The chief push of the research described in this paper was to develop a simplified method of accurately gauging the impact of assorted convection on the chilling capacity of a ceiling beaming panel in automatically ventilated infinites. The simplified correlativity for assorted convection heat transportation was derived from established mixed and natural convection correlativities. It was found that the entire capacity of ceiling radiant chilling panels can be enhanced in assorted convection state of affairss by 5 % to 35 % under normal operating temperatures.
Presently. most ceiling radiant chilling panel ( CRCP ) public presentation estimations are based on natural convection merely. This is reflected in ASHRAE ( 2000 ) literature. where the analysis is based upon the natural convection heat transportation work of Min et Al. ( 1956 ) . and the European CRCP capacity evaluation criterion. DIN 4715 ( 1997 ) . which uses natural convection as the trial status. However. Kochendorfer ( 1996 ) found that in existent edifices. chilling end products of CRCPs are significantly higher ( 25 % ) than measured panel capacities tested in the research lab under DIN 4715 conditions. In existent edifices. mechanical airing systems are normally used. and the walls are non adiabatic. If the higher public presentation of CRCPs is ignored in the design stage. unneeded panel country is specified and the cost of the panels is inordinate.
The two major beginnings of dependable building-related natural convection heat transportation coefficients are Awbi and Hatton ( 1999 ) and Min et Al. ( 1956 ) . The natural convection coefficient proposed by Min et Al. is as follows: H c = 2. 13 ? ( T a – T autopsy )
A figure of plants referenced in the literature that trade with assorted convection include Chen et Al. ( 1989 ) . Fisher and Pedersen ( 1997 ) . and Awbi and Hatton ( 2000 ) . Awbi and Hatton proposed assorted convection heat transportation coefficients for het room surfaces partly covered by air jet. The correlativity for a het floor or cooled ceiling is as follows: H degree Celsius = ( h cn + H californium )
Jae-Weon Jeong is a doctorial pupil and Stanley A. Mumma is a professor in the Department of Architectural Engineering. The Pennsylvania State University. University Park. Pa.
? 2003 ASHRAE. This papers is non to be distributed without written permission from ASHRAE.
HVAC & A ; R RESEARCH
Table 1. Coefficients for Correction Function
a1 0. 12933333 a6 -0. 049091666 a2 1. 294888889 a7 0. 00417 a3 0. 051308333 a8 0. 001202777 a4 -0. 29422 a9 -0. 000111666 a5 0. 016286666
0. 308 2. 175h cn = ————– ( T a – T autopsy ) 0. 076 De
( 2b )
H californium = 4. 25 ? W
0. 575 ?V
( 2c )
SIMPLIFIED MIXED CONVECTION COEFFICIENT
In this research. the assorted convection heat transportation coefficient developed by Awbi and Hatton ( 2000 ) was extensively analyzed to deduce a simplified assorted convection coefficient that can be more easy used in the design phase of a CRCP system. Awbi and Hatton’s assorted convection correlativity for a cooled ceiling ( Equation 2 ) is a map of the characteristic diameter of a infinite ( De ) . space-to-panel temperature difference ( ?T ) . diffusor breadth ( W ) . and diffuser discharge air speed ( V ) . Forced convection effects. the difference between natural convection coefficients and assorted convection coefficients. for assorted ?T and V values were calculated utilizing Equations 1 and 2. severally. Equation 3a returns the forced convection consequence in W/m2?K. whose needed coefficients are presented in Table 1. The concluding signifier of the simplified assorted convection correlativity. a consequence of adding the forced convection consequence to the natural convection coefficient ( Equation 1 ) . is presented in Equation 3b. degree Fahrenheit ( V. ?T ) = a 1 + a 2 ( V ) + a 3 ( V ) + a 4 ( ?T ) + a 5 ( ?T ) + a 6 ( V ? ?T ) a 7 ( V ? ?T ) + a 8 ( V ? ?T ) + a 9 ( V ? ?T ) h hundred = degree Fahrenheit ( V. ?T ) + 2. 13 ? ?T 0. 31 2 2 2 2 2 2
Convective heat transportation coefficients were computed for the infinite illustrated by Figure 1 utilizing the simplified assorted convection equation every bit good as the equations of Chen et Al. ( 1989 ) . Fisher and Pedersen ( 1997 ) . Min et Al. ( 1956 ) . and Awbi and Hatton ( 2000 ) . The comparings for assorted ?Ts and Vs are presented in Figure 2 and Figure 3. severally. While non presented in those figures. it can be shown that the convection coefficients are insensitive to the infinite characteristic diameter ( De ) and the diffusor breadth ( W ) .
