We
are solving series of problems based on the concept transmission of heat. In
this lesson we are going to solve problems based on conduction, convection and
radiation. These three are the different modes of transmission of heat.
Conduction happens via solid medium, convection happens via fluid medium and
for the radiation, we don’t need any medium for the propagation. In the case of
conduction, molecules of the solid body vibrates about its mean position and
pass the heat energy to the next particle and there is no permanent
displacement of the particle. Thus it is the slowest method of transmission of
heat and it happens via solids because the molecular force of attraction is
strongest.

**Problem**

In
a rod heat is passing through in a study state and the temperature at the both
ends is different as given in the problem. If the length of the rod is one
meter, we need to find the temperature at a point who is at a distance of 60 centimetre
from the first end.

**Solution**

We
know that the rate of heat flow in a solid material it is directly proportional
to the area of cross section, temperature difference and is inversely
proportional to the length of the rod. Taking that into consideration a
proportionality constant is defined. In a given rod rate of flow will be the
same but as the length of the rod varies, temperature of the body also varies.
Taking that into consideration, we can solve the problem as shown in the
diagram below.

**Problem**

An
aluminium rod area of cross section and coefficient of conductivity is given to
us and a study of rate of flow of heat 360 calorie per minute is given to us in
the problem. We need to find the temperature gradient of the rod and the
problem is given as shown in the diagram below.

**Solution**

Temperature
gradient is defined as the ratio of temperature per unit length. We can get the
value of this temperature gradient from the definition of coefficient of
thermal conductivity. Problem is solved as shown in the diagram below.

**Problem**

One
end of a metal bar is in ice and the end is in contact with stream as shown in
the diagram below. Coefficient of thermal conductivity is given to us and we
need to find the amount of the ice that melts per minute.

**Solution**

We
know that there is certain amount of heat flows in the rod per second and we
can find it using the definition of coefficient of thermal conductivity. This
heat energy is used in converting ice into water. All transferred heat is used
to convert ice into water. We can get the mass of the ice converted using the
definition of latent heat. It is defined as the amount of heat required to
convert unit mass of substance from one state to the other. Using these
definitions, we can solve the problem as shown in the diagram below.

**Problem**

Three
rods of same length and area of cross section are joined in parallel. Their
respective coefficient of thermal conductivity is given to us and we need to
find the effective thermal conductivity of the system. Problem is as shown in
the diagram below.

**Solution**

We
know that when rods are connected in parallel, the temperature at common point
will be the same but the rate of flow of the total heat is the sum of
individual values. Taking that into consideration, we can solve the problem as
shown in the diagram below.

**Problem**

Water
is changing into ice at zero degree centigrade and atmospheric temperature is
much less than that as shown in the diagram below. If the time taken for the
formation of ice layer of thickness one centimetre is seven hours we need to
find the time taken for the formation of ice layer of thickness two centimetre.

**Solution**

We
can prove that the time taken for the formation of ice layer is directly
proportional to the square of thickness of the layer. Taking that into
consideration, we can solve the problem as shown in the diagram below.

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