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Convective Heat Transmission - Air Velocity and Air Flow Volume

A hot or cold vertical surface generates vertical air flow - air velocity and volume flow calculator

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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

vc = 0.65 [g l dt / (273 + te)]1/2                                              (1)

where

vc = 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 = te - ts= temperature difference between surface and room environment

ts = surface temperature (oC)

te = surrounding environment - ambient - temperature (oC)

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

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 (te - ts) / (273 + te)]0.4 l1.2                                            (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 (5oC) window with height 2 m in a room with temperature 20oC can be calculated as

vc = 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 (80oC) radiator with height 1 m in a room with temperature 20oC can be calculated as

vc = 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

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