What do you mean by thermal conductivity?

shashank Saxena
13 Points
14 years ago

Thermal conductivity

In solids, heat is transferred through conduction. We will study conduction of heat through a solid bar in the following sector.

Consider a solid bar of thickness d and area of cross-section A. The left side of bar is maintained at QA temperature and right side at QB

Let us suppose QAQB

Heat flows from higher temperature to lower temperature after some time, the temp of each section becomes constant with time. This is known as steady state.
In steady state, if  Q Amount of heat crosses through any cross section in time  T, then

and

or,

K: coefficient of thermal conductivity.

For a small thickness Dx along the direction of heat and whose thickness dx is small and temperature difference is ?Q

[Secondary information]
Quantity  dq/dV  called the temperature gradient and minus sign indicates that dq/dV is negative along the direction of heat flow.

[Secondary Information]

We can compose the equation with the Ohm's Law
V1 - V2 = I.R

I =

Similarly

hence X / KA   is called thermal resistance rth.

Rth = X / KA