Simulation and optimisation of the ventilation in a chimney-dependent solar crop dryer

sa e , M aDepartment of Engineering, De Montfort University, Queens Building, The Gateway, Leicester LE1 9BH, UK b area ratio is around 4:1, above which the system then approaches saturation without any real variation. The drying-chamber roof incli- chimney-dependent solar crop dryer (CDSCD) showed that a solar chimney used in conjunction with angled roof of the drying chamber (the so-called tent-dryer eﬀect) can improve the ventilation through the dryer. Determining the opti- mum design conﬁguration that will ensure best ventilation for any particular application is essential for ensuring best ⇑ Corresponding author. Present address: Kumasi Polytechnic, PO Box 854, Kumasi, Ghana. Tel.: +233 540 743 551. E-mail addresses: [email protected] (J.K. Afriyie), hobina @dmu.ac.uk (H. Rajakaruna), [email protected] (M.A.A. Nazha), [email protected] (F.K. Forson). Available online at www.sciencedirect.com Solar Energy 85 (2011) nation and the chimney height are critical for the design in the geographical regions far from the equator, whereas the decisive parameters in the regions close to the equator are the drying chamber height and the area ratio of the dryer ﬂoor to chimney cross section. A high drying chamber with a short solar chimney is generally favoured at locations close to the equator, whereas a short drying chamber with a high solar chimney is suitable for regions far away from the equator. � 2011 Elsevier Ltd. All rights reserved. Keywords: Natural ventilation; Solar chimney; Simulation code 1. Introduction Natural convection solar crop dryers are reported to per- form poorly due to low ventilation in the dryers, especially the direct-mode type with no air preheating device (Ekechukwu, 1999). However, recent accounts on chimneys suggest that heated chimneys can improve the ventilation in a room (Bansal et al., 2004; Chen et al., 2003; Ekechukwu and Norton, 1997; Ferreira et al., 2008). A recent investiga- tion carried out by the authors (Afriyie et al., 2009) on a Department of Engineering Systems, Faculty of Engineering, Science and the Build Environment, London South Bank University, Borough Road, London SE1 0AA, UK cDepartment of Mechanical Engineering, Faculty of Mechanical and Agricultural Engineering, College of Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana Received 29 June 2009; received in revised form 7 March 2011; accepted 19 April 2011 Available online 11 May 2011 Communicated by: Associate Editor I. Farkas Abstract As published earlier on the performance of a chimney-dependent solar crop dryer (CDSCD) designed by the authors, the solar chim- ney can be combined with an appropriately inclined roof of drying chamber for ventilation improvement in the dryer. Mathematical models and a computer code are now developed to simulate the ventilation in relation to the design of the CDSCD. This is done for situations without any crop (no-load) in the dryer, to relate the ventilation to the external dimensions. The pressure-loss and bulk-ﬂuid-temperature coeﬃcients are deduced empirically from trials on the physical model. The simulation code predicts the ventila- tion to within 5% and the temperatures to within 1.5% of observed data, conﬁrming the validity of the code as an eﬀective design tool for the CDSCD. Results of parametric studies performed with the code indicate that, maximum airﬂow can be achieved when the inlet-exit Simulation and optimi in a chimney-depend J.K. Afriyie a,⇑, H. Rajakaruna a 0038-092X/$ - see front matter � 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2011.04.019 tion of the ventilation nt solar crop dryer .A.A. Nazha b, F.K. Forson c www.elsevier.com/locate/solener 1560–1573 J.K. Afriyie et al. / Solar Energy 85 (2011) 1560–1573 1561 Nomenclature A characteristic area (m2) cp speciﬁc heat capacity of air (J/kg K) Cp the wind pressure coeﬃcient g acceleration due to gravity (m/s2) Gr Grashof number h convection heat transfer coeﬃcient (W/m2 K) hr radiation heat transfer coeﬃcient (W/m 2 K) H characteristic height (m) I irradiation (W/m2) k thermal conductivity (W/m K) K pressure resistance coeﬃcient to the airﬂow L characteristic length (m) _m air mass ﬂow rate (kg/s) Nu Nusselt number performance. A design tool capable of arriving at this opti- mum will also be a standard ensuring against proliferation of inappropriate and ineﬃcient structures that might emerge due to the fact that CDSCD type dryers are cheap and easy to construct. Such a standard design tool can be developed using modelling and simulation procedures. Ventilation simulations available so far have generally been for solar chimneys of uniform cross-section, either alone or on top of a structure (Gan, 1998; Sakonidou et al., 2008), embedded in a wall (Marti-Herrero and Heras-Celemin, 2007; Mathur et al., 2006), window (Chantawong et al., 2006) or roof (Aboulnaga, 1998; Chung- loo and Limmeechokchai, 2009). The current study, how- ever, combines the vertical chimney of uniform cross- section in series with the inclined roof of the drying chamber. The model developed therefore accounts for the heating eﬀects in the structure and incorporates the roof angle, inlet to exit and dryer-ﬂoor to chimney-cross-section area ratios. Pb base (ﬂoor) perimeter (m) Pr Prandtl number q00 heat ﬂux to the chimney air (W/m2) Q heat transfer to the air in the drying chamber (W) Ra Rayleigh number S radiant heat ﬂux absorbed by a surface (W/m2) T absolute temperature of air (K) U overall heat transfer coeﬃcient (W/m2 K) V local wind speed (m/s) v air velocity (m/s) W uniform width of the chimney and drying cham- ber (m) a absorptivity of a surface b air thermal expansion coeﬃcient = 1/T (1/K) c mean temperature approximation constant for the air bulk e emissivity of surface h roof tilt angle to the vertical plane (�) q air density (kg/m3) r Stefan–Boltzman constant (W/m2 K4) s transmittance of glazing DH diﬀerence in height between dryer