A) \[{{k}_{1}}+{{k}_{2}}\]
B) \[\frac{{{k}_{1}}+3{{k}_{2}}}{4}\]
C) \[\frac{3{{k}_{1}}+{{k}_{2}}}{4}\]
D) \[\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]
Correct Answer: B
Solution :
Both the cylinders are in parallel for the heat flow from one end as shown Then \[{{K}_{eq}}=\frac{{{K}_{1}}{{A}_{1}}+{{K}_{2}}{{A}_{2}}}{{{A}_{1}}+{{A}_{2}}}\] Where \[{{A}_{1}}=\] Area of cross-section of inner cylinder \[{{A}_{1}}=\pi {{r}^{2}}\] \[{{A}_{2}}=\]Area of cross section of cylindrical shell \[=\pi [(2{{R}^{2}}-{{R}^{2}})]\] \[=3\pi {{R}^{2}}\] \[{{K}_{eq}}=\frac{{{K}_{1}}{{(\pi R)}^{2}}+{{K}_{2}}{{(3\pi R)}^{2}}}{\pi {{R}^{2}}+3\pi {{R}^{2}}}\] \[=\frac{{{K}_{1}}+3{{k}_{2}}}{4}\]You need to login to perform this action.
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