Convection Heat Transfer

Convection is the transfer of heat (and in general other physical quantities) resulting from the flow of fluid over a surface. For the purpose of the present discussion the fluid is air and the surface is an element of a building. If the convective air flow is driven by external forces – for example wind or mechanical ventilation – it is referred to as forced convection. The term natural convection describes convection arising from buoyancy.

It is found by experiment that convective heat transfer can be accurately described by equations of the form

                                                                                            ( 12)

where

               is the heat flux (W/m ² ) from the air to the surface,

               is the bulk air temperature (ºC ),

               is the mean surface temperature (ºC ), and

and      are coefficients.

For forced convection at sufficiently high air velocities it is found that, to a good approximation,

                                                                                                                            (13)

and the process is thus linear.

For natural convection, although n is usually somewhat greater than 1, its value is often sufficiently close to 1 for the approximation

                                                                                            (14)

to be reasonably accurate. In this relation,

  is the convective heat transfer coefficient.

To cater for significant departures of n from unity, two approaches are possible.

In the first approach, the heat transfer equation (12) is linearised into the form (14), using a constant value of hc that gives a good approximation to the true behaviour at typical values of the temperature difference.

The second approach re-introduces the nonlinearity by allowing hc to be a function of the temperature difference. The value of hc is updated successively with computed values of this difference and convergence to a consistent solution is achieved by iteration.

ApacheSim gives the user control over which of these approaches is adopted.

 

Convection occurring at the external surfaces of the building is predominantly wind-driven forced convection.

In ApacheSim external forced convection is modelled with a wind speed dependent convective heat transfer coefficient calculated from McAdams’ empirical equations [1]

                                                                            ( 15)

                                                                                              (16)

where

  is the wind speed (m/s) read from the simulation weather file.

Variables on the simulation weather file are recorded at hourly intervals. Linear interpolation is applied between the recorded values to compute values at each simulation time-step.

Provision is made in the constructions database program APcdb for the user to override this calculation procedure with a fixed value for the external convection coefficient.

 

The ApacheSim user has a number of options for modelling convection heat transfer between air masses inside the building and the adjacent building elements:

·       Fixed convection coefficients specified by CIBSE

·       Variable convection coefficients calculated according to CIBSE procedures

·       Variable convection coefficients calculated from the relations proposed by Alamdari & Hammond.

·       Convection coefficients as set by European standard BS EN 15265.

·       User-specified fixed convection coefficients

 

The first four options may be selected from the Simulation Options facility of the ApacheSim interface. The fifth option will apply to any constructions for which fixed internal surface coefficients are applied in the constructions database program APcdb. For such constructions the fixed value will override the method selected in the Simulation Options interface.

 

The CIBSE ‘Simple Model’ for Heat Loss and Heat Gain calculations [1] are based on a constant (average) convection coefficient (W/m²K) for internal surfaces:

                                                                                                         ( 17)

CIBSE Guide Volume C [2] provides a procedure for calculating convection coefficients as functions of surface orientation, air-surface temperature difference and mean room air velocity. Since these coefficients are dependent on air-surface temperature difference and other dynamically varying simulation variables they must be applied as part of an iterative calculation procedure.

The internal convection coefficient is expressed as

                                                                                                              (18)

where

,

                             is a coefficient depending on surface orientation,

                             is a coefficient depending on mean air speed and

                             is an exponent (as in equation 0 ).

Values for C, n and f are taken from CIBSE Guide C Tables C3.12 and C3.13:

 

Surface type                                                                        C                        n

Vertical surfaces                                                             1.4                       1.33

Horizontal surfaces (upward heat flow)               1.7                       1.33

Horizontal surfaces (downward heat flow)        0.64                      1.25

Mean room air speed (m/s)                    f

0.0                                                                     1.0

0.5                                                                     1.3

1.0                                                                     1.7

2.0                                                                     2.4

3.0                                                                     3.1

 

In ApacheSim values of f are calculated from the following formula, which reproduces the values in Table C3.13 to sufficient accuracy:

                                                                                                              ( 19)

where

  is the mean room air velocity (m/s)

Values of mean room air velocity are estimated in ApacheSim from ventilation rates and room geometry.

Alamdari & Hammond [4] established by empirical means a procedure for calculating convection coefficients for internal surfaces. Since they vary with temperature difference, these coefficients must be applied within an iterative calculation procedure.

For vertical surfaces, and horizontal surfaces for which the convective heat flow is upward, the Alamdari and Hammond expression is

                                                   (20)

where

,

  is the characteristic length of the surface, and

and      are coefficients.

For a wall or window, the characteristic length, L, is the height of the space of which it forms a boundary. For a horizontal surface, L is the diameter of the space.

The coefficients a and b are set as follows:

                                                                                        a            b

Vertical surface                                                       1.50     1.23

Horizontal surface (upward heat flow)         1.40     1.63

 

For horizontal surfaces for which the convective heat flow is downward, the expression is

                                                                                             (21)

BS EN 15265 specifies the following values for the internal surface convection coefficient:

Surface orientation                                              h_c (W/m²K)                  

Vertical                                                                     2.5

Horizontal (upward heat flow)                       5.0

Horizontal (downward heat flow)                 0.7

 

The constructions database program APcdb provides an option to fix the convection coefficients for any construction type. If this option is selected, the specified convection coefficient will be applied wherever the construction type is used in the building, overriding the method specified in Simulation Options.