The <str<strong>on</strong>g>12th</str<strong>on</strong>g> <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g> <str<strong>on</strong>g>Symposium</str<strong>on</strong>g> <strong>on</strong> <strong>District</strong> <strong>Heating</strong> <strong>and</strong> <strong>Cooling</strong>,September 5 th to September 7 th , 2010, Tallinn, Est<strong>on</strong>iaTHEORYIn this secti<strong>on</strong> a theoretic analysis of the impact offorced airflow <strong>on</strong> heat output from radiator with a lengthof (L) 1 m <strong>and</strong> height of (h) 0.59 m is described. Theradiator is in this study approximated by a flat verticalplate. The indoor temperature is assumed to bec<strong>on</strong>stant at 21°C <strong>and</strong> equal to T inf .Heat outputThe heat output from the radiator to the room arisesfrom c<strong>on</strong>vecti<strong>on</strong> <strong>and</strong> radiati<strong>on</strong>. The heat transferprocess from heating water to the room through aradiator is summarized in equati<strong>on</strong> 1 [7], [8].Q m c ( T T) ( k A)(1)spsssrk is the heat transfer (c<strong>on</strong>vecti<strong>on</strong>) from the water to thesurrounding metal, c<strong>on</strong>ducti<strong>on</strong> through the metal <strong>and</strong>c<strong>on</strong>vecti<strong>on</strong> from the outer surface of the radiator to theroom according to equati<strong>on</strong> 2.1 1metal 1(2)k watermetalmetalc<strong>on</strong>v The dominating parameters in this equati<strong>on</strong> are thec<strong>on</strong>vecti<strong>on</strong> <strong>and</strong> radiati<strong>on</strong> between the radiator <strong>and</strong> theroom (α c<strong>on</strong>v <strong>and</strong> α rad ), while the other terms, in this case,can be neglected. This results in a new equati<strong>on</strong> forenergy output, see equati<strong>on</strong> 3.Q Q Q A A (3)radc<strong>on</strong>vc<strong>on</strong>vc<strong>on</strong>vThe temperature Δθ is the logarithmic meantemperature difference according to equati<strong>on</strong> 4.Tss TsrTss TilnT Tsriradradrad(4)3Q C (7)radT mC<strong>on</strong>vecti<strong>on</strong>The c<strong>on</strong>vecti<strong>on</strong> that arises due to the temperaturedifference between the radiator surface <strong>and</strong> thesurrounding air is a functi<strong>on</strong> of the Nusselt number (Nu),see equati<strong>on</strong> 8. Nu h(8)c<strong>on</strong>v/The heat output due to c<strong>on</strong>vecti<strong>on</strong> is divided into threesecti<strong>on</strong>s, natural, mixed <strong>and</strong> forced c<strong>on</strong>vecti<strong>on</strong>.For natural c<strong>on</strong>vecti<strong>on</strong>, the Nu number is dependent <strong>on</strong>the Rayleigh number (Ra), which is a product of thePr<strong>and</strong>tl number (Pr) <strong>and</strong> the Grashof number (Gr). Forair, Pr can be c<strong>on</strong>sidered c<strong>on</strong>stant, Pr=0.71, wile3hGr g (9) 21/T inf 1/ T iwhere g is the gravity force, ν is kinematic viscosity <strong>and</strong>β is the coefficient of expansi<strong>on</strong>.Several empirical relati<strong>on</strong>s describing Nu are available.In this study a relati<strong>on</strong> described by Churchill has beenused [9], see equati<strong>on</strong> 10 <strong>and</strong> 11.0.250.67 Ra9Nu 0.68 Ra 10 (10)9 /16 4 / 9[1 (0.492/ Pr) ]Nu0.50.387 Ra 0.825 [1 (0.492 / Pr)1/ 6]9 /16 8 / 279Ra 10 (11)For forced c<strong>on</strong>vecti<strong>on</strong> the Nu number is calculated byequati<strong>on</strong>s described by Holman [10], see equati<strong>on</strong>s 12<strong>and</strong> 13.Nu 0.664 Re0.5 Pr 1/35Re 510 (12)Radiati<strong>on</strong>According to Trüschel [8] the heat output from radiati<strong>on</strong>can be estimated according to equati<strong>on</strong> 5.Qrad 4 radrad AradAA radradradiator (1 radT)3m Arad Where the temperature, T m , is the mean temperature ofthe radiator surface <strong>and</strong> the surfaces in the rooms, seeequati<strong>on</strong> 6. For a panel radiator the A rad /A radiati<strong>on</strong> =1 [8].Tm Tradiator Troom,surface( Tsf T ) / 2 TSince the A rad <strong>and</strong> emissivity, ε rad , are c<strong>on</strong>stant for aspecific radiator, the relati<strong>on</strong> can be simplified toequati<strong>on</strong> 7.sr2i(5)(6)1/30.857Nu Pr(0.037 Re 871)5 10 Re 10(13)<strong>and</strong> the Reynolds number, Re, is described as:u LRe (14)The product of Gr/Re 2 describes the dominating type ofc<strong>on</strong>vecti<strong>on</strong>. If Gr/Re 2 >10, natural c<strong>on</strong>vecti<strong>on</strong> isdominating, if Gr/Re 2 ≈1, both natural <strong>and</strong> forcedc<strong>on</strong>vecti<strong>on</strong> is of importance <strong>and</strong> if Gr/Re 2
