Question

Glass plate can be made stronger by inducing compressive residual surface stresses. This is done by a process called thermal tempering. The glass is heated to a temperature between the softening point (~750 K) and the glass transition temperature (~600 K). It is then cooled to room temperature. In this problem, it is cooled in a stream of air. What is the heat transfer coefficient when a 1.5 m x 1.5 m glass plate at 700 K first begins to cool in the air with a free stream velocity of 25 m/s? Use the correlation given below:

Nu = 0.037 Pr^(1/3) * (Re^(0.8) – 15,500)

b) Why are compressive residual surface stresses introduced by this method of cooling?

Answer 1

1) Prandtl Number , Pr is given by

where

• is the  absolute or dynamic viscosity (kg/ms)
• C_p specific heat (J/kg K)
• K is the thermal conductivity (W/m K)

For dry air (assuming the temp of the air is 300 K) the above values are known to be:

, and

therefore

we get Prandtl Number as

The Reynolds number is given by

where

• U is the velocity of the fluid (m/s), U=25 m\s
• x the length along which the fluid flows (m), x=1.5 m
• is the density of the fluid (Kg/m³), =1.16 kg\m³
• is the  absolute or dynamic viscosity (kg/m s) = 1.86 x10^5

therefore

We are given the relation:

which is the Nusselt Number and is also given by

therefore

which gives the heat transfer coefficient as  

b) Compressive residual surface stresses introduced due to the differential cooling that is taking place, glass is not a very good conductor of heat and different parts will cool at different rates, this causes the residual surface stress within the material.