Convective Heat Transmission - Air Velocity and Air Flow Volume

A hot or cold vertical surface will generate a vertical upwards or downwards air flow as indicated in the figure below.

The air velocity in the center of a convective air flow in parallel to the hot or cold surface - at a vertical distance - can be estimated as:

Air Velocity

v_c = 0.65 [g l dt / (273 + t_e)]^1/2                                              (1)

where

v_c = velocity in center of airflow (m/s)

g = acceleration of gravity (9.81 m/s²)

l = vertical distance from bottom (or top) of the surface (m)

dt = t_e - t_s= temperature difference between surface and room environment

t_s = surface temperature (^oC)

t_e = surrounding environment - ambient - temperature (^oC)

For a cold surface where the air will flow downwards - the value will be negative.

• Convective Air Flow from a single Heat Source

Air Volume

Convective air flow volume at a vertical distance generated by the hot or cold surface can be calculated as

Q = 0.019 [g (t_e - t_s) / (273 + t_e)]^0.4 l^1.2                                            (2)

where

Q = air flow volume (m³/s per meter surface width)

Example - Convective Air Flow from a Cold Window

The air velocity at the lower level of a cold (5^oC) window with height 2 m in a room with temperature 20^oC can be calculated as

v_c = 0.65 [(9.81 m/s²) (2 m) ((20 ^oC) - (5 ^oC)) / (273 + (20 ^oC))]^1/2

    = 0.65 m/s

The air flow volume (for a window with width 1m) can be calculated as

Q = 0.019 [(9.81 m/s²) ((20 ^oC) - (5 ^oC) / (273 + (20 ^oC))]^0.4 (2 m)^1.2

    = 0.033 m³/s

    = 119 m³/h

Example - A Heating Element (or Radiator) and Convective Air Flow

The air flow velocity at the top of a hot (80^oC) radiator with height 1 m in a room with temperature 20^oC can be calculated as

v_c = 0.65 [(9.81 m/s²) (1 m) ((80 ^oC) - (20 ^oC) / ((273 K) + (20 ^oC))]^1/2

    = 0.92 m/s

The air flow volume (for radiator with width 1 m) can be calculated as

Q = 0.019 [(9.81 m/s²) ((80 ^oC) - (20 ^oC) / ((273 K) + (20 ^oC))]^0.4 (1 m)^1.2

    = 0.025 m³/s

    = 90.4 m³/h

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm