(A) In this system,the two materials are arranged in parallel with respect to the direction of heat flow.For parallel arrangement,the equivalent therm

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(A) In this system,the two materials are arranged in parallel with respect to the direction of heat flow.For parallel arrangement,the equivalent thermal conductivity $K_{eq}$ is given by $K_{eq} = \frac{K_1 A_1 + K_2 A_2}{A_1 + A_2}$.The area of the inner cylinder is $A_1 = \pi R^2$.The area of the outer cylindrical shell is $A_2 = \pi (2R)^2 - \pi R^2 = 4\pi R^2 - \pi R^2 = 3\pi R^2$.The total area is $A = A_1 + A_2 = \pi R^2 + 3\pi R^2 = 4\pi R^2$.Substituting these values into the formula:$K_{eq} = \frac{K_1(\pi R^2) + K_2(3\pi R^2)}{4\pi R^2}$.$K_{eq} = \frac{K_1 + 3K_2}{4}$.

Class 11 Physics 10-2.Heat Transfer Thermal Resistance and it's Combination

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$A$ cylinder of radius $R$ is made of a material with thermal conductivity $K_1$. It is surrounded by a cylindrical shell of a material with thermal conductivity $K_2$,having an inner radius $R$ and an outer radius $2R$. The two ends of this composite system are maintained at two different temperatures. There is no heat loss from the surface of the cylinder in the steady state. Find the equivalent thermal conductivity of the system.

A
$\frac{K_1 + 3K_2}{4}$
B
$K_1 + K_2$
C
$\frac{K_1 + 8K_2}{9}$
D
$\frac{8K_1 + K_2}{9}$

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10-2.Heat Transfer

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Thermal Resistance and it's Combination

$A$ ring consisting of two parts $ADB$ and $ACB$ of same conductivity $k$ carries an amount of heat $H$. The $ADB$ part is now replaced with another metal keeping the temperatures $T_1$ and $T_2$ constant. The heat carried increases to $2H$. What should be the conductivity of the new $ADB$ part? Given $\frac{l_{ACB}}{l_{ADB}} = 3$.

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Three rods of same dimensions are arranged as shown in the figure. They have thermal conductivities ${K_1}, {K_2}$ and ${K_3}$. The points $P$ and $Q$ are maintained at different temperatures. For the heat to flow at the same rate along the path $PRQ$ and the path $PQ$,which of the following options is correct?

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Two diagonally opposite corners of a square made of four thin rods of the same material and same dimensions are at temperatures $40^{\circ} C$ and $10^{\circ} C$. If only heat conduction takes place,then the temperature difference between the other two corners will be .......... $^{\circ} C$.

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The dimensions of thermal resistance are

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$A$ rod $CD$ of thermal resistance $10.0 \; K/W$ is joined at the middle of an identical rod $AB$ as shown in the figure. The ends $A$,$B$,and $D$ are maintained at $200^{\circ}C$,$100^{\circ}C$,and $125^{\circ}C$ respectively. The heat current in $CD$ is $P$ watt. The value of $P$ is ... .

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Two diagonally opposite corners of a square made of four thin rods of the same material and same dimensions are at temperatures $40^{\circ} C$ and $10^{\circ} C$. If only heat conduction takes place,then the temperature difference between the other two corners will be .......... $^{\circ} C$.

The dimensions of thermal resistance are

$A$ rod $CD$ of thermal resistance $10.0 \; K/W$ is joined at the middle of an identical rod $AB$ as shown in the figure. The ends $A$,$B$,and $D$ are maintained at $200^{\circ}C$,$100^{\circ}C$,and $125^{\circ}C$ respectively. The heat current in $CD$ is $P$ watt. The value of $P$ is ... .

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