# Thermal Conductivity – Numerical problems

Here, in this post, we will solve a bunch of numerical problems based on **Thermal Conductivity**. We have related posts on this that you can refer to if you want to revise the theory and formula derivation of thermal conductivity.

**Thermal conductivity – definition, values, significance, formula****Thermal conductivity – derivation of formula, dimensional formula**

## Numerical problems on Thermal Conductivity

**1 ) **

The thermal conductivity of copper is 390 W/m/K. **Calculate the rate of heat flow** through a copper bar whose area is 4.0 cm^{2} and whose length is 0.50 m, if there is a temperature difference of 30°C maintained between its ends.

**Solution**:

**2**)

Find out the rate of flow of heat through a bar made of two materials in contact, as shown in the drawing below.

Let the thermal conductivity of B be 400 W/m/K while that for C is 50 W/m/K.

Solution:

Start by finding the temperature at the interface, θ say.

This rate must be the same through B and through C.

Equating them,

[400 x A x (100- θ)]/2 = [ 50 x A x ( θ -30)]/1.2

=> solving we get θ = 88°C.

Now to get the rate of flow, we will substitute θ = 88°C into the flow equation for either bar.

Thus, considering bar B, rate of flow of heat = [400 x A x (100- θ)]/2 = [400 x 1×10^{-4} x (100- 88)]/2 = 0.24 W