A Comparison of Correlations for Heat Transfer from Inclined Pipes

Transcription

1 A Comparion of Correlation for Heat Tranfer from Inclined Pipe Krihperad Manohar Department of Mechanical and Manufacturing Engineering The Univerity of the Wet Indie St. Augutine, Trinidad and Tobago Wet Indie Kimberly Ramroop Department of Mechanical and Manufacturing Engineering The Univerity of the Wet Indie St. Augutine, Trinidad and Tobago Wet Indie Abtract A review of literature on heat tranfer coefficient indicated very little work reported for cro-flow pipe arrangement at variou angle of inclination. In thi tudy forced airflow at 1.1 m/ and 2.5 m/ acro 2 teel pipe of diameter 0.034m and 0.049m were examined with pipe orientation inclined at 30 and 60 degree to the horizontal poition. A comparion of the experimentally determined N u and the conventional method uing exiting correlation for horizontal pipe in cro-flow howed that at 30 degree inclination, 1.1 m/, N u value were in good agreement. However, there were large difference at 60 degree inclination, 2.5 m/. Comparing experimental data with the correlation of Churchill, Zhukauka, Hilpert, Fand and Morgan howed that for 30 degree inclination the deviation from experimental N u at 1.1 m/ ranged from 2% to 18% and 2% to 8% for the 0.034m and 0.049m pipe, repectively, while at 2.5 m/ the deviation ranged from 12 % to 31% and 20% to 41% for the 0.034m and 0.049m diameter pipe, repectively. At 60 degree inclination the deviation from experimental N u at 1.1 m/ ranged from 19% to 45% and 27 % to 41% for the 0.034m and 0.049m pipe, repectively, while at 2.5 m/ the deviation ranged from 48% to 65% and 29% to 52% for the 0.034m and 0.049m diameter pipe, repectively. Keyword: Convective heat tranfer, Inclined pipe, Heat tranfer correlation. 1. INTRODUCTION In the tudy of thermodynamic the average heat tranfer coefficient, h, i ued in calculating the convection heat tranfer between a moving fluid and a olid. Thi i the ingle mot important factor for evaluating convective heat lo or gain. Knowledge of h i neceary for heat tranfer deign and calculation and i widely ued in manufacturing procee, oil and ga flow procee and air-conditioning and refrigeration ytem. The heat tranfer coefficient i critical for deigning and developing better flow proce control reulting in reduced energy conumption and enhanced energy conervation. Application of external flow forced convection heat tranfer coefficient range from the deign of heat exchanger and aircraft bodie to the tudy of forced convection over pipe. International Journal of Engineering (IJE), Volume: 4, Iue: 4 268

2 With the continued increae in deign complexity and the modernization of proce plant facilitie, the tudy of forced convection over cylindrical bodie ha become an important one [1]. By the formulation of correlation, which conit of dimenionle parameter, uch a elt number (), Reynold number (Re) and Prandtl number (Pr), for different geometrie, the value of h can be calculated without having to analyze experimental data in every poible convective heat tranfer ituation that occur. Dimenionle number are independent of unit and contain all of the fluid propertie that control the phyic of the ituation and involve one characteritic length. It i advantageou to preent data in the form of dimenionle parameter ince it extend the applicability of the data. However, correlation uing dimenionle number are developed for particular geometrie and ituation and are applicable within that range. Therefore, it i impractical to ue correlation developed for horizontal pipe to determine the h for inclined pipe. 2. PRESENTLY USED CORRELATIONS Preently there are many correlation to predict the heat tranfer from heated vertical or horizontal pipe in both forced and natural convection ituation. A review of literature on heat tranfer coefficient indicated that very little experimental work ha been done on inclined pipe in the recent pat with little or no concluive work reported for cro-flow pipe arrangement at variou angle of inclination. Generally, for deign purpoe cro flow correlation for horizontal pipe are being ued to determine heat tranfer coefficient for inclined orientation. Few correlation exit for inclined pipe with natural convection and none exit for inclined pipe in forced convection flow. Following i a brief overview of the mot common correlation that are being ued for a horizontal pipe in cro-flow. 2.1 Hilpert Hilpert [2] wa one of the earliet reearcher in the area of forced convection from heated pipe urface. He developed the correlation: hd D C Re m D k TABLE I. HILPERT S CONSTANTS FOR FORCED CONVECTION Re D C m , ,000-40,000, where the value of C and m, are given on Table I. Hilpert calculation were done uing integrated mean temperature value, not mean film temperature value, and with inaccurate value for the thermophyical propertie of air. The thermal conductivity value of air ued by Hilpert were lower (2-3%) than the mot recent publihed reult [3]. Thi reulted in the value of elt number calculated by the Hilpert correlation to be higher than they hould be. 1 3 Pr (1) International Journal of Engineering (IJE), Volume: 4, Iue: 4 269

