As a designer working for a major electric appliance manufacturer you are required to estimate the amount of fiberglass insulation packing (k=0.035 W/m K) that is needed for a kitchen oven shown in figure below. The fiberglass layer is to be sandwiched between a 2 mm thick aluminum cladding plate on the outside and 5 mm thick stainless steel plate on the inside that forms the core of the oven. The insulation thickness is such that the outside cladding temperature does not exceed 40 °C when the temperature at inside surface of the oven is 300 °C. Also the air temperature in the kitchen varies from 15 °C to 33 °C, and the average heat transfer coefficient between the outer surface of the oven and air is estimated to be 12 W/(m2 K). Determine the thickness of fiber glass insulation that

Question

is required for these conditions. What is the outer surface temperature when the inside surface of the oven is at 475 °C? How much fiberglass insulation [k = 0.035 W/(m K)] is needed to guarantee that the outside temperature of a kitchen oven will not exceed 43°C? The maximum oven temperature to be maintained by the convectional type of thermostatic control is 290°C, the kitchen temperature may vary from 15°C to 33°C and the average heat transfer coefficient between the oven surface and the kitchen is 12 W/(m2 K).

GIVEN
• Kitchen oven wall insulated with fiberglass sandwiched between aluminum cladding and steel
• Fiberglass thermal conductivity (k) = 0.035 W/(m K)
• Thickness of Al cladding (LAl)=0.002 m, thickness of ss plate (Lss)=0.005 m
• Convective transfer coefficient on the outside of wall ( ch ) = 12 W/(m2 K)
• Maximum oven temperature (Ti) = 300°C
• Kitchen temperature (T?) may vary: 15°C < T? < 33°C FIND
• Thickness of fiberglass (L) to keep the temperature of the outer surface of the oven (Two) at 40°C or less
ASSUMPTIONS
• One dimensional, steady state heat transfer prevails
• The temperature of the inside of the wall (Twi) is the same as the oven temperature
• The thermal resistance of the metal wall of the oven is negligible
PROPERTIES AND CONSTANTS
Fiber glass (kfg)=0.035 W/m K Aluminum(kAl)=164 W/m K Stainless steel (kss)=14.4 W/m K

Answer 1

Total conduction resistance for the wall is



For steady state conditions, the heat transfer by conduction through the wall,

must be equal to the heat transfer by convection from the outer surface of the wall,



By examination of the above equation, the greatest thickness required for a given Two will occur when Twi and T? are at their maximum values



By examination of the above equation, the greatest thickness required for a given Two will occur when Twi and T? are at their maximum values



In a real design a slightly thicker layer of insulation should be chosen to provide a margin of safety in

case the convective heat transfer coefficient on the outside of the wall in some circumstances is less

than expected due to the location of the oven in the kitchen or other unforeseen factors.