Convective Heat - Air Velocity and Volume of Air Flow

A hot or cold vertical surface will generate a vertical airflow - calculate air velocity and volume of the air flow

A hot or cold vertical surface will generate a vertical air flow up or down.

The air velocity in the center of a convective flow in parallel to the hot or cold surface can be estimated with the equation:

Air Velocity

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

where

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

g = 9.81 - acceleration of gravity (m/s²)

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

t_s = temperature surface (^oC)

t_e = temperature surrounding environment (^oC)

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

Air Volume

The convective air flow volume generated at a certain height by the hot or cold surface can be calculated as

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

where

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

Example - Convective Air Flow Cold Window

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

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

    = - 0.65 m/s

The air flow volume can be calculated as

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

    = 0.033 m³/s

    = 119 m³/h

Example - Convective Air Flow Heating Element - Radiator

The air flow velocity at the top level of a hot (80^oC) radiator (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 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

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