Question

The indoor temperature of an oven can go up to 250 degrees Celsius. There is a 2 mm thick sheet metal material inside and outside of the oven wall. There is a 10 mm insulation material between the oven wall. It is desirable that this temperature should not exceed 30 degrees Celsius in order not to damage the outside of the oven by hand. Find the amount of heat (W) discharged from the furnace unit area and unit time and the energy consumed if the furnace operates for 2 hours.
k_Insulation = 0.0.35 W / m.K
k_sheet metal = 40 W / m.K
h = 25 W / m ^ 2.K

Answer 1

Let,

Indoor temperature of the oven, T_i= 250⁰C

Thickness of sheet metal inside the oven, L₁ = 2 mm = 0.002 m

Thickness of insulation, L₂= 10 mm = 0.01 m

Thickness of sheet metal outside the oven, L₃= 2 mm = 0.002 m

Outdoor temperature of the oven at the wall, T_o = 30⁰C

Operation time, t = 2 hours = 2 x 60 x 60 seconds = 7200 seconds

Heat transfer coefficient inside the oven, h = 25 W/m².K

Thermal conductivity of insulation, k^' = 0.035 W/m.K

Thermal conductivity of sheet metal, k" = 40 W/m.K

Equivalent thermal resistance of the network per unit area is R_eq

Here,

Convective resistance inside the oven,

Conductive resistance due to sheet metal inside the oven,

Conductive resistance due to insulation,

Conductive resistance due to sheet metal outside the oven,

Therefore,

We know,

Heat transfer per unit area per unit time,

Hence, the amount of heat discharged from the oven per unit area and unit time is 7.6758 W/m²

Energy consumed in two hours,

Hence the energy consumed if the oven operates for 2 hours is 4861.88 kJ/m²