Experimental Prediction of Nusselt Number and Coolant Heat Transfer Coefficient in Compact Heat Exchanger Performed with İ 178 Method

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1 Experimental Prediction of Nusselt Number and Coolant Heat Transfer Coefficient in Compact Heat Exchanger Performed with İ 78 Method A. R. Esmaeili Sany M.Sc. Graduated, Mechanical Engineering Department, Sharif University of Technology SAIPA Automotive Company M. H. Saidi Professor, School of Mechanical Engineering Sharif University of Technology, Tehran, Iran J. Neyestani M.Sc. Graduated, Mechanical Engineering Department, Sharif University of Technology SAIPA Automotive Company Corresponding Author* Received: Dec. 9,009 Accepted in revised form: Mar. 5,00 Abstract In this Study, radiator performance for passenger car has been studied experimentally in a wide range of operating conditions. Experimental prediction of Nusselt number and heat transfer coefficient for coolants in radiator tubes are also performed with İ 78 method. The total effectiveness coefficient of radiator and heat transfer coefficient in air side is calculated via trial and error method considering experimental data. The Colburn factor and pressure drop are also estimated for this heat exchanger. Examples of application demonstrate the practical usefulness of this method to provide empirical data which can be used during the design stage. Keywords: &RPSDFW +HDW ([FKQJHU +HDW 7UDQVIHU &RHHILFLHQW XVVHOW XPEHU İ 78 Method 6 The Journal of Engine Research/Vol. 8 / Spring 00

4 A New Approach for Inlet Diffuser of Automotive Catalytic Converter Considering Conversion Efficiency of Pollutants Effectiveness can be expressed as a function of 78, the capacity ratio and heat exchanger configuration: H H 78, Cr, )ORZ $UUDQJPHQW (8) 7KHUH DUH PDQ\ HTXDWLRQV IRU İ WKDW DUH REWDLQHG E\ GLIferent authors, but in real condition and for one row tube radiators, we can use equations (9) and (0): exp Cr. e 78 Cr H 78.C r ª e exp «Cr H Cmin CDLU Cmin CZDWHU (0) Pr 8 c $c t $h hh K K0 $c hc K0 X (3) I $ (0) I. Re E 000. PrE 0.5 I.7. Pr 3.58 ln Re E 3.8 () (4) A= surface area in which U is based. For a flat tube heat exchanger it can be shown that [8]: hc tanh.l (5) KG KI hc.l KG The most commonly used relationship for laminar flow (Re<300) is the correlation proposed by Seider and Tate in 936 [8]. 0.4 (6) Dh 3 PE X.86 Re. Pr.. L P Z Where, () To facilitate the comparison of different heat exchanger geometries, the heat transfer coefficient is normally made into a non-dimensional number using Stanton number, St, or Colburn factor, j, and compared at constant Reynolds number, Re [8]. St K I 4 u )ORZ $UHD Wetted 3HULPHWHU Modification to the Petukhov model, by Gnielinski using experimental data has extended the correlation to include the transitional range (300<Re<0000) where most automotive radiators operate [8]: And total surface efficiency, Ș $I (9) K Where fanning friction factor, f is given by [8]: () If we assume the fin efficiency,și, then equation () can be rewritten to give: 8 h $h (8) And c RW 8 o $o 8 L $L (7) h Prandtl number, Pr is defined as: P.CP Dh º» ¼ k P Where the overall heat transfer coefficient, U, comprises three separate resistances as shown in equation (): 8$ Reynolds number, Re is defined as: UX'h Re (9) The flow of heat from the hot coolant to the cold air, can be represented by Newton's Law of cooling as shown in equation (): () Q 8$ 7 7 h x X FRQYHFWLYH heat IOX[ IOXLG heat FDSDFLW\ rate hc U.X.C p (3) Colburn factor is defined as [8]: j St. Pr 3 (4) Using the following procedure, Colburn factor (j) can be determined: - For best accuracy select data for a coolant flow rate where Re> As the inlet and outlet temperatures and flow rates are known on both sides of the heat exchanger calculate effectiveness, could be calculated using equation (7). - Using the appropriate İ 78 relationship, 78, and using equation (5) 8$, could be calculated. - Using the Gnielinski correlation of equations () and The Journal of Engine Research/Vol. 8 / Spring 00 65

5 A.R. Esmaeli Sany / M.H. Saidi / J. Neyestani () the coolant side Nusselt number is obtained. - Then, in equation (7), Nusselt number is converted to heat transfer coefficient, hh. - Substitute for hh, $h, t and k into equation (5): 8$ t $h hh K K 0 $c hc 8 c $c (5) To give, 8$ k K 0 $c hc (6) Where constant k is given by: t $h hh K k (7) Substituting equation (4) into equation (7), gives equation (8). k 8$ $I K I hc $c $ (8) - Using the fin efficiency relationships equations of (4) and (5), we can solve fin efficiency, ȘI and air side heat transfer coefficient, hc. As fin efficiency is a function of heat transfer coefficient, the solution will be iterative. - Stanton Number can, then, be determined using equation (3) and Colburn factor using equation (4). Air-side pressure drop in radiator Following Kays and London results, air-side pressure drop can be calculated from the following relationship [8]: º G ªentrance effect flow acceleration. (9) core friction - exit effect»¼ g U L «'P ª º UL «K c G» U G «o» (30).» g UL «U $ UL «I U Ke L» U o ¼» $c U m «'P Error and accuracy analysis It is obvious that any empirical study has special errors, such as application, operating, environmental, dynamic and calculating. Type K thermocouples are more frequently used in indus- 66 The Journal of Engine Research/Vol. 8 / Spring 00 try. They are usually calibrated in the range 0 C to 00 C, with expanded uncertainty of ±.0 C up to 000 C. We calibrated all thermocouples with comparison method and repeatability of all instruments is examined. To notice response time error, we read all data after reaching 98 percentage of standard value. Reproducibility of procedures is other the criteria to be confidence of experimental data, and then we almost repeated any of exams for two times. We used all indicators with 0 times resolution higher than accuracy that we have accepted. For uncertainly analysis in equation, we can use the method below; R I x, x,..., x n ª wr wr º wr W R «u W u W... u Wn» «wx wx wx n»¼ wq wq C p.h 7hL 7ho, m h 7hL 7ho wm h wc p.h wq w7hl m h C p.h, wq w7ho m h C p.h For special test; m h OLW 60 r 5%, 7hL min 7ho 83 r $ C, C p.h W 0.0, W WRWDO XQFHUWDLQO\ 90 r $ C j 400 r 0.3% kg.k, W3, W 4 WR u % Q Indeed, the total uncertainly in radiator heat loss equation is 8.8%. Results and discussion At constant engine speed, increment of air flow in front of vehicle causes that temperature of the engine compartment air the reduced. Also, air velocity growth in this cavity affects heat transfer coefficient of engine body and raises the heat loss of the engine and other solid parts of this space. Fig. 4 shows the component of energy balance at 3000 rpm and 6 km/hr. The influence of engine speed on distribution of energy is presented in Fig. 5. Increment of engine speed decreases time of heat transfer and increases motion of cylinder gas which leads to engine heat transfer coefficient rising. Gas

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