

Total resistance = $R + \frac{R}{3} + \frac{R}{5} + R$ $= \frac{38}{15} R = \frac{38}{15} \frac{L}{K A}$ Heat flow rate = $\frac{d θ}{d t} = \frac{T_{A} - T_{E}}{R e q}$

$= \frac{100 - 0}{\frac{38}{15} \frac{L}{K A}} \Rightarrow \frac{750}{19} \frac{K A}{L}$

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