7. A rod of 3 cm diameter and 20 cm length is maintained at 100 0C at one end and 10 0C at the other end. These temperature conditions are attained when there is heat flow rate of 6 W. If cylindrical surface of the rod is completely insulated, determine the thermal conductivity of the rod material?

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7. A rod of 3 cm diameter and 20 cm length is maintained at 100 0C at one end and 10 0C at the other end. These temperature conditions are attained when there is heat flow rate of 6 W. If cylindrical surface of the rod is completely insulated, determine the thermal conductivity of the rod material?

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7. A rod of 3 cm diameter and 20 cm length is maintained at 100 0C at ...

Thermal Conductivity of a Rod

Introduction:
The thermal conductivity of a material refers to its ability to conduct heat. It is the measure of the rate of heat transfer through a material under given conditions of temperature and pressure. In this scenario, we have a rod with a temperature gradient and we need to determine its thermal conductivity.

Given Data:
Diameter of the rod= 3 cm
Length of the rod= 20 cm
Temperature of one end= 100 0C
Temperature of the other end= 10 0C
Heat flow rate= 6 W

Formula:
The formula for thermal conductivity is given by:

Q = -KA (dT/dx)

where,
Q= Heat flow rate (W)
K= Thermal conductivity (W/m.K)
A= Cross-sectional area of the rod (m2)
dT/dx= Temperature gradient (K/m)

Solution:
We can calculate the temperature gradient as follows:

dT/dx= (100 - 10)/0.2= 450 K/m

The cross-sectional area of the rod can be calculated using the formula:

A= πd2/4

where,
d= Diameter of the rod

A= π(0.03)2/4= 7.07 x 10-4 m2

Substituting the values in the formula for thermal conductivity, we get:

6= -K x 7.07 x 10-4 x 450

K= 0.03 W/m.K

Conclusion:
Hence, the thermal conductivity of the rod material is 0.03 W/m.K.

Answered by Engineers Club · View profile

Community Answer

7. A rod of 3 cm diameter and 20 cm length is maintained at 100 0C at ...

Explanation: Q = k A

– t

)/δ = 0.318 k

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