Ceiling RADIANT COOLING PANEL MODEL
The steady-state analytical CRCP theoretical account developed by Conroy and Mumma ( 2001 ) was used to gauge enhanced panel chilling capacity with assorted convection. The CRCP theoretical account is based on the landmark work of Hottel and Whillier ( 1958 ) . q o = U O ( T a – T autopsy ) MCp ( T fo – T fi ) T autopsy = T fi + ( 1 – F R ) A P FR U O
( 4 ) ( 5 )
VOLUME 9. NUMBER 3. July 2003
Figure 1. Schematic of Model Space
Figure 2. Assorted Convection Heat Transfer Coefficients for Various ?T ( V = 2 m/s. De = 3 m. V = 0. 5 m )
Figure 3. Assorted Convection Heat Transfer Coefficients for Various V ( ?T =8°C. De = 3 m. V = 0. 5 m )
This analytical CRCP theoretical account requires cognition of the overall heat transportation coefficient ( Uo ) . However. finding of Uo is non achieved explicitly since the infinite temperature ( Ta ) is by and large non the same temperature as the area-weighted mean temperature ( AUST ) of the surfaces exposed to the CRCPs. In rule. the entire heat flux ( qo ) is the summing up of the convective heat flux ( qc ) and the radiation flux ( qr ) . as shown in Equation 7a. and each heat flux can be expressed as Equation 7b and 7c. severally. qo = qc + qr Q degree Celsius = H degree Celsius ? ( T a – T autopsy ) Q R = H R ? ( AUST – Tpm )
( 7a ) ( 7b ) ( 7c )
Uo can be easy determined by summing the convective heat transportation coefficient ( hc ) and the radiant heat transportation coefficient ( hour ) . presuming Ta = AUST ; nevertheless. that premise is by and large non true. Therefore. in this work. the tantamount overall heat transportation coefficient ( Ue ) has been defined as follows: qo U vitamin E = ———————— ( T a – T autopsy )
By replacing Equation 7 into Equation 8. the concluding signifier of Ue becomes qc + qr ( AUST – T autopsy ) U e = ————————- = H degree Celsius + H R ? ———————————– . ( T a – T autopsy ) ( T a – T autopsy )
The radiant heat transportation coefficient ( Equation 10 ) found in the literature ( ASHRAE 2000 ) is h R = 5 ? 10
? [ ( AUST + 273 ) + ( T pm + 273 ) ] ? [ ( AUST + 273 ) + ( T pm + 273 ) ] .
The approximative look for AUST ( Kilkis et al. 1994 ) was used in this survey. AUST ? T a – vitamin D ? omega 7 omega ? when ( T oa – 45 )
( 11a ) ( 11b )
26°C ? Toa ? 36°C.
vitamin D = room place index with values as noted below: 0. 5 for an interior infinite. 1. 0 for a room with one outdoor exposed side with fenestration less than 5 % of the entire room surface country or 2. 0 for a room with fenestration greater than 5 % . and 3. 0 for a room with two or more outdoor exposed sides.
The tantamount overall heat transportation coefficient ( Ue ) defined in Equation 9 can be used in topographic point of the overall heat transportation coefficient ( Uo ) in the panel theoretical account ; nevertheless. Ue can non be determined explicitly because the average panel surface temperature ( Tpm ) is unknown. This unknown Tpm can be determined by work outing the panel theoretical account equations ( Equations 4 through 7 ) and Equation 9 for given boundary conditions iteratively. Once Ue and Tpm have converged. other measures. such as the panel chilling capacities ( qo. qc. and qr ) and heat transportation coefficients ( hc and hour ) can be determined.
CONVECTIVE AND RADIATIVE HEAT FLUX
The entire chilling capacity of the CRCP. when placed in the infinite illustrated in Figure 1. is presented in Figure 4. The panel heat transportation is strongly a map of air speed due to the increasing convective heat transportation. As may be noted. the radiative heat transportation is basically insensitive to the air speed since the panels operate with a really little H2O temperature rise. or a about changeless surface temperature. The convective heat fluxes calculated with the simplified correlativity and Awbi and Hatton’s correlativity closely agree. The rate of entire chilling sweetening by sing the assorted convection consequence is presented in Figure 5. It shows that the entire chilling capacity of a beaming panel can be enhanced dramatically by air gesture.
Panel chilling capacity is enhanced significantly when assorted convection is considered. However. when the diffusor discharge air speed is less than 2 m/s. the impact of assorted convection on the panel chilling capacity is little. Therefore. the correlativity for the natural convection heat transportation coefficient can be used to gauge panel chilling capacity alternatively of the assorted convection correlativity for low speeds.
HVAC & A ; R RESEARCH
Figure 5. Panel Cooling Capacity Enhancement The chilling panel capacity. when sing assorted convection. is enhanced 5 % to 35 % when the panel surface temperature is at typical design temperature. Consequently. applied scientists have been undervaluing the panel chilling capacity in automatically ventilated infinites by from 5 % to 35 % . Better design tools are expected to cut down the needed panel country and initial cost.
Fiscal aid from ASHRAE’s Grant-In-Aid plan is greatly appreciated.
Ap Cp De Fr hc hcf hcn hour M P qc qr = panel country. M2 = specific heat of the fluid. kJ/kg?K = characteristic diameter of room surface ( 4 Ac /P ) . m = panel heat removal factor = assorted convection coefficient. W/ m2? K = forced convection coefficient. W/ m2?K = natural convection coefficient. W/ m2?K = radiant heat transportation coefficient. W/ m2?K = mass flow rate to the panel. kg/s = parametric quantity of the room. m = convective heat flux to the panel. W/m2 = radiant heat flux to the panel. W/m2 qo Ta Tfi Tfo Tpm ?T Uo Ue V W = = = = = = sum reasonable heat flux to the panel. W/m2 room air temperature. °C panel recess unstable temperature. °C panel mercantile establishment unstable temperature. °C average panel surface temperature. °C temperature difference between the infinite and the panel average surface temperature. °C overall heat transportation coefficient. W/ m2?K equivalent overall heat transportation coefficient. W/ m2?K diffuser discharge air speed. m/s breadth of nozzle diffusor. m
ASHRAE. 2000. 2000 ASHRAE Handbook—HVAC Systems and Equipment. Atlanta: American Society of Heating. Refrigerating and Air-Conditioning Engineers. Inc. Awbi. H. B. . and A. Hatton. 1999. Natural convection from heated room surfaces. Energy and Buildings 30:233-244. Awbi. H. B. . and A. Hatton. 2000. Assorted convection from heated room surfaces. Energy and Buildings 32:153-166. Chen. Q. . C. Meyers. and J. V. D. R. Kooi. 1989. Convective heat transportation in suites with assorted convection. International Seminar on Indoor Air Flow
Forms in Ventilated Spaces. Feb. 1989. Liege. Belgium. pp. 69-82.
Conroy. C. L. . and S. A. Mumma. 2001. Ceiling beaming chilling panels as a feasible distributed parallel reasonable chilling engineering integrated with dedicated out-of-door air systems. ASHRAE Transactions 107 ( 1 ) : 578-585. DIN. 1997. Boom 4715. Cooling surfaces for suites ; Part 1: Measurement of the public presentation with free flow. Deutsches Institut pelt Normung. Fisher. D. E. . and C. O. Pedersen. 1997. Convective heat transportation in constructing energy and thermic burden computations. ASHRAE Transactions 103 ( 2 ) : 137-148. Hottel. H. C. . and A. Whillier. 1958. Evaluation of flat-plate aggregator public presentation. Trans. of the Conference on the Use of Solar Energy 2 ( 1 ) : 74. University of Arizona Press. Kilkis. B. I. . S. S. Sager. and M. Uludag. 1994. A simplified theoretical account for beaming warming and chilling panels. Simulation Practice and Theory 2 ( 2 ) : 61-76. Kochendorfer. C. 1996. Standard testing of chilling panels and their usage in system planning. ASHRAE Transactions 102 ( 1 ) : 651-658. Min. T. C. . L. F. Schutrum. G. V. Parmelee. and J. D. Vouris. 1956. Natural convection and radiation in a panel heated room. Heating Shrieking and Air Conditioning ( HPAC ) May: 153-160.