Minor edits below in italics:
Radiator performance is obviously just as important to a comfortable home as heat pump performance, so reasonably accurate rating at off-design inlet temperatures is quite important in radiator selection and study, especially as radiators in heat pumped systems normally run substantially cooler than boiler-fed radiators.
But despite its apparent simplicity, the well known equation for radiator performance at off-design DT:
Qrated = Qdesign x (DTrated/DTdesign)^1.3
contains a number of pitfalls for the unwary:
- Qdesign, the design heat output quoted by the manufacturer for any given domestic radiator (type/size/model) is based (in Europe) on tests undertaken in accordance with BS EN 442 (2014). As a minimum, EN 442 requires that the heat output test result Q be quoted at DT50 (specifically 75degC inlet/65degC outlet water, 20degC air inlet). This test water DT (10degC) is important because the test water flow rate M can be back-calculated (from Q = M.Cp.(T1-T2)). But when installed in the home, the water DT will probably not be 10degC, and the actual flow rate M may also be varying:
- With a fixed speed circulating pump, flow to any particular radiator may be affected by operation of TRVs on other radiators
- A PWM-controlled pump only varies system flow – not an individual radiator flow – to maintain a given DT.
- Even if you know Qdesign and DTdesign (=DT50), how is DTrated defined? Is it (T1 – Troom)? Or (Tave – Troom), where Tave = (T1+T2)/2? If the latter, how can T2 be predicted? Worse still, is it based on the MTD of the water and air temperatures? If the latter, both t2 and T2 would require prediction (and the design case t2 is not published in any case).
- Further, the above equation does not specify the rating parameters. Is it applicable only if water flow is held constant and (T1-T2) varied? Or only if (T1-T2) is held constant and water flow varied? Or can both vary?
- Some manufacturers’ test results may not replicate home installation conditions. For example, the test results probably include radiation losses (which can be relatively significant) from both the front and back radiator faces, whereas in the home installation the radiation from the rear face effectively disappears once the wall on which the radiator is located reaches radiator temperature.
The above uncertainties call into question the reliability of such a simple equation.
A little more detail can be derived by applying the heat balance equation:
Q = M.Cp.(T1-T2) = m.cp.(t2-t1) = U.A.MTD
- Upper case = water side, lower case = air side, 1 = inlet, 2 = outlet.
- Cp and cp are usually evaluated at Tave and tave.
- 1/U = 1/H + 1/h where H = Hnc + Hfc (water side natural and forced convection coefficients, typically high so neglected), and h = hnc + hr (air side natural convection and radiation coefficients). The latter can be estimated from the Nusselt and Stefan-Boltzmann equations respectively. U is normally referred to the effective radiator face area A.
- MTD = LMTD.F where LMTD= ((T1-t1)-(T2-t2))/ln((T1-t1)-(T2-t2)) and the correction factor F is dependent upon radiator flow pattern. Typically this is assumed to approximate a TEMA type X heat exchanger (cross-flow, with one shell side pass – the air – and two tube side passes – the water) and the appropriate equations applied.
Assuming constant volumetric water flow, this allows (with considerable trial-and-error calculation) estimation of T2 and t2 for various values of T1 in a given radiator arrangement, and thus Qrated.
A mathematical (spreadsheet) model of the above indicates that for a 600H x 1200W Type 20 radiator (2 panels, no fins), the exponent in the above rating equation based on DTrated = (T1+T2)/2 - t1 should be about 1.5 rather than 1.3. (If I look at DTrated = T1-t1, the exponent varies with T1, so of limited value.)
Note - Radiator performance at different water flow rates, or the effect of glycol, has not yet been studied, so the above 1.5 exponent may not be widely applicable.
Any questions or comments please?
Sarah