3 2.2 Fand and Kewani Fand and Kewani [4, 5] reviewed of the work of Hilpert and recalculated the value of the contant C and m in equation 1 uing more accurate value for the thermophyical propertie of air. The contant propoed by Fand and Kewani are given on Table II. TABLE II. FAND S CONSTANTS Re D C m Zuakauka Another correlation propoed by Zukauka [6] for convective heat tranfer over a heated pipe wa f c Re m f Pr 0.37 f Pr f Pr w 0.25 (2) where the value of c and m are given on Table III. Except for Pr w, all calculation were done at the mean film temperature. TABLE III. ZUAKAUKAS CONSTANTS Re D C m (10) (10) Churchill and Berntein Churchill and Berntein [7, 8] propoed a ingle comprehenive equation that covered the entire range of Re D for which data wa available, a well a a wide range of Pr. The equation wa recommended for all Re D.Pr > 0.2 and ha the form Re + Pr Re D D 1 D + (3) , ( 0.4 ) + Pr Thi correlation wa baed on emi-empirical work and all propertie were evaluated at the film temperature. 2.5 Morgan Morgan [9] conducted an extenive review of literature on convection from a heated pipe and propoed the correlation hd D C Re m D k where the value of C and m are given on Table IV. 1 3 Pr 4 5 (4) International Journal of Engineering (IJE), Volume: 4, Iue: 4 270

4 3. EXPERIMENTAL PROCEDURE TABLE IV. MORGAN S CONSTANTS Re D C m Tet Apparatu A low velocity circular cro-ection wind tunnel wa deigned and built to experimentally determine h for circular pipe in cro flow arrangement at varying angle of inclination to the horizontal. The apparatu wa deigned to accommodate tet pecimen centrally acro the diameter of the wind tunnel a hown in Figure 1(a). The wind tunnel tet ection wa 1.5 m in diameter and 3 m long after which the tunnel wa tapered to a diameter of 1 m to accommodate the attachment of a 1 m diameter variable peed extractor fan, Figure 1(b). In thi arrangement the wind flowed tranverely acro the tet pecimen. The wind tunnel wa contructed from 3 mm thick galvanized teel heet and reinforced with an outer wooden frame. (a) (b) Figure1. Photograph of tet apparatu ceramic end of heater thermocouple heater power tubular teel pipe wire electric heater wooden end piece thermocouple thermocouple wooden mounting piece lead wire 0.1m 0.51m 0.51m 0.1m Figure 2. Schematic of tet pecimen 3.2 Tet Specimen Two tet pecimen of outer diameter m and m were prepared from tandard chedule 40 teel pipe. The tet pecimen were 1.22 m long with a 1.07 m long, m diameter electric International Journal of Engineering (IJE), Volume: 4, Iue: 4 271

