An architect is asked to determine the heat loss through a wall of a building constructed as shown in the sketch. The space between wall is 10 cm and contains air. If the inner surface is at 20°C and the outer surface is at – 8°C, (a) estimate the heat loss by natural convection. Then determine the effect of placing a baffle (b) horizontally at the mid- height of the vertical section (B), (c) vertically at the center of the horizontal section (C), and (d) vertically half-way between the two surfaces (D).

Question

GIVEN

• Air filled wall construction as shown above

• Inner wall temperature (Ti) = 20°C

• Outer wall temperature (To) = – 8°C

• Wall spacing (?) = 10 cm = 0.1 m

• Wall height (L) = 3 m

• Wall width (w) = 6 m

FIND

The rate of heat loss by natural convection (qc) for the wall (a) without baffles (b) with a horizontal baffle at a mid-height of the wall-baffle B (c) with a vertical baffle at the center of the horizontal section-baffle C (d) with a vertical baffle midway between the walls-baffle D

ASSUMPTIONS

• Wall temperatures are constant and uniform

• Steady state conditions

• Baffle thickness is negligible

PROPERTIES AND CONSTANTS

for dry air at the mean temperature of 6°C

Thermal expansion coefficient (?) = 0.00359 1/K

Thermal conductivity (k) = 0.0241 W/(m K)

Kinematic viscosity (?) = 14.4 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Answer 1

(a) The Grashof and Rayleigh numbers based on the space between the walls (d) are



The aspect ratio (L/?) = (3 m)/(0.1 m) = 30

The correlation for this geometry is



The rate of heat loss is



(b) With baffles at mid-height, the Rayleigh number is unchanged, but L = 1.5 m, L/? =

(1.5 m)/(0.1 m) = 15



These baffles actually increase the rate of heat transfer by 23%.

(d) The temperature of the vertical baffles is assumed to be approximately equal to the average of the wall temperatures (6°C).

for dry air at the mean temperatures for the

two enclosed spaces:



The Rayleigh numbers for the two sections are



For the inside section



For the outside section



The aspect ratio is L/? = 3/0.05 = 60



Although this is beyond the range of the correlation, will be used to estimate the Nusselt numbers



Inside section



Outside section



These two thermal resistances are in series: therefore, the total resistance is their sum and the rate of heat transfer through the wall is



This represents a 59% decrease in rate of heat transfer from the unbaffled case.

(d) Since the width of the enclosed space does not enter into the calculation of the heat transfer coefficient, this baffle will have no effect on the rate of heat transfer.