Estimate the rate of convective heat transfer across a 1-m-tall double-pane window assembly in which the outside pane is at 0°C and the inside pane is at 20°C. The panes are spaced 2.5 cm apart. What is the thermal resistance (‘R’ value) of the window if the rate of radiative heat flux is 84 W/m2?
GIVEN
• Double-pane window assembly
• Height (H) = 1 m
• Spacing (?) = 2.5 cm = 0.025 m
• Pane temperatures
? Inside (Ti) = 20°C
? Outside (To) = 0°C
• Radiative heat flux (qr/A) = 84 W/m2
FIND (a) The rate of convective heat transfer (qc/A) (b) The thermal resistance (R)
ASSUMPTIONS
• Steady state
• Conduction through the window frame is negligible
PROPERTIES AND CONSTANTS
for dry air at the mean temperature of 10°C
Thermal expansion coefficient (?) = 0.00354 1/K
Thermal conductivity (k) = 0.0244 W/(m K)
Kinematic viscosity (?) = 14.8 × 10–6 m2/s
Prandtl number (Pr) = 0.71
(a) The aspect ratio for the window is
The Grashof and Rayleigh numbers based on the spacing are
The Nusselt number for an enclosed space with H/? = 40 and 109 < Ra? 107 is
The rate of heat transfer by convection is given by
(b) The ‘R’ value must satisfy the following equation
The ‘R’ value is usually expressed in English units
The R value is approximately 1.
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