Inner surface of a cylindrical shell of length l and of material of thermal conductivity k is kept at constant temperature T1 and outer surface of the cylinder is kept at constant temperature T2 such that (T1>T2) as shown in figure. Heat flows from inner surface to outer surface radially outward. Inner and outer radii of the shell are R and 2R respectively. Due to lack of space this cylinder has to be replaced by a smaller cylinder of length l2 inner and outer radii R4 and R respectively and thermal conductivity of material nk. If rate of radially outward heat flow remains same for same temperatures of inner and outer surface i.e., T1 and T2, then find the value of n.

Inner surface of a cylindrical shell of length l and of material of th

1.	Inner surface of a cylindrical shell of length l and of material of thermal conductivity k is kept at constant temperature T1 and outer surface of the cylinder is kept at constant temperature T2 such that (T1>T2) as shown in figure. Heat flows from inner surface to outer surface radially outward. Inner and outer radii of the shell are R and 2R respectively. Due to lack of space this cylinder has to be replaced by a smaller cylinder of length l2 inner and outer radii R4 and R respectively and thermal conductivity of material nk. If rate of radially outward heat flow remains same for same temperatures of inner and outer surface i.e., T1 and T2, then find the value of n.
Answer» Inner surface of a cylindrical shell of length $l$ and of material of thermal conductivity $k$ is kept at constant temperature $T_{1}$ and outer surface of the cylinder is kept at constant temperature $T_{2}$ such that $(T_{1} > T_{2})$ as shown in figure. Heat flows from inner surface to outer surface radially outward. Inner and outer radii of the shell are $R$ and $2 R$ respectively. Due to lack of space this cylinder has to be replaced by a smaller cylinder of length $\frac{l}{2}$ inner and outer radii $\frac{R}{4}$ and $R$ respectively and thermal conductivity of material $n k$ . If rate of radially outward heat flow remains same for same temperatures of inner and outer surface i.e., $T_{1}$ and $T_{2}$ , then find the value of $n$ .

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