inlet and out- let (m) DProof pressure drop at the roof DT diﬀerence in temperature between dryer inlet and outlet (K) Dw wall thickness (m) Subscripts a atmospheric air 2. Simulation model 2.1. The airﬂow model Fig. 1 shows a schematic side view of the functional archi- tecture of the CDSCD. Air enters the dryer through the bot- tom inlet, absorbs energy from the drying chamber, encounters the inclined roof and enters the solar chimney where it is heated again by the chimney absorber before it exits into the environment. The air is heated in the chimney to maintain a higher temperature inside the solar chimney than in the drying chamber. This makes the chimney air less dense than the air in the drying chamber, to enhance the ﬂow of air up the whole structure. The CDSCD has uniform width from the base to the top. The current modelling pro- cess examines the structure under no-load conditions (i.e. without any crop in the dryer) to investigate the dependence of ventilation on the external design features of the CDSCD. b drying-chamber base c chimney cover (glazing) ch chimney ch, f chimney air ch, i chimney inlet dc drying-chamber glazing dc, f drying-chamber air f air in the dryer f–c, p–c, etc. for energy interaction between air and chimney glazing, or between the absorber and the glazing, etc. i dryer inlet o dryer outlet p chimney absorber plate roof drying-chamber roof s sky vw vertical walls of the drying chamber ney ner airﬂow through the system is (Afonso and Oliveira, 2000; Ekechukwu and Norton, 1997; Incropera et al., 2007): qbgðT o � T iÞDH ¼ Kiq v 2 i þ DP roof þ Koq v 2 o : ð1Þ Assuming a complete displacement of air and neglecting friction along the walls, the buoyancy pressure equation for Fig. 1. Functional architecture of a chim 1562 J.K. Afriyie et al. / Solar E 2 2 The left-hand side (LHS) of the above equation is the buoyancy pressure head which is balanced on the right- hand side (RHS) by the various pressure resistances. The terms on the RHS are the pressure resistances due to con- traction, bending and expansion at inlet, contraction at the drying-chamber roof, and bending and contraction at out- let of the dryer respectively. Together with the principle of continuity, DProof becomes DP roof ¼ 1 2 Kroof _m2 qAbAch;i : ð2Þ The airﬂow model is derived from Eqs. (1) and (2) and rearranged with reference to exit conditions as vo ¼ 1ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Ki AoAi � �2 þ Kroof A 2 o AbAch;i þ Ko r ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ2bgDTDHp ð3Þ The numerator forms the driving force whilst the denomi- nator forms the resistance part of the model. Ventilation can be improved by either strengthening the driving force part or weakening the resistance part, or both. The mass ﬂow is _m ¼ qAovo ¼ 1ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Ki AoAi � �2 þ Kroof A 2 o AbAch;i þ Ko r qAo ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ2bgDTDHp ð3aÞ Taking the local wind eﬀect into account, the exit velocity and mass ﬂow rate become -dependent direct-mode solar crop dryer. gy 85 (2011) 1560–1573 vo ¼ 1ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Ki AoAi � �2 þ Kroof A 2 o AbAch;i þ Ko r ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ2bgDTDH þ Cpv2aq ð4Þ _m ¼ 1ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Ki AoAi � �2 þ Kroof A 2 o AbAch;i þ Ko r qAo ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ2bgDTDH þ Cpv2aq ð4aÞ Afonso and Oliveira (2000) suggest an average Cp value of 0.25. For a CDSCD of known dimensions, DT is calculated from To from the heating model. Ki, Kroof and Ko are deter- mined empirically, as explained in Section 2.4 (empirical relations). Neglecting pressure variations in comparison to temperature variations, from the drying chamber to the chimney, b is derived from Incropera et al. (2007) for the whole system for an ideal gas as b ¼ 1ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ T ch;f � T dc;f p ð5Þ 2.2. The heating models The following assumptions are made in formulating the heating models: The above relation is transformed in terms of the chimney bulk ﬂuid temperature Tch,f by using the bulk ﬂuid temper- ature relation (Hirunlabh et al., 1999; Ong, 2003; Ong and Chow, 2003) to T ch;f ¼ cch;f T o þ ð1� cch;f ÞT ch;i or T o ¼ T ch;f � ð1� cch;f ÞT ch;i cch;f : ð9Þ Eq. (8a) and (9) are combined and rearranged to give where q00 ¼ MchðT ch;f � T ch;iÞ; with Mch ¼ _mcpcch;f W chHch The subscripts f–c, p–c, etc. are used to denote the interac- tion between air and chimney glazing or chimney cover (f–c), or between the absorber plate and the cover (p–c), etc. These conventions have been used throughout the mod- Fig. 2. Schematic representation of the thermal circuits. (a) (Top) Thermal circuit for the chimney. (b) (Bottom) Thermal circuit for the drying chamber. ner and this is simpliﬁed using Fig. 2a, to Sp ¼ hp–f ðT p � T ch;f Þ þ hr;p–cðT p � T cÞ þ Up–aðT p � T aÞ ð7Þ Energy balance of chimney air (Tch,f); Energy received from absorber plate by convec- tion = energy stored by the air + energy lost to the cover by convection which is simpliﬁed with the help of Fig. 2a, to hp–f ðT p � T ch;f Þ ¼ q00 þ hf –cðT ch;f � T cÞ ð8Þ where q00W chHch ¼ _mcpðT o � T ch;iÞ 1. The air media within the structure are non-partici- pating in the radiant energy transmission. 2. The heat transfer processes are steady and one dimensional. 3. The glazing is opaque to the diﬀuse radiation from the chimney absorber and drying chamber base. 4. The dryer inlet and chimney inlet gaps are very small compared to other dimensions of the drying chamber, so that the drying-chamber walls together form a complete enclosure over the base. 5. The walls are isothermal. This sets a deﬁnite direc- tion for the one-dimensional heat ﬂow from the walls into the ﬂuid medium, as heat ﬂows perpen- dicular to an isothermal. 2.2.1. The chimney heating model The models for determining the chimney temperatures Tc, Tch,f and Tp are derived for steady-state energy bal- ances, considering that the chimney gap is very small in comparison to the width, as follows (Hirunlabh et al., 1999; Ong, 2003; Ong and Chow, 2003): Energy balance of chimney cover (Tc); Absorbed energy from irradiation + energy received from chimney ﬂuid by convection + radiant energy received from the absorber surface = energy lost into the surroundings and with the help of the thermal circuit diagram in Fig. 2a, this is simpliﬁed, using the respective terms, to Sc þ hf –cðT ch;f � T cÞ þ hr;p–cðT p � T cÞ ¼ Uc–aðT c � T aÞ ð6Þ Energy balance of chimney absorber plate (Tp); Absorbed energy from irradiation = energy lost by con- vection to the chimney ﬂuid + energy lost by radiation onto the chimney cover + energy lost through the chim- ney-absorber wall into the surroundings J.K. Afriyie et al. / Solar E or q00 ¼ _mcp W chHch ðT o � T ch;iÞ ð8aÞ gy 85 (2011) 1560–1573 1563 el formulations. Using the following substitutions and with the help of the thermal circuit diagram of Fig. 2b, ner the balance equation becomes AdcSdc þ hf�dcAdcðT dc;f � T dcÞ þ hr;b�dcAbðT b � T dcÞ ¼ Udc�aAdcðT dc � T aÞ ð13Þ Energy balance of the base or ﬂoor (Tb); Energy absorbed from irradiation = energy transferred to the drying-chamber air by convection + radiant energy transferred to the drying-chamber glazing + energy lost through the base to the surroundings which through the help of Fig. 2b, becomes AbSb ¼ Abhb–f ðT b � T dc;f Þ þ Abhr;b–dcðT b � T dcÞ þ AbUb–aðT b � T aÞ ð14Þ Energy balance of drying-chamber air (Tdc,f): Energy stored by the air = energy received by convec- tion from the base – energy lost by convection to the drying-chamber glazing Uc–a þ hr;p–c þ hf –c ¼ C1; hp–f þ hf –c þMch ¼ C2; hp–f þ hr;p–c þ Up–a ¼ C3; followed by these substitutions C1C2 � h2f –c ¼ D1 hf –chr;p–c þ C1hp–f ¼ D2 hr;p–cC2 þ hf –chp–f ¼ D3 hr;p–chp–f þ hf –cC3 ¼ D4 hf –cðSc þ Uc–aT aÞ ¼ E1 C1MchT ch;i ¼ E2 hf –cðSp þ Up–aT aÞ ¼ E3 hr;p–cMchT ch;i ¼ E4 solutions to the simultaneous Eqs. (6)–(8) for the chimney temperatures are obtained as T ch;f ¼ D4ðE1 þ E2Þ þ D2ðE3 � E4ÞD1D4 � D2D3 ð10Þ T p ¼ D1T ch;f � E1 � E2D2 ð11Þ T c ¼ C2T ch;f � hp�f T p �MchT ch;ihf�c ð12Þ 2.2.2. The drying-chamber heating model The drying-chamber models, for determining Tdc,f, Tdc and Tb are formulated for steady-state conditions as follows: Energy balance of glazing (Tdc); Energy absorbed from irradiation + energy received by convection from the drying-chamber air + radiant energy received from the drying-chamber base = energy lost to the surroundings 1564 J.K. Afriyie et al. / Solar E which simpliﬁes according to Fig. 2b to Q ¼ hb–f AbðT b � T dc;f Þ � hf –dcAdcðT dc;f � T dcÞ where Q ¼ _mcpðT ch;i � T iÞ so that the equation for the drying-chamber becomes _mcpðT ch;i � T iÞ ¼ hb–f AbðT b � T dc;f Þ � hf –dcAdcðT dc;f � T dcÞ: The above equation is transformed in terms of Tdc,f, using the bulk-ﬂuid temperature relations, into hf –dcAdcT dc � _mcpcdc;f þ hf –dcAdc þ hb–f Ab ! T dc;f þ hb–f AbT b ¼ � _mcp cdc;f T i ð15Þ where the bulk-ﬂuid relation is given as T dc;f ¼ cdc;f T ch;i þ ð1� cdc;f ÞT i or T ch;i ¼ T dc;f � ð1� cdc;f ÞT i cdc;f : ð16Þ The subscripts f–dc, b–dc, etc. denote the interaction be- tween air and drying-chimney glazing (f–dc), or between the drying-chamber base absorber and the drying-chamber glazing (b–dc), etc. After rearranging the above equations with the follow- ing primary substitutions F 1 ¼ hf –dcAdc; F 2 ¼ _mcpcdc;f þ hf –dcAdc þ hb–f Ab; F 3 ¼ hb–f Ab G1 ¼ hf –dc þ hr;b–dc AbAdc þ Udc–a; G2 ¼ hr;b–dc Ab Adc ; H 1 ¼ hb–f þ hr;b–dc þ Ub–a; and then with the following secondary substitutions J 1 ¼ G1F 2 � F 1hf –dc; J 2 ¼ F 1G2 þ G1F 3; J 3 ¼ F 1hb–f þ F 2hr;b–dc; J 4 ¼ F 1H 1 þ F 3hr;b–dc K1 ¼ F 1ðSdc þ Udc–aT aÞ; K2 ¼ G1 _mcpcdc;f T i; K3 ¼ F 1ðSb þ Ub–aT aÞ; K4 ¼ hr;b–dc _mcpcdc;f T i solutions to the simultaneous Eqs. (13)–(15) are obtained as T dc;f ¼ J 4ðK1 þ K2Þ þ J 2ðK3 � K4ÞJ 1J 4 � J 2J 3 ; ð17Þ T b ¼ J 1T dc;f � K1 � K2J 2 : ð18Þ _mcp gy 85 (2011) 1560–1573 T dc ¼ F 2T dc;f � F 3T b � cdc;f T i F 1 ð19Þ hr;dc–a ¼ redcðT dc þ T sÞðT 2dc þ T 2s ÞðT dc � T sÞ=ðT dc � T aÞ ner 2.2.3. Heat transfer coeﬃcients The various heat transfer coeﬃcients for the chimney and drying-chamber heating models are deﬁned below. 2.2.3.1. Chimney heat transfer coeﬃcients. Uc–a ¼ hr;c–a þ hc–a ð20aÞ where hr;c–a ¼ recðT c þ T sÞðT 2c þ T 2s ÞðT c � T sÞ=ðT c � T aÞ: ð20bÞ T s ¼ 0:0552T 1:5a ð20cÞ from Ong (2003). A number of models have been proposed for the wind induced heat transfer coeﬃcient between the wall surface and the surroundings as noted by Duﬃe and Beckman (2006). But there is no well established model that is appli- cable to all situations. However, in situations similar to the current study, one equation that has been used on a num- ber of occasions with acceptable results is (Ong, 2003; Ong and chow, 2003) hc–a ¼ 5:7þ 3:8V ð20dÞ From the assumptions 1–3 in Section 2.2, the radiation heat transfer coeﬃcient between the chimney absorber plate and the cover is given by hr;p–c ¼ rðT p þ T cÞðT 2p þ T 2cÞ 1 ep þ 1ec � 1 ; ð20eÞ based on Duﬃe and Beckman (2006), Incropera et al. (2007) hf –c ¼ kf –cNuf –cHch ð20fÞ hp–f ¼ kp–f Nup–fHch : ð20gÞ For both the chimney absorber and glazing (Incropera et al., 2007) Nu¼0:68þ 0:67Ra 1=4 1þ 0:492Pr � �9=16h i4=9 ; for laminar flow ðRa < 109Þ Nu¼ 0:825þ 0:387Ra 1=6 1þ 0:492Pr � �9=16h i8=27 8>< >: 9>= >; 2 ; for turbulent flow ðRa > 109Þ ð20hÞ where e.g. Rap–f = Grp–fPrp–f, Grp–f ¼ gbp–f ðT p�T f ÞH 3 ch m2p–f ; Prp–f ¼ cp;p–f lp–fkp–f . The physical properties of air are related to the surface- ﬂuid mean ﬁlm temperatures, e.g. Tp–f = (Tp + Tf)/2, using J.K. Afriyie et al. / Solar E the handbook data range of 300–350 K (Ong, 2003; Ong and chow, 2003) as; ð21bÞ hdc–a ¼ 5:7þ 3:8V ð21cÞ With the assumptions 1–4 in Section 2.2, the radiation heat transfer coeﬃcient between the drying-chamber base and the wall enclosure is given by hr;b–dc ¼ rAb ðT b þ T dcÞðT 2b þ T 2dcÞ 1�eb ebAb þ 1Ab þ 1�edc edcAdc ð21dÞ (Duﬃe and Beckman, 2006; incropera et al., 2007) hb–f ¼ kb–f Nub–fL ; ð21eÞ Nub�f ¼ 0:54Ra1=4b–f ð104 6 Rab–f 6 107Þ ð21fÞ Nub–f ¼ 0:15Ra1=3b–f ð107 6 Rab–f 6 1011Þ ð21gÞ L ¼ Ab Pb ; Rab–f ¼ Grb–f Prb–f ; Grb–f ¼ gbb–f ðT b � T dc;f ÞL 3 m2b–f ; Prb–f ¼ cb–flb–f kb–f hf –dc ¼ hf –vwAvw þ hf –roof AroofAdc ð21hÞ lp–f ¼ ½1:846þ 0:00472ðT p–f � 300Þ� � 10�5 qp–f ¼ 1:1614� 0:00353ðT p–f � 300Þ kp–f ¼ 0:0263þ 0:000074ðT p–f � 300Þ cp;p–f ¼ 1:007þ 0:00004ðT p–f � 300Þ � �� 103 bp–f ¼ 1 T p–f ; mp–f ¼ lp–f qp–f ; ap–f ¼ kp–fqp–f cp–f ; etc: The above relations, based on the pivot temperature of 300 K, are also valid for temperatures just below 300 K. Up–a ¼ 1Dwp kp þ 1hp–a ; ð20iÞ with hp–a calculated similar to hc–a in (20d). The total radi- ation Ich onto the chimney collector surface may come in various proportions of direct, diﬀuse and reﬂected (either from the ground or neighbouring surfaces). It may be given as the monthly, daily or hourly average total radiation. Those absorbed by the chimney collector and absorber sur- faces at any instance are respectively Sc ¼ acIch ð20jÞ and Sp ¼ scapIch ð20kÞ 2.2.3.2. Drying-chamber heat transfer coeﬃcients. Udc–a ¼ hr;dc–a þ hdc–a ð21aÞ gy 85 (2011) 1560–1573 1565 where Adc = Avw + Aroof. For the vertical walls of the dry- ing chamber, ¼ gbf –dcðT dc � T dc;f ÞHdc and Pr ¼ cp;f –dclf –dc : the drying chamber. The physical model has three diﬀerent replaceable roofs positioned at angle 81�, 64� and 51� respectively, with respect to the vertical plane. One of three sheets of diﬀerent widths is used to cover part of the dryer inlet so that the experiment could be conducted for inlet gap 0.03 m, 0.05 m or 0.07 m. The walls of the chamber consisted of a glazing material (Lexan sheet). The chimney is of rectangular cross-section of width 440 mm, uniform gap 80 mm and height 625 mm. The exit had a gap of 30 mm, a straight width of 335 mm and rounded ends of 15 mm radius. Like the drying chamber, the normal chimney was all-round glazed, except the back wall which was constructed of wood with the inner surface painted black to serve as chimney absorber for heating the air in the chimney. 2.3.2. Instrumentations setup nergy 85 (2011) 1560–1573 m2f –dc f –dc kf –dc The physical properties of air are evaluated as in Eqs. (20). For the inclined roof facing downwards with h from 0 to 60�, hf–roof is determined by replacing g with gcosh and Hdc with Hroof in the Grf–dc equation (Incropera et al., 2007). For h above 600, the Grf–dc is interpolated between 60� and 90� as information for that range is lacking. Ub–a ¼ 1Dwb kb þ 1hb–a ð21kÞ with hb–a calculated similar to hdc–a in Eq. (21c). Similar to Eqs. (20j) and (20k), the radiant energy absorbed by the drying-chamber glazing and base absorber surfaces at any instance are respectively Sdc ¼ adcIdc ð21lÞ and Sb ¼ sdcabIdc ð21mÞ 2.3. Physical experiments Experiments have been performed physically on a labo- ratory model to obtain the necessary data to help establish the relations that are empirical to this particular structure and also to obtain more data to be used to validate the results of the modelling process. 2.3.1. The laboratory model of the dryer A laboratory model of a direct-mode dryer was designed and constructed with three replaceable drying-chamber roofs, each at a diﬀerent angle with respect to the vertical plane. Roof angles 81� (close to that of a cabinet dryer), 64� and 51� were used. The width of the drying chamber was 440 mm (normal to the airﬂow) and the length was 420 mm. The total height of the chamber was 530 mm. hf –vw ¼ kf –dcNuf –dcHdc ð21iÞ Nuf –dc ¼ 0:68þ 0:67Ra1=4f –dc 1þ 0:492Prf –dc � �9=16 4=9 ; for laminar flow ðRaf –dc < 109Þ Nuf –dc ¼ 0:825þ 0:387Ra1=6f –dc 1þ 0:492Prf –dc � �9=16 8=27 8>>>< >>>: 9>>>= >>>; 2 ; for turbulent flow ðRaf –dc > 109Þ ð21jÞ Raf –dc ¼ Grf –dcPrf –dc; Grf –dc 3 1566 J.K. Afriyie et al. / Solar E The base of the chamber was made of wood (40 mm thick) with the top surface painted black to serve as absorber in Eight infra red lamps (each 100 W) are set up in front over the structure to illuminate the chimney and drying chamber, to simulate the irradiation from the sun. The irra- diation onto the surfaces is measured by a pyranometer (Kipp and Zonen “Compensated Moll Thermopile”, type CA 1 No. 754379) connected to a micro-galvanometer (type AL 4, with ±1% accuracy at full-scale deﬂection). Measurements are taken at 15 points on the chimney sur- face and at 12 points on the drying-chamber surfaces, and the readings (in mV) are averaged out for each surface. The mean incident radiation in W/m2 on a surface is com- puted from the manufacturer’s formula in the form: I ¼ ð44:6þ rXÞ rX V v Sf where rX is the internal resistance of the micro-galvanome- ter in ohms, Vv is the scale voltage reading in milli-volts, and Sf is the thermopile sensitivity factor (corresponding to the aperture of the instrument). The correction factor for Kipp and Zonen instruments, based on the inclination Fig. 3. Schematic diagram showing the positions of temperature-measur- ing sensors. A FORTRAN computer code is developed to provide ner where Ddc ¼ 2gbdcDT dcHdc; Dch ¼ 2gbchDT chHch: A method of trial and error is used with assumed values of Ki in Eq. (22), together with measured data from the physical experiments. For each angle, the Kroof values hap- pen to be most closely consistent with Ki = 1.9, for all the drying-chamber inlet gaps. This Ki value gives an inlet ﬂow coeﬃcient (which is the square root of the reciprocal of Ki) of 0.72. This is just slightly above the approximate ﬂow coeﬃcient of 0.7 obtained by Flourentzou et al. (1998), for a similar inlet design. Substituting for Kroof values in Eq. (23) for all the conﬁgurations results in an averagely consistent Ko of 1.28. The Kroof values however follow the relation 2.4. Empirical relations For the pressure coeﬃcients, the buoyancy equation is applied separately to the chimney and the drying chamber. The respective ﬁnal equations are Kroof ¼ AbAch;i A2i ðDdc v2i � KiÞ ð22Þ Ko ¼ Dchv2o � Kroof A 2 o AbAch;i ð23Þ of the surface, lies around unity, with deviations as small as 0.5% and below, for the inclination angles between 0�and 90� (Duﬃe and Beckman, 2006). As shown in Fig. 3, two thermocouple probes (type K; range 0–200 �C) are positioned in the air stream along the height of the chimney (one probe at chimney inlet and one in the middle) to measure the air temperature at these heights. Three similar probes are spread at various heights in the drying chamber. Also, similar probes are each attached to the chimney absorber and glazing at the inlet, middle and exit levels of the chimney and at the base of the drying chamber. Inlet and exit velocities are mea- sured with a hand-held anemometer (type TA 400; range 0–2 m/s, logarithmic scale). 2.3.3. Tests overview Trials are conducted in turns for a given roof angle of drying chamber and a given inlet gap. All the three gaps (0.03 m, 0.05 m and 0.07 m) are tried one after the other for each of the three roof angles (81�, 64�and 51�) so that a total of nine experiments are performed in the physical trials. In each experiment, the lamps are switched on over the structure and the data are taken hourly at various points, for a 5-h steady-state period. Fluctuations from environmental conditions are evened out by using average values in these periods. J.K. Afriyie et al. / Solar E Kroof ¼ 11:233 � h2 � 19:522 � hþ 8:7662 ð24Þ solutions to the mathematical models. As can be seen from the models, the temperatures, airﬂow and heat transfer coeﬃcients are mutually dependent; therefore, an iterative procedure is used for their determination with initial guesses of the temperatures, as outlined in Fig. 4. 3.2. Validation of the simulation code In order to gain conﬁdence in the simulation code as a tool for predicting the ventilation performance of the dryer, a validation process is performed to ascertain the accuracy of the code within acceptable limits. Results recorded from experimentations on the physical structure are compared with those predicted by the simulation code, using the dimensions of the dryer and the pertaining exper- imental conditions as input to the code. Causes of any wide deviation between the recorded and simulated values are examined for adjustments to be made where necessary. For the physical trials, the chimney and drying-chamber bulk ﬂuid temperatures are determined from the averages of the values recorded at various positions in the chimney and drying chamber respectively. These average values are conﬁrmed with those obtained using Eqs. (9) and (16). The same dimensions and the prevailing environmen- From the second-order polynomial relations established after plotting the recorded temperatures T against their heights h in both the chimney and drying chamber, the bulk temperatures Tch,f and Tdc,f are determined from the relation T f ¼ R H 0 Tdh H ¼ a 3 H 2 þ b 2 H þ c ð25Þ The constants a, b and c are obtained from the various h–T curves. From Eqs. (9) and (16), the relations of cch and cdc to inlet and outlet temperatures of the chimney and drying chamber become respectively cch ¼ T ch;f � T ch;i T o � T ch;i : ð26Þ cdc ¼ T dc;f � T i T ch;i � T i ð27Þ The calculated cch averages at 0.756 for all the drying chamber conﬁgurations; not so much diﬀerent from the 0.74–0.75 found experimentally and used by earlier researchers (Hirunlabh et al., 1999; Ong, 2003; Ong and Chow, 2003). But cdc is found to relate to h as cdc ¼ �0:3856h2 þ 1:084h� 0:0844 ð28Þ 3. Discussions 3.1. The computer simulation code gy 85 (2011) 1560–1573 1567 tal conditions in the trials of the Physical CDSCD model have been used to run the simulation code. The general input simulation parameters are listed in the Appendix. eﬀect. A limiting factor, though, would be the chimney gap which needs to be limited to avoid reverse ﬂow in the solar chimney. According to Ong and Chow (2003), there is no reverse ﬂow for chimney gaps up to 0.3 m for radiation intensity values of 200–650 W/m2. Chen et al. (2003) Fig. 4. Flow chart for the simulation code; The equations used for each calculation are shown in brackets. RDm = |(Tm,nw � Tm)/Tm|; where nw denotes a newly recalculated value and m is one of the following: ch,f; c; p; dc,f; dc; b. 1568 J.K. Afriyie et al. / Solar Ener Table 1 compares the simulation results (headed Sim) with those recorded from physical trials (headed Phys) of the model. The simulation code predicts the temperatures to within 1.5% relative diﬀerence1 (RD). The deviations of the predicted velocities are slightly higher, generally within 5% RD, with the exceptional case of roof angle 81�and Inlet Gap 0.07 m having 7.2% RD. 3.3. Sensitivity analysis of the code outcome Diﬀerent inlet areas and roof angles have been used for the validation process. The RHS of an airﬂow model (Eq. (3)) has a numerator which is the driving force of the airﬂow and a denominator which forms the resistance part of the airﬂow. Selecting a particular roof angle gives rise to a given roof resistant coeﬃcient Kroof with opposing weights of the coeﬃcients of the angle and the square of the angle in Eq. (24). Kroof causes the resistance part to dictate the outcome of the airﬂow model. Setting the roof angle also sets the mean temperature approximation constant cdc, also with opposing weight of the coeﬃcients in Eq. (28). The knowl- edge of cdc is further used to determine the chimney inlet temperature Tch,i via Eq. (19), and then the exit temperature To through Eq. (9) and subsequently DT, which forms part of the driving force of the airﬂow model. Thus the roof angle tends to dictate the code outcome through a balance of the resistance part with Kroof and the driving-force part with DT. On the other hand, setting the inlet area Ai for a given outlet area Ao, with other parameters intact, tends to dictate the code outcome through the resistance part of the airﬂow model. The somehow high deviations between the velocity values predicted by the code and those recorded physically are generally attributable to the metallic frame- work of the laboratory CDSCD model which oﬀers some extra resistance to the air ﬂow. These extra ﬂow resistances, though signiﬁcant for the small size of the laboratory model, could not be accounted for by the simulation code. Also the physical processes do not necessarily go exactly by the assumptions made in formulating the heating models, and this could cause some prediction inaccuracies. For instance in reality, the air media within the structure could actually be participating in the radiant energy transmission. Further, the drying chamber does not form a complete enclosure over the base as assumed to make possible the use of Eq. (21d). Not every physical phenomenon could be considered in the mathematical model formulations. However, considering the generally small RDs, the resulting simulation code could be described as fairly accurate. Using dimensionless ratios rather than absolute dimensional val- ues, in various parametric studies could ensure consistent levels of accuracy for any structure that is dynamically sim- ilar to the current model. Better predictions are even expected on a large-scale dryer with minimised framework 1 The relative diﬀerence for the validation process is deﬁned as Sim�Phys Phys � 100%. gy 85 (2011) 1560–1573 reported that there is reverse ﬂow for chimney gaps larger than 0.4 m. T ab le 1 R es u lt s co m p ar is o n s o f S im u la ti o n (h ea d ed S im ) an d P h ys ic al tr ia ls (h ea d ed P h ys ); ea ch w it h th e re la ti ve d iﬀ er en ce R D b el o w it . R D = |( S im � P h ys )/ P h ys |� 10 0% . R o o f A n gl e 81 0 R o o f A n gl e 64 0 R o o f A n gl e 51 0 In le t G ap 0. 03 m In le t G ap 0. 05 m In le t G ap 0. 07 m In le t G ap 0. 03 m In le t G ap 0. 05 m In le t G ap 0. 07 m In le t G ap 0. 03 m In le t G ap 0. 05 m In le t G ap 0. 07 m T i /K 29 4. 00 29 5. 33 29 6. 00 29 4. 67 29 6. 83 29 5. 17 29 5. 17 29 7. 67 29 6. 50 S im P h ys S im P h ys S im P h ys S im P h ys S im P h ys S im P h ys S im P h ys S im P h ys S im P h ys T d c ,f /K 29 5. 89 29 9. 48 29 7. 04 29 8. 30 29 7. 64 29 8. 22 29 6. 40 29 9. 70 29 8. 40 29 9. 57 29 6. 64 29 6. 86 29 6. 71 30 0. 06 29 9. 06 29 9. 89 29 7. 82 29 7. 99 R D /% 1. 21 0. 42 0. 20 1. 11 0. 39 0. 08 1. 13 0. 28 0. 06 T b /K 30 2. 68 30 5. 00 30 3. 94 30 5. 17 30 4. 59 30 5. 50 30 3. 28 30 7. 00 30 5. 40 30 6. 83 30 3. 66 30 5. 33 30 3. 71 30 7. 67 30 6. 15 30 8. 17 30 4. 96 30 7. 17 R D /% 0. 77 0. 40 0. 30 1. 23 0. 47 0. 55 1. 30 0. 66 0. 72 T c h ,i /K 29 6. 79 30 2. 17 29 7. 85 29 9. 83 29 8. 42 29 9. 17 29 7. 38 30 2. 83 29 9. 28 30 0. 83 29 7. 46 29 7. 83 29 7. 86 30 3. 17 30 0. 08 30 1. 67 29 8. 79 29 9. 17 R D /% 1. 81 0. 67 0. 25 1. 83 0. 52 0. 12 1. 78 0. 53 0. 13 T c h ,f /K 29 9. 74 30 4. 22 30 0. 51 30 2. 78 30 0. 99 30 2. 97 30 0. 32 30 4. 03 30 1. 91 30 3. 63 30 0. 00 30 1. 37 30 0. 78 30 3. 82 30 2. 72 30 4. 28 30 1. 33 30 2. 66 R D /% 1. 50 0. 76 0. 66 1. 23 0. 57 0. 46 1. 01 0. 52 0. 44 T p /K 31 3. 72 31 4. 46 31 4. 83 31 3. 92 31 5. 42 31 4. 38 31 4. 30 31 5. 54 31 6. 24 31 4. 58 31 4. 47 31 3. 17 31 4. 79 31 6. 21 31 7. 02 31 6. 38 31 5. 85 31 5. 58 R D /% 0. 23 0. 29 0. 33 0. 39 0. 52 0. 42 0. 45 0. 20 0. 08 T c /K 31 1. 88 31 2. 54 31 3. 06 31 2. 38 31 3. 68 31 2. 31 31 2. 47 31 3. 48 31 4. 50 31 3. 10 31 2. 74 31 1. 08 31 2. 97 31 4. 27 31 5. 29 31 4. 77 31 4. 14 31 3. 56 R D /% 0. 21 0. 22 0. 44 0. 32 0. 44 0. 53 0. 41 0. 16 0. 18 T o /K 30 0. 67 30 4. 83 30 1. 35 30 3. 83 30 1. 80 30 4. 33 30 1. 25 30 4. 33 30 2. 74 30 4. 50 30 0. 80 30 2. 50 30 1. 70 30 4. 00 30 3. 55 30 5. 33 30 2. 13 30 3. 83 R D /% 1. 39 0. 83 0. 84 1. 02 0. 58 0. 56 0. 76 0. 59 0. 56 v o /m /s 0. 40 1 0. 39 0 0. 46 2 0. 44 0 0. 48 5 0. 45 0 0. 40 6 0. 40 3 0. 47 0 0. 45 0 0. 49 6 0. 48 8 0. 40 7 0. 39 8 0. 47 3 0. 47 2 0. 49 9 0. 51 7 R D /% 2. 77 4. 73 7. 18 0. 70 4. 31 1. 49 2. 05 0. 30 3. 48 J.K. Afriyie et al. / Solar Energ 3.4. Parametric studies and optimisation of the ventilation process In order to determine the optimum dimensions of the dryer for eﬀective ventilation, the airﬂow through the dryer is examined in relation to various design parameters of the dryer, under a given irradiation condition. The velocity at exit of the dryer is used as the indicator for the ventilation performance. In each parametric study, the simulation code is run a number of times with diﬀerent values of the parameter that is being examined, while all the other parameters, together with the irradiation values remain constant. The parameters studied are the drying-chamber roof angle, inlet-exit area ratio, chimney/drying-chamber height ratio and the drying-chamber-ﬂoor/chimney- cross-section area ratio. These are reviewed as follows: 1. Roof angle: trials are conducted for ten diﬀerent angles of inclination of the drying-chamber roof (i.e. roof inclinations from 40�to 85� with respect to the vertical plane). 2. Inlet-exit area ratio: this study is made up of trials for 19 diﬀerent inlet areas for a ﬁxed exit area. The ratios range from 1.1:1 up to 7.8:1. Beyond this ratio, some other parts of the design would need to be adjusted (i.e. some other parameter would need to change). 3. Chimney/drying-chamber height ratio: this parame- ter variations are of two kinds: i. The chimney height is varied for a constant drying-chamber height. Nine ratios are tested, ranging from 0.2:1 up to 1.8:1. ii. The total height of the dryer is kept constant so that the height of drying chamber reduces as the chimney height increases. The ratios range from 0.1:1 to 1.8:1 with seven trials. For a ratio beyond 1.8:1, some other design parameter would have to change. 4. Drying-chamber-ﬂoor/chimney-cross-section area ratio: this study has ten trials with diﬀerent dry- ing-chamber ﬂoor areas for a given chimney cross- sectional area in ratios from 5.0:1 to 7.25:1. Each parametric study consists of two airﬂow trials under diﬀerent external conditions; trial 1 and trial 2. Trial 1 inputs the same irradiation values (Ich = 390.78 W/m 2, Idc = 186.6 W/m 2) as those used for the above validation processes (see the Appendix). With higher irradiation on a vertical surface than a horizontal surface, this simulates an irradiation proﬁle of a geo- graphical area far from the equator. Trial 2 repeats all the parametric studies in trial 1, but the irradiation values on the chimney and drying chamber are interchanged to simulate the conditions of a location near the equator. y 85 (2011) 1560–1573 1569 The results of the parametric studies are shown in Figs. 5–8. Fig. 5 shows the dependence of the velocity on the roof tilt angle with respect to the vertical plane. Trial 2 (with higher radiation onto the horizontal base of the drying chamber than onto the vertical absorber of the chimney) records higher velocity values, even for high roof angles, than trial 1 (where the radiation values have been inter- changed). These results are attributable to the fact that, with regard to natural ventilation, a heated horizontal absorber surface is more eﬀective in transferring heat to maintain an upwards ﬂow or air than a vertical absorber surface. Comparing structures of similar dimensions at dif- ferent latitudes, the dryer near the equator makes more use of the drying chamber, with its horizontal base absorber, than the vertical chimney absorber. The reverse is the case for regions of high latitudes. Thus, the design seems to be more tolerant of higher roof angles in areas near the Fig. 5. Exit velocities vo for diﬀerent roof angles h of drying chamber for the two trials of diﬀerent irradiations. 1570 J.K. Afriyie et al. / Solar Energy 85 (2011) 1560–1573 Fig. 6. Exit velocities vo for diﬀerent inlet-exit area ratios Ai/A o of the CDSCD for the two trials of diﬀerent irradiations. ner J.K. Afriyie et al. / Solar E equator than in areas far away, as suggested by the curves of the two trials. The relationship between the inlet-exit area ratio and the velocity is plotted in Fig. 6. The velocity peaks around the area ratio 4:1, above which no real vari- ation is found as the system approaches saturation, regard- less of the irradiation scenario. An increase in the inlet area for a given exit area, with other dimensions still intact, rep- resents a lowering of the denominator or resistance side of the airﬂow model (Eq. (3)). This represents an increase in the exit velocity. On the other hand, as the inlet area increases, a higher mass ﬂow of air is allowed into the structure with velocity increases, and therefore resistance Fig. 7. Exit velocities for diﬀerence chimney/drying-chamber height ratios. (a) total height of dryer with varying ratios of chimney height to drying-chamber h in other parameters e.g. h. Fig. 8. Exit velocities for diﬀerent area ratios gy 85 (2011) 1560–1573 1571 increases, at various sections (see Eqs. (1) and (2)). Also, high mass ﬂow of air into the drying chamber tends to reduce the temperatures at various sections and therefore tends to reduce DT, and this causes a reduction in the driv- ing force of the airﬂow model. At some point (presumably above the ratio 4) the increased resistances at those sections and the reduced driving force tend to even out any eﬀect from the increase of inlet area with regard to velocity increase, giving rise to the saturation. Fig. 7 compares the eﬀects of two diﬀerent kinds of chimney/drying-cham- ber height ratios. In Fig. 7a the chimney height varies for a given drying-chamber height, whilst Fig. 7b has varying (Top) Using a ﬁxed height of drying chamber. (b) (Bottom) Using a ﬁxed eight; the next ratio after 1.7949 (i.e. for Hdc = 0.29) would require changes of dryer ﬂoor to chimney cross section. infra-red lamps m2 m Heiselberg, P., Li, Y., 2003. An experimental investigation of a ner height ratios of chimney to drying chamber for a ﬁxed total height of dryer. Fig. 7a shows an increase in the airﬂow as the chimney height increases. Increasing the chimney height for a ﬁxed drying-chamber height tends to increase both DH and DT in the airﬂow model, so that there is an increase in the velocity. This supports the assertion by Eke- chukwu and Norton (1997) that, for a given height of dry- ing chamber, there is no limit to the height of solar chimney for ventilation improvement. The velocity variations in the two trials follow similar trends. Fig. 7b shows velocity increase for increasing heights of the chimney with decreas- ing drying-chamber heights in trial 1. The results of trial 2 are opposite those of trial 1. With high chimney heights, the dryer is able to make better use of the high radiation falling onto the vertical surface, in trial 1. On the other hand, when the height of drying chamber is high, the roof of the chamber move up, enhancing the buoyancy and therefore the upward natural convection in the drying chamber, and this is more eﬀectively done when there is more radiation into the drying chamber as in trial 2. The two trials in Fig. 7b suggest that, for a ﬁxed total height of dryer, the airﬂow increases in areas far away from the equator (trial 1) for high chimneys with short drying cham- bers, but the situation is reversed at locations near the equator (trial 2). As shown in Fig. 8, the ventilation is improved by increasing the dryer ﬂoor area for a given chimney cross-section. Increasing the ﬂoor area enlarges the ﬂoor surface for both convection and radiation, boost- ing the buoyancy in the drying chamber. In each parametric study, the CDSCD does better in trial 2, suggesting that the system is more suitable in places near the equator than those far from the equator. Far away from the equator, the emphases of the design should be on the dry- ing-chamber roof inclination and the chimney height (see Figs. 5 and 7). Near the equator, the priority should be to increase the drying chamber height (Fig. 7b) and the area ratio of the dryer ﬂoor to chimney cross section (Fig. 8). 4. Conclusion Mathematical models and computer codes have been developed to simulate the ventilation of the CDSCD. The airﬂow and temperature predictions are generally within 5% and 1.5% respectively of the recorded data. The result- ing simulation code can therefore serve as an eﬀective tool for designing the CDSCD for optimum ventilation. Results of the parametric studies suggest that the drying-chamber roof inclination and the chimney height are critical in regions far from the equator, whereas in regions close to the equator the decisive parameters are the drying chamber height and the area ratio of the dryer ﬂoor to chimney cross section. A high drying chamber and a short chimney is favoured in a location near the equator, whereas a location far from the equator favours a short drying chamber with a high chimney. Finally, maximum ventilation can be 1572 J.K. Afriyie et al. / Solar E achieved for inlet-exit area ratios around 4:1, above which the system approaches saturation. solar chimney model with uniform wall heat ﬂux. Building and Environment 38, 893–906. Chungloo, S., Limmeechokchai, B., 2009. Utilization of cool ceiling with roof solar chimney in Thailand: The experimental and numerical analysis. Renewable Energy 34 (3), 623–633. Chen, Z.D., Bandopadhayay, P., Halldorsson, J., B Duﬃe, J.A., Beckman, W.A., 2006. Solar Engineerin Processes, third ed. John Wiley and Sons, Inc., Hobok yrjalsen, C., Win, M.M., 2006. Investigation on thermal performa solar chimney walls. Solar Energy 80, 288–297. nce of glazed ment 40 (10), 1302–1308. Chantawong, P., Hirunlabh, J., Zeghmati, B., Khedari, J., Teekasap, S., window-sized solar chimneys for ventilation. Building and Environ- Bansal, N.K., Mathur, J., Mathur, S., Meenaski, J., 2004 . Modelling of Afriyie, J.K., Nazha, M.A.A., Rajakaruna, H., Forson Experimental investigations of a chimney-dependent so Renewable Energy 34 (1), 217–222. lar crop dryer. ment. Energy and Buildings 32, 71–79. , F.K., 2009. Afonso, C., Oliveira, A., 2000. Solar chimneys: simulatio n and experi- Aboulnaga, M.M., 1998. A roof solar chimney assisted natural ventilation in buildings in hot arid climat conservation approach in Al-Ain city. Renewable Energ by cavity for es: an energy y 14, 357–363. References and drying-chamber base drying-chamber glazing Emissivity of chimney absorber 0.98 and drying-chamber base Emissivity of chimney and 0.66136 drying-chamber glazing Absorptivity of chimney absorber 0.98 drying-chamber glazing Absorptivity of chimney and 0.66136 from the infra-red lamps Transmissivity of chimney and 0.33864 Irradiation on drying-chamber glazing 186.6 W/ 2 Appendix. The general input parameters for the validation processes, either determined in the laboratory or assumed from generally accepted ﬁgures in the literature, are listed below: Dryer outlet area 0.01076 m2 Chimney gap 0.08 m Dryer width (uniform throughout the height of dryer) 0.44 m Chimney height 0.60 m Drying-chamber height 0.49 m Thickness of chimney-absorber wall (wood with cardboard back cover) 0.0121 m Thickness of drying-chamber base (wood) 0.04 m Length of drying-chamber base 0.42 m Thermal conductivity of chimney-absorber wall (wood with cardboard back cover) 0.1716 W/ mK Thermal conductivity of drying-chamber base (wood) 0.18 W/mK Irradiation on chimney glazing from the 390.78 W/ gy 85 (2011) 1560–1573 g of Thermal en, New Jersey. Ekechukwu, O.V., 1999. Review of solar-energy drying systems II: an overview of solar drying technology. Energy Conversion and Man- agement 40, 616–655. Ekechukwu, O.V., Norton, B., 1997. Design and measured performance of a solar chimney for natural circulation solar energy dryers. Renewable Energy 10 (4), 81–90. Ferreira, A.G., Maia, C.B., Cortez, M.F.B., Valle, R.M., 2008. Technical feasibility assessment of a solar chimney for food drying. Solar Energy 82, 198–205. Flourentzou, F., Van Der Maas, J., Roulet, C.A., 1998. Natural ventilation for passive cooling: measurement of discharge coeﬃcients. Energy and Buildings 27, 283–292. Gan, G., 1998. A numerical study of solar chimney for natural ventilation of buildings with heat recovery. Applied Thermal Engineering 18, 1171–1187. Hirunlabh, J., Kongduang, W., Namprakai, P., Khedari, J., 1999. Study of natural ventilation of houses by a metallic solar wall under tropical climate. Renewable Energy 18, 109–119. Incropera, F.P., De Witt, D.P., Bergman, T.L., Lavine, A.S., 2007. Introduction to Heat Transfer, ﬁfth ed. John Wiley & Sons, Inc., Hoboken, New Jersey. Marti-Herrero, J., Heras-Celemin, M.R., 2007. Dynamic physical model for a solar chimney. Solar Energy 81, 614–622. Mathur, J., Bansal, N.K., Mathur, S., Jain, M., Anupma, 2006. Experimental investigations on solar chimney for room ventilation. Solar Energy 80, 927–935. Ong, K.S., 2003. A mathematical model of a solar chimney. Renewable Energy 28, 1047–1060. Ong, K.S., Chow, C.C., 2003. Performance of a solar chimney. Solar Energy 74, 1–17. Sakonidou, E.P., Karapantsios, T.D., Balouktsis, A.I., Chassapis, D., 2008. Modeling of the optimum tilt of a solar chimney for maximum airﬂow. Solar Energy 82, 80–94. J.K. Afriyie et al. / Solar Energy 85 (2011) 1560–1573 1573 Simulation and optimisation of the ventilation in a chimney-dependent solar crop dryer 1 Introduction 2 Simulation model 2.1 The airflow model 2.2 The heating models 2.2.1 The chimney heating model 2.2.2 The drying-chamber heating model 2.2.3 Heat transfer coefficients 2.2.3.1 Chimney heat transfer coefficients 2.2.3.2 Drying-chamber heat transfer coefficients 2.3 Physical experiments 2.3.1 The laboratory model of the dryer 2.3.2 Instrumentations setup 2.3.3 Tests overview 2.4 Empirical relations 3 Discussions 3.1 The computer simulation code 3.2 Validation of the simulation code 3.3 Sensitivity analysis of the code outcome 3.4 Parametric studies and optimisation of the ventilation process 4 Conclusion Appendix References

Simulation and optimisation of the ventilation in a chimney-dependent solar crop dryer

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