Thermal Dynamics

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Thermal Dynamics is the study of the properties of heat energy and the methods of heat transfer. Heat
transfer takes place in 3 main ways: conduction, convection and radiation. The process of conduction in thermal dynamics is dependent on the factors such as heat transfer coefficient of the material, area, thickness through which the heat is transferred and the change in temperature.

Example 1: Calculate the rate of heat transfer through a rectangular window of length 1.5m and
width 0.8m and thickness of 45mm with a coefficient of heat transfer of 0.18W/m°C. The
temperature inside the house is 24°C and temperature outside the house is -2°C.

The rate of heat transfer, R= (k* A* ?T)/ d

Here, k= coefficient of heat transfer= 0.18W/m°C
A= Area through which the heat is transferred= rectangular window= (1.5m* 0.8m) = 1.2m2

?T=final temperature– initial temperature= 24°C- (-2)°C = 26°C

d= thickness= 45mm= 0.045m

So, Rate, R= (0.18* 1.2* 26)/ 0.045= 124.8W

Example 2: Heat is transferred through a rectangular object. If thickness through which the heat is transferred is increased by 4 times, then how does the rate of heat transfer change?

Let the rate of heat transfer, R1= (k* A* ?T)/ d1

Now, given d2= 4d1

So the new rate of heat transfer, R2= (k* A* ?T)/ d2

So, R2= (k* A* ?T)/ 4d1

This implies: R2= [(k* A* ?T)/ d1] * 1/4

Therefore, R2= R1* 1/4==>R2= R1/ 4.
Hence, if the thickness is increased by 4 times, then the rate of heat transfer becomes 1/4th the original rate.