5 tubular heater centrally located inide the pipe a hown in Figure 2. Six thermocouple were placed at the outer urface of the pipe. The thermocouple lead wire were paed through the annular pace and the thermocouple fixed at the pipe outer urface through hole drilled at the appropriate location. The tet piece were repectively centrally upended and rigidly fixed with the wooden mounting piece diagonally acro the wind tunnel at a ditance of 0.75 m from the leading edge. The circular ection tet chamber allowed the inclination angle of the tet pecimen to be varied eaily. 3.3 Temperature Meaurement The pipe urface temperature wa monitored with the Pico TC-08 data logger via K-type thermocouple. With K-type thermocouple the TC-08 ha a reolution of o C and an accuracy of 0.3% over the temperature range 120 o C to 1050 o C. The ix thermocouple were trategically located on the pipe urface a how in Figure 2. To check for uniform pipe urface temperature and urface temperature tability preliminary heating tet were conducted to verify the tet arrangement. Equilibrium condition were approached within 30 minute of heating and were verified by ubequently monitoring the ix thermocouple at 5 econd time interval for twenty minute. Equilibrium condition were taken a being etablihed when the variation in temperature reading from the ix thermocouple over a twenty-minute period wa within 0.75 %. The fluctuation with individual temperature reading were < 0.2 % over the equilibrium twenty-minute period. A plot of one et of temperature reading for the 0.034m and the 0.049m diameter pipe at 75 o orientation to the horizontal with no fan (zero air velocity) i hown on Figure Pipe urface temperature (deg. C) m φ pipe m φ pipe Thermocouple location along pipe (m) Figure 3. A plot of one et of temperature reading for pipe at 75 o orientation to the horizontal with no fan (zero air velocity). 3.4 Tet Procedure The peed of the extractor fan wa firt adjuted to provide the target air velocity in the wind tunnel. The electric heater wa then powered at 90 W. The power wa upplied and monitored by the MICROVIP MK1 energy analyzer. The accuracy of the primary meaurement (voltage and current) of thi intrument i 1%. The apparatu wa continuouly monitored (temperature reading were recorded at 5 interval) with preliminary meaurement to determine uniformly heated pipe urface, airflow tability and etablihment of equilibrium condition. After equilibrium, temperature reading were recorder for ten minute and the average value over thi ten-minute period calculated a the experimental reult for the tet. The power wa then witched off and the tet pipe allowed to cool to room temperature. Thi procedure wa repeated three time for each tet International Journal of Engineering (IJE), Volume: 4, Iue: 4 272

6 variation and the average of the three tet reult wa calculated and ued to determine the heat tranfer coefficient, h. 3.5 Tet Conducted For the m and the m diameter pipe tet were conducted at 0, 15, 30, 45, 60, 75 and 90 degree inclination to the horizontal for air flow velocitie of 0.00 m/, 0.80 m/, 1.35 m/ and 2.50 m/, for every cae. For each tet, after etablihing equilibrium condition, data for the pipe urface temperature, wind tunnel wall temperature, ambient air temperature, wind peed acro the tet pecimen and power to the heater were recorded. The repective experimentally determined heat tranfer coefficient, h, wa calculated for every cae and the elt number, N u, determined. 4. CALCULATIONS The meaured power input to the heater wa taken a the total heat lo from the pipe urface under equilibrium condition. The radiative heat lo component wa calculated and the convective heat lo component wa then determined from equation (5). The average heat tranfer coefficient, h, wa then calculated from the convective heat tranfer component of equation (5). Q total conv rad 4 4 ( T ) + DL ( T T ) Q + Q hπ DL T εσπ (5) The h wa then ued to determine the average elt number, Where hd k urr N u, from equation (6). o (6) N u average elt number h average heat tranfer coefficient (W/m 2 K) k thermal conductivity of fluid (air) (W/m.K) D 0 pipe outer diameter (m) The wa alo calculated for the correponding tet condition with the commonly ued correlation of Hilpert, Fand and Kewani, Zukauka, Churchill and Berntein, and Morgan. The calculated reult are given on Table V. 4.1 Experimental Uncertainty The experimental N u wa calculated from equation (6) uing the experimentally determined h from equation (5). The value of h depend on the meaured power (voltage and current) and meaured temperature value. From equation (5) and (6) the relationhip for the experimentally determined N u i given by equation (7). Q Q πdl( T T W εσ ( T T D ) k πdl( T T ) ) k total rad urr 1 (7) From the theory of uncertainty analyi [10, 11]the uncertainty in experimentally determined elt number,, from the relation in equation (7) i given by equation (8) International Journal of Engineering (IJE), Volume: 4, Iue: 4 273

7 W W + T T T + 4 T urr T W T T W T urr 5 (8) Alo, the error aociated with the power, W, i Where: W Voltage (V) X Current (I) W W V V I + I 1% +1% W Energy Meter Reading (W) V Voltage (V) I Current (A) T Surface Temperature ( o C) T urr Surrounding Temperature ( o C) T Ambient Air Temperature ( o C) Error aociated with W Error aociated with MICROVIP MK1 T Error aociated with Pico TC-08 For value of number i W W 2% and T T 0.3%, the uncertainty in experimentally determined elt W W T % + 10(0.3%) 5% T International Journal of Engineering (IJE), Volume: 4, Iue: 4 274

