TITLE.PM5

808 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th15-2.pm5

15.2.9. Critical thickness of insulation

15.2.9.1. Insulation-General aspects
Definition. A material which retards the flow of heat with reasonable effectiveness is
known as ‘Insulation’. Insulation serves the following two purposes :
(i) It prevents the heat flow from the system to the surroundings ;
(ii) It prevents the heat flow from the surroundings to the system.
Applications :
The fields of application of insulations are :
(i) Boilers and steam pipes
(ii) Air-conditioning systems
(iii) Food preserving stores and refrigerators
(iv) Insulating bricks (employed in various types of furnaces)
(v) Preservation of liquid gases etc.
Factors affecting thermal conductivity
Some of the important factors which affect thermal conductivity (k) of the insulators (the
value of k should be always low to reduce the rate of heat flow) are as follows :
1.Temperature. For most of the insulating materials, the value of k increases with in-
crease in temperature.
2.Density. There is no mathematical relationship between k and ρ (density). The common
understanding that high density insulating materials will have higher values of k in not
always true.
3.Direction of heat flow. For most of the insulating materials (except few like wood) the
effect of direction of heat flow on the values of k is negligible.
4.Moisture. It is always considered necessary to prevent ingress of moisture in the insu-
lating materials during service, it is however difficult to find the effect of moisture on the
values of k of different insulating materials.
5.Air pressure. It has been found that the value of k decreases with decrease in pressure.
6.Convection in insulators. The value of k increases due to the phenomenon of convection
in insulators.
15.2.9.2. Critical Thickness of Insulation
The addition of insulation always increases the conductive thermal resistance. But when
the total thermal resistance is made of conductive thermal resistance [(Rth)cond.] and convective
thermal resistance [(Rth)conv.], the addition of insulation in some cases may reduce the convective
thermal resistance due to increase in surface area, as in the case of a cylinder and a sphere, and
the total thermal resistance may actually decrease resulating in increased heat flow. It may be
shown that the thermal resistance actually decreases and then increases in some cases.
‘‘The thickness upto which heat flow increases and after which heat flow decreases is
termed as Critical thickness. In case of cylinders and spheres it is called ‘Critical radius’.

A. Critical thickness of insulation for cylinder :
Consider a solid cylinder of radius r 1 insulated with an insulation of thickness (r 2 – r 1 ) as
shown in Fig. 15.25.
Let, L = Length of the cylinder,
t 1 = Surface temperature of the cylinder,
tair = Temperature of air,