The <str<strong>on</strong>g>12th</str<strong>on</strong>g> <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g> <str<strong>on</strong>g>Symposium</str<strong>on</strong>g> <strong>on</strong> <strong>District</strong> <strong>Heating</strong> <strong>and</strong> <strong>Cooling</strong>,September 5 th to September 7 th , 2010, Tallinn, Est<strong>on</strong>iaImpact of air speed <strong>on</strong> space heating temperatureResults from the theoretical analysis, using theequati<strong>on</strong>s above, are shown in Fig. 2 to Fig. 4. The heatoutput for a radiator designed for the temperatureprogram 60/45 °C is illustrated as a functi<strong>on</strong> of the airspeed in Fig. 2. The supply temperature <strong>and</strong> the massflow through the radiator are kept c<strong>on</strong>stant. Two caseshave been derived, <strong>on</strong>e with heat output <strong>on</strong>ly fromc<strong>on</strong>vecti<strong>on</strong>, <strong>and</strong> <strong>on</strong>e with heat output from both radiati<strong>on</strong><strong>and</strong> c<strong>on</strong>vecti<strong>on</strong>. With ε=0.9, the share of heat outputfrom radiati<strong>on</strong> will be 65% at DOT.C <strong>and</strong> % (W/m 2 K)15010050T sf(C)T sr,c<strong>on</strong>v(C)% additi<strong>on</strong>al Q, c<strong>on</strong>vT sr,rad&c<strong>on</strong>v(C)% additi<strong>on</strong>al Q, rad&c<strong>on</strong>v00 2 4 6 8 10 12 14 16air speed (m/s)30201000 2 4 6 8 10 12 14 16air speed (m/s)Fig. 2 Calculated heat output improvements at T ss=60 °C,T sr0=45 °C with increasing airspeed. m s is kept c<strong>on</strong>stant.As seen, the additi<strong>on</strong>al heat output from the radiator isincreasing rapidly when the air flow is increased. Withradiati<strong>on</strong> taken into account, the increase is somewhatlower since the mean temperature, T m , is decreased,see equati<strong>on</strong> 7.In Fig. 2 the heat output is increasing. In Fig. 3 <strong>and</strong>Fig. 4 the supply temperature to the radiator is reducedinstead to keep the heat output c<strong>on</strong>stant. New T ss <strong>and</strong>T sr can now be calculated under the assumpti<strong>on</strong> that thetotal heat output <strong>and</strong> the mass flow (m s ) through theradiator are c<strong>on</strong>stant. The impact of the air flow isdescribed for three different heat loads (Q rel =100%,50%, 25%) with st<strong>and</strong>ard 60/45 °C temperatureprogram as a reference. See Fig. 3.Temperature ( C)6055504540353025T ss0= 60C , Q rel= 100 %T sr0= 45C , Q rel= 100 %T ss0= 43.1C , Q rel= 50 %T sr0= 35.6C , Q rel= 50 %T ss0= 33.6C , Q rel= 25 %T sr0= 29.9C , Q rel= 25 %200 5 10 15 20 25 30air velocity (m/s)Fig. 3 Possible T ss <strong>and</strong> T sr to for three heat load situati<strong>on</strong>sat different air speeds. Q rad=65% at DOT.New temperature programs have been derived for somemoderate air speeds, see Fig. 4. As seen the impact ofan increased air flow, expressed in °C, is larger at highrelative heat load.Temperature ( C)65605550454035302520NEW TEMPERATURE PROGRAMT sf0U= 0.0m/sT sr0U= 0.0m/sU= 0.5m/sU= 1.0m/sU= 2.0m/sU= 3.0m/s150 20 40 60 80 100relative heatoutput (%)Fig. 4 New space heating temperature programs atdifferent air speeds. Red lines: T ss, Blue lines: T sr.Q rad=65% at DOT.In the calculati<strong>on</strong>s performed, the radiator is assumed tohave the same heat output from both sides of theradiator. The air flow is assumed to be uniformlydistributed through the length <strong>and</strong> height of the panelradiator. This is not the case in the real add-<strong>on</strong>-fanblower applicati<strong>on</strong>s, however, <strong>on</strong>e can expect resultsfollowing the same pattern.EXPERIMENTAL STUDYTo investigate the performance of the add-<strong>on</strong>-fanblower, two radiators of different type were supplied withsuch device during the heating seas<strong>on</strong> 2009/2010. Thepower supply to the fans was scheduled to switch <strong>on</strong><strong>and</strong> off while the mass-flow (m s ) through the radiatorwas kept at a c<strong>on</strong>stant level.Field study objectThe radiators are situated in two offices at LundUniversity. The original temperature program for the24
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produce heat and electricity. Fluct
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