8 TABLE V. CALCULATED NUSSELT NUMBER m diameter pipe International Journal of Engineering (IJE), Volume: 4, Iue: 4 275

9 CALCULATED NUSSELT NUMBER m diameter pipe International Journal of Engineering (IJE), Volume: 4, Iue: 4 276

10 5. DISCUSSION The tet apparatu deigned for determination of h functioned on the fundamental principle of an energy balance when equilibrium condition were etablihed. Due to the lack of publihed data for mixed convective heat lo from inclined pipe comparion of the experimental finding with imilar publihed work wa limited. Under the circumtance, the experimentally determined wa compared with the calculated from the commonly ued correlation of Hilpert, Fand and Kewani, Zukauka, Churchill and Berntein, and Morgan on Table 5. For all tet condition the Morgan and Fand correlation yielded the ame. A comparion of the experimentally determined N u and the conventional method uing exiting correlation for horizontal pipe in cro-flow howed that at 30 o inclination, 1.1 m/, N u value were generally in good agreement. For thi condition the m and 0.049m diameter pipe howed maximum and minimum deviation of 18% and 1%, and 8% and 2%, repectively. The larget difference occurred with the 60 o inclination, 2.5 m/. For thi condition the m and 0.049m diameter pipe howed maximum and minimum deviation of 65% and 48%, and 52% and 29%, repectively. For the 30 o, 2.5 m/ condition the m and 0.049m diameter pipe howed maximum and minimum deviation of 31% and 12%, and 41% and 20%, repectively. For the 60 o, 1.1 m/ condition the m and 0.049m diameter pipe howed maximum and minimum deviation of 45% and 19%, and 41% and 27%, repectively. The reult on Table 5 indicate that a air velocity increaed, the difference between experimental value of N u and value obtained from the correlation for horizontal cylinder in cro-flow alo increaed. The experimental reult howed that a the angle of inclination increaed, the N u decreaed, indicating reduced overall heat tranfer from the urface a expected. However, the calculated value of N u from the publihed correlation do not how thi expected trend. Therefore, the ue of correlation developed for forced convection from horizontal pipe to calculate h for inclined pipe under forced airflow condition, epecially if the angle of inclination from the horizontal poition i large, will reult in erroneou reult. N u 6. CONCLUSIONS There i an urgent need for the formulation of correlation for convective heat tranfer under mixed flow condition with inclined pipe orientation. The tudy how that the ue of horizontal pipe correlation for calculating heat lo from inclined pipe orientation yield erroneou reult of ignificant magnitude. Deigner and engineer need to be guided when uing horizontal pipe correlation for incline pipe calculation a there may be ignificant error. 7. WORK IN PROGRESS At preent work i being done with pipe oriented at 15 o, 30 o, 45 o, 60 o, 75 o and 90 o to the horizontal. Tet are being conducted at three low peed air velocitie, to determine the effect of forced airflow on the heat tranfer from the urface of the inclined pipe. 8. REFERENCES 1. Jiheng Li and J. Tarauk. Local Free Convection Around Inclined Cylinder in Air: An Interferometric Study, Experimental Thermal and Fluid Science, 5: Hilpert, R. Heat Tranfer from Cylinder, Forch. Geb. Ingenieurwe, 4: Incropera F. and D. De Witt. Fundamental of Heat and Ma Tranfer, 5 th Edition, USA International Journal of Engineering (IJE), Volume: 4, Iue: 4 277

11 4. Fand, R. M. and K. K. Kewani. A Continuou Correlation Equation for Heat Tranfer from Cylinder to Air in Croflow for Reynold mber from 10-2 to 2(10) 5, International Journal of Heat and Ma Tranfer, 15: Fand, R.M. and K. K. Kewani. Recalculation of Hilpert Contant, Tranaction of ASME, pp Zukauka, A. Heat Tranfer From Tube in Croflow, Advance in Heat Tranfer, 8: Churchill, S.W. and H. H. S. Chu. Correlating Equation for Laminar and Turbulent Free Convection From a Horizontal Cylinder, International Journal of Heat And Ma Tranfer, 18: Churchill, S. W. and M. Berntein. A correlating Equation for Forced Convection from Gae and Liquid to a Circular Cylinder in Croflow, J. Heat Tranfer, 99: Morgan, V. Heat Tranfer from Cylinder, Advance in Heat Tranfer, 11: Manohar, K., Yarbrough, D. W. and Booth, J. R. Meaurement of Apparent Thermal Conductivity by the Thermal Probe Method, Journal of Teting and Evaluation, 28(5): Coleman, H. W. and Steller, W. G. Experimentation and Uncertainty Analyi for Engineer, 2 nd Ed., John Wiley and Son, New York, pp (1999). International Journal of Engineering (IJE), Volume: 4, Iue: