(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

Difficult

$A$ 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

In a composite rod,when two rods of different lengths $l_1$ and $l_2$ and of the same cross-sectional area are joined end to end,if $K$ is the effective coefficient of thermal conductivity,then the value of $(l_1 + l_2)/K$ is

Medium

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Two slabs $A$ and $B$ of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab $A$ is twice that of $B$. The coefficient of thermal conductivity of slab $A$ is twice that of $B$. The first surface of slab $A$ is maintained at $100^{\circ} C$, while the second surface of slab $B$ is maintained at $25^{\circ} C$. The temperature at the contact of their surfaces is (in $^{\circ} C$)

DifficultTS EAMCET 2008

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$A$ copper rod of length $18 \ cm$ and a steel rod of length $6 \ cm$ are joined together to form a composite rod of uniform cross-section. The temperature of the free end of the copper rod is $100 \ ^\circ C$ and the temperature of the free end of the steel rod is $0 \ ^\circ C$. What is the temperature at the junction in $^\circ C$? (Thermal conductivity of copper is $9$ times that of steel. The rod is in a steady state.)

Difficult

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Two rods of equal length and diameter have thermal conductivities $3$ and $4$ units respectively. If they are joined in series, the thermal conductivity of the combination would be

MediumWBJEE 2009

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Two cylindrical rods $A$ and $B$ made of different materials are joined in a straight line. The ratios of lengths,radii,and thermal conductivities of these rods are $\frac{L_A}{L_B} = \frac{1}{2}$,$\frac{r_A}{r_B} = 2$,and $\frac{K_A}{K_B} = \frac{1}{2}$. The free ends of rods $A$ and $B$ are maintained at $400 \ K$ and $200 \ K$,respectively. The temperature of the rods' interface is . . . . . . $K$,when equilibrium is established.

MediumJEE MAIN 2025

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In a composite rod,when two rods of different lengths $l_1$ and $l_2$ and of the same cross-sectional area are joined end to end,if $K$ is the effective coefficient of thermal conductivity,then the value of $(l_1 + l_2)/K$ is

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