Research & Reviews: Journal of Engineering and Technology

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1 Research & Revews: Journal of Engneerng and Technology Case Study to Smulate Convectve Flows and Heat Transfer n Arcondtoned Spaces Hussen JA 1 *, Mazlan AW 1 and Hasanen MH 2 1 Department of Mechancal Engneerng, Unversty Technology, Malaysa 2 Machne and Mechancal Department, Unversty of Technology, Baghdad, Iraq Research Artcle Receved date: 02/11/2015 Accepted date: 16/11/2015 Publshed date: 25/11/2015 *For Correspondence Hussen JA, Department of Mechancal Engneerng, Unversty Technology, Malaysa E-mal: hussenutm@yahoo.com.my Keywords: Convectve flow, CHTC, Temperature feld, ACH. ABSTRACT In ths paper, three-dmensonal fnte-volume numercal procedure has been used to solve the convectve heat transfer coeffcent (CHTC) and temperature dstrbuton for two dfferent geometres of nternal room wth sde heated surfaces. A model room havng the sze of cm dmensons s consdered n ths smulaton. The temperature feld s determned for varous combnatons of ar-change per hour (5, 10, 15 and 20) and geometrcal parameters to show some of the flow feld characterstcs. INTRODUCTION Numerous theoretcal and expermental expressons amng at modelng the convectve heat exchange of buoyancy-drven flows along vertcal surfaces have been proposed. Ste phane Fohanno [1] developed a modelng of convectve heat transfer from nteror vertcal buldng surfaces subect to a unform heat flux densty. A smplfed relaton gvng the average convectve heat transfer coeffcent as a functon of the wall heght and the wall heat flux densty was proposed n order to be readly used n buldng smulaton. Lar [2] studed combned heat transfer of natural convecton and radaton n a 2D square cavty. The contnuty, momentum and energy equatons were solved by a fnte volume method to obtan the temperature, velocty and heat flux dstrbutons nsde the partcpatng medum. The heat transfer and flow characterstcs of the cavty were analyzed at a broad range of Raylegh numbers ( ) and optcal thcknesses (0 100). The results showed that the varaton n radatve Nusselt number wth optcal thckness s several tmes larger than that of convectve Nusselt number at the same Ra. Refet Karadag [3] determned the relaton between radatve and convectve heat transfer coeffcent at the celng for a cooled celng room of whch floor surface s solated. The room dmensons were dmensons (3 3 3, and m) and thermal condtons (Tc = 0-25ºC, Tw = 28-36ºC). The results showed that the ratos of radatve heat transfer coeffcents to convectve heat transfer coeffcents ncreases as the temperature dfferences ncrease. Petter Wallenten [4] measured the convectve heat transfer coeffcent at an outer ambent wall wth a wndow exposed to natural clmate n a room wth and wthout furnture. The convectve heat transfer was calculated as the dfference between the heat flow through the buldng element and the calculated long-wave radaton. T ref was chosen as the vertcal average n the mddle of the room. A flow responsve method was used by Ian Beausolel-Morrson [5] to advance the modellng of convectve heat transfer at nternal buldng surfaces. The algorthm dynamcally controls the modellng of convecton by assgnng approprate equatons to each nternal surface each tmestep of the smulaton. A new approach usng ESP-r smulatons was developed by Ian Beausolel-Morrson [6] to demonstrate the mxed convecton wthn mechancally ventlated rooms. ESP-r smulatons performed wth the mxed flow model ndcate that the predcton of heatng and coolng loads s hghly senstve to the treatment of surface convecton. Francesco Causone [7] evaluated the heat transfer coeffcents between radant celng and room n typcal condtons of occupancy of an offce or resdental buldng. In expermental results, a lttle hgher average value of the total heat transfer coeffcents was found of about 13.2 W m -2 K -1, for a cooled celng, compared to 11 W m -2 K -1 from the lterature. 19

2 Governng Equatons MATHEMATICAL MODEL The fundamental set of equatons that govern the flow of a flud are derved from Newton's second law. The equatons are called the Naver-Stokes equatons, and for ncompressble flud the full nstantaneous equatons take the form: ρu) ρu ρv) ρuv ρw) ρuw ) ρvu ) ρv ) ρvw ) ρwu ) ρwv ) ρw u u u = µ [ v v v = µ [ w w w = µ [ Where: ( u, v and w ) are the stream wse, lateral and vertcal velocty components respectvely,( x, y and z ) are the correspondng drectons to the velocty components, µ s the flud vscosty, ρ s the flud densty, p s the pressure. It s more compact to wrte equaton (1) to (3) n Cartesan tensor notaton as: ρu ) ρu u u u = [( )] Sb Where the suffxes and represent the three-co-ordnate drecton upon expanson back to equatons (1) to (3), S b are buoyancy source or snk terms and t s the tme. Conservaton Equatons for Scalar Property The conservaton equatons governng the dsperson of certan scalar propertes of the flow, such as enthalpy temperature, turbulence knetc energy K or turbulence dsspaton rate ε, have smlarty of form. They can therefore be represented by a sngle dfferental equaton for some general scalar property ( ) as follows: ρ) J =. ( ρu ) S (5) Where S represents a source or snk for, and J, s the dffuson n drecton. The form of the latter flux wll be dscussed below. The scalar property flux J, n equaton (5) can be related to gradent of velocty components and scalar propertes respectvely. In constant-property flows ths consttutve relaton s as follows [8] : µ J, = ( ) (6) σ Where µ and σ are the dynamc vscosty and Prandtl /Schmdt number of flud respectvely. Computatonal Detals Predcaton of ar flow and convectve heat transfer wthn an enclosure were performed numercally by solvng the conservaton laws whch expressed n terms of ellptc partal dfferental equatons by an teratve method. The ndependent varable of the problem are the three-component (x,y,z) of Cartesan Co-ordnate system. The man dependent varables are the u, v, w velocty components ( ), pressure (p), temperature (T), turbulent knetc energy (K) and ts dsspaton rate (ε ).By usng a lne-by-lne soluton technque n conuncton wth a tr-dagonal matrx algorthm (TDMA), all dependent varables were solved, and a three-dmensonal block adustment procedure also appled n a lne-by-lne manner was employed to ensure contnuty. The hybrd dfference scheme s used n the convectve terms and the ntegrated source term s lnear zed. Both these practces are wdely used to enhance numercal stablty. A grd of non-unform ntervals s employed wthn the calculaton doman n (x), (y) and (z) drectons wth the grd nodes concentrated near the walls and nlet and outlet grll. Boundary Condtons The boundary condtons of the sold boundary whch s used n the soluton for the present problem s that no-slp condton s appled on the velocty at all sx walls, and frcton s calculated by nvokng ''wall-functon ''. RESULTS AND DISCUSSION Numercal analyss based on fnte volume method s used to solve three dmensonal unsteady flows for two dfferent (1) (2) (3) (4) 20

3 geometres of nternal room wth sde heated surfaces. A model room havng the sze of cm dmensons wth two dfferent ar source poston s consdered n ths smulaton as shown n Fgure 1. The convectve heat transfer coeffcent and temperature dstrbuton for room wth two dfferent ar source postons are nvestgated. Fgure 1. Schematc dagram of the three confguratons (a) wall heatng wth near nput ar hole (b) wall heatng wth far nput ar hole. Heat Transfer Coeffcent (HTC) Fgure 2 shows the varaton of the heat transfer coeffcents wth the temperature dfference n geometry (a) at the 5 ACH for dfferent wall temperatures. It can be seen from the fgure that heat transfer coeffcents ncrease proportonal to the wall temperatures. By usng of the Fgure, a new correlaton for the heat transfer coeffcent has been developed as: CHTC=0.163*(T heater -T nlet ) Seres1, 26.65, 6.75 CHTC (W/m.k) Seres1, 22.4, 5.55 Seres1, 24.6, 6.38 ΔT=Theater - T nlet (oc) Temperature Dstrbuton Fgure 2. Flm coeffcent wth dfferent nlet temperature at (5 ACH) for geometry (a). Influence of ar change per hour (ACH) on the temperature profle s consdered at X = and X= m for two dfferent geometres of nternal room wth sde heated surfaces. In case of the ar source poston near the heated wall (geometry a), the warm ar can reach lower levels of temperature 21ºC at 20 ACH n X= m as shown n Fgure 3. As expected, the temperature n the central regon of X= m at 5 ACH assume low values about of 19ºC and the temperature dstrbuton are close to the end of regon at 20 ACH (Fgure 4). Fgure 3. Temperature maps for geometry (A) for dfferent flow rate at (X= ). 21

4 Fgure 4. Temperature maps for geometry (A) for dfferent flow rate at (X= ) a. In case of the ar source poston far away from the heated wall (geometry b), as foreseen, the range of temperature wthn the regon at X= m vares from 19ºC to 33ºC at 5 ACH and from 19ºC to 25ºC at 20 ACH as shown n Fgure 5. In the other sde, only the mddle porton of the regon at X= m wth 20 ACH s closed to the ntal condton of 21ºC whle the temperature dstrbuton range occurs near the edges of regon from 24ºC to 26ºC (Fgure 6). Fgure 5. Temperature maps for geometry (B) for dfferent flow rate at (X= ). Fgure 6. Temperature maps for geometry (B) for dfferent flow rate at (X= ). CONCLUSIONS The current work presents a model to predct the convectve heat transfer coeffcent (CHTC) and temperature dstrbuton n nternal room wth sde heated surfaces. The temperature feld s determned for varous combnatons of ar-change per hour. 22

5 From the results of program, the present computer program may be used to predct the flow patterns and the nternal and external convecton heat transfer coeffcents for complex flows. The authors declare that there s no conflct of nterests. CONFLICT OF INTERESTS REFERENCES 1. Ste phane F and Gullaume P. Modellng of natural convectve heat transfer at an nternal surface, Energy and Buldngs 2006; 38: Lar K, et al. Combned heat transfer of radaton and natural convecton n a square cavty contanng partcpatng gases, Internatonal Journal of Heat and Mass Transfer 2011; 54; Refet K. The nvestgaton of relaton between radatve and convectve heat transfer coeffcents at the celng n a cooled celng room, Energy Converson and Management 2009; 50: Petter W. Convectve heat transfer coeffcents n a full-scale room wth and wthout furnture, Buldng and Envronment 2001; 36: Beausolel MI. The adaptve smulaton of convectve heat transfer at nternal buldng surfaces, Buldng and Envronment 2002; 37: Beausolel MI. An algorthm for calculatng convecton coeffcents for nternal buldng surfaces for the case of mxed flow n rooms, Energy and Buldngs 2001; 33: Francesco C, et al. Expermental evaluaton of heat transfer coeffcents between radant celng and room, Energy and Buldngs 2009; 41: Durmuşa A and Daloğlu B. Numercal and Expermental Study of Ar Flow by Natural Convecton n a Rectangular Open Cavty: Applcaton n a Top Refrgerator, Expermental Heat Transfer, 2008; 21: Ths artcle was publshed under the specal ssue, Trends n engneerng and technologcal development:some recent advances handled by Edtor. Dr. Hu Pan, Unversty of Macau, Macao SAR 23