A) \[{{K}_{1}}+{{K}_{2}}\]
B) \[\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]
C) \[\frac{{{K}_{1}}+3{{K}_{2}}}{4}\]
D) \[\frac{3{{K}_{1}}+{{K}_{2}}}{4}\]
Correct Answer: C
Solution :
Both the cylinders are in parallel, for the heat flow from one end as shown. Hence \[{{K}_{eq}}=\frac{{{K}_{1}}{{A}_{1}}+{{K}_{2}}{{A}_{2}}}{{{A}_{1}}+{{A}_{2}}}\]; where A1 = Area of cross-section of inner cylinder = pR2 and \[{{A}_{2}}=\]Area of cross-section of cylindrical shell \[=\pi \{{{(2R)}^{2}}-{{(R)}^{2}}\}=3\pi {{R}^{2}}\] Þ \[{{K}_{eq}}=\frac{{{K}_{1}}(\pi {{R}^{2}})+{{K}_{2}}(3\pi {{R}^{2}})}{\pi {{R}^{2}}+3\pi {{R}^{2}}}=\frac{{{K}_{1}}+3{{K}_{2}}}{4}\]You need to login to perform this action.
You will be redirected in
3 sec