Question 846: Thermodynamics & KTG

Question

A composite slab consists of two materials having coefficient of thermal conductivity $$\mathrm{K}$$ and $$2 \mathrm{~K}$$, thickness $$\mathrm{x}$$ and $$4 \mathrm{x}$$ respectively. The temperature of the two outer surfaces of a composite slab are $$\mathrm{T}_2$$ and $$\mathrm{T}_1\left(\mathrm{~T}_2 > \mathrm{T}_1\right)$$. The rate of heat transfer through the slab in a steady state is $$\left[\frac{\mathrm{A}\left(\mathrm{T}_2-\mathrm{T}_1\right) \mathrm{K}}{\mathrm{x}}\right] \cdot \mathrm{f}$$ where '$$\mathrm{f}$$' is equal to

Accepted Answer

$$\begin{array}{ll} 
&\mathrm{R}_{\mathrm{eq}}=\mathrm{R}_1+\mathrm{R}_2 \
\because & \mathrm{R}_1=\frac{\mathrm{x}}{\mathrm{KA}}, \mathrm{R}_2=\frac{4 \mathrm{x}}{2 \mathrm{KA}} \
	herefore & \mathrm{R}_{\mathrm{eq}}=\frac{\mathrm{x}}{\mathrm{KA}}+\frac{2 \mathrm{x}}{\mathrm{KA}}=\frac{3 \mathrm{x}}{\mathrm{KA}}
\end{array}$$
Rate of heat transfer of composite slab is given by,
$$\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{T}_2-\mathrm{T}_1}{\mathrm{R}_{\mathrm{eq}}}=\frac{\mathrm{KA}\left(\mathrm{T}_2-\mathrm{T}_1ight)}{3 \mathrm{x}}$$
$$	herefore \quad \mathrm{f}=\frac{1}{3}$$

Answer

1

Answer

$$\frac{2}{3}$$

Answer

$$\frac{1}{2}$$

Answer

$$\frac{1}{3}$$

Thermodynamics & KTG

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