Radiative fraction of electric baseboard heater not included in baseboard's total heating rate

asked 2023-07-18 05:05:30 -0500

Liebwin
41 ●4

updated 2023-07-24 07:01:35 -0500

Hello,

Does anyone know, why the Baseboard Total Heating Rate is not equal to the Baseboard Electricity Rate and not equal to the sum of Baseboard Radiant Heating Rate and Baseboard Convective Heating Rate?

I am trying to model a single room exposed to a constant outdoor condition. For indoor heating I use an electric baseboard heater (operative temperature controlled), which allows me to specify the radiative fraction and distribute it to specific surfaces and people. I ensured that all fractions to people and surfaces sum up to unity:

Frac_people + Frac_surfaces = 1

Where for me Frac_people=0.

Now: the output variables for the baseboard heating indicate the total electric consumed power, which is the same as the sum of the convective and the radiative fraction. From the I/O reference, I understood that the total heating rate should also be the sum of the two and with an efficiency of 1 equal to the electric power.

Baseboard Electricity Rate = Baseboard Total Heating Rate / Efficiency

Baseboard Total Heating Rate = Baseboard Convective Heating Rate + Baseboard Radiant Heating Rate

However, for me the output of the baseboard total heating rate is equal to the convective part only, leaving out the radiant fraction and is therefore also lower than the electricity rate.

I tried changing the radiative fraction, which only changed the value of the Baseboard Radiant Heating Rate. Only in the case of Frac_rad=0 the overall balance seem to add up.

Does anyone have an idea?

Many thanks in advance - I am happy to provide more information if needed!

Unfortunately I am new here and can not upload any files yet?! :/

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@Liebwin you can upload your file to Google Drive, Dropbox, or a similar file-hosting service and then share the URL here for others to access.

Aaron Boranian ( 2023-07-18 10:26:38 -0500 )edit

Thanks @Aaron Boranian, here the link to the idf and used epw: IDF epw

Liebwin ( 2023-07-18 11:21:02 -0500 )edit

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answered 2023-07-24 08:06:06 -0500

Liebwin
41 ●4

After some investigative simulations, reading the Engineering Reference and the I/O Reference multiple times, I realised that the descriptions in the documentations were a bit misleading and resulted in a wrong assumption on my side.

Basically the output Baseboard Total Heating Rate is not the the total system output power, as a sum of the radiant and convective heating:

Baseboard Total Heating Rate  ≠  Baseboard Radiant Heating Rate + Baseboard Convective Heating Rate

but rather the total heating rate that actually reaches the zone (directly or indirectly) via convection and is equal to equation 15.734 (Engineering Reference):

Baseboard Total Heating Rate  =  q_req = (q_surf,c - q_surf,z) +  q_conv + q_people

where (q_ surf,c - q_ surf,z) is the heating which gets actually delivered to the zone through convection at the surfaces after being absorbed by the wall. This is only a fraction of Baseboard Radiant Heating Rate (q_ rad) which gets absorbed by specified surfaces of the zone – the remainder gets either conducted through the wall, stored in the wall (q_ cond) or re-emitted by radiation to other walls ( q_ reflec):

(q_surf,c - q_surf,z)  =  q_rad - (q_cond + q_reflec)

So:

Baseboard Electricity Rate = q / efficiency
Baseboard Total Heating Rate: q = q_ rad + q_ conv
Baseboard Radiant Heating Rate: q_ rad = q * Frac_ rad
Baseboard Convective Heating Rate q_ conv = q * (1 - Frac_ rad)
Baseboard Total Heating Rate (should better be called "Baseboard Total Zone Heating Rate"): q_ req = (q_ surf,c - q_ surf,z) + q_ conv + q_ people

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Radiative fraction of electric baseboard heater not included in baseboard's total heating rate

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