Question

When a sheet of glass is moved from an annealing oven at Tg to a cooler environment Ts, it needs to be cooled slowly to prevent it from breaking. Neglecting radiation, write an energy balance on a unit-area of the planar interface (i.e. an infinitesimally small volume) between the glass and the air. Your balance should account for conductive heat flux (k) from the bulk glass into the interface, and heat flux out of the interface due to convection (h). Solve your balance to obtain a simple expression for an upper bound to the thermal gradient in the glass during the cooling process.

Answer 1

attached below is the detailed solution

dT/dx | x= l = -h/k ( Tg - Ts )

Step-by-step explanation:

conductive heat flux = k

heat flux due to convection = (h)

To obtain the initial thermal gradient ATTACHED BELOW IS THE ENERGY BALANCE AND THE INITIAL THERMAL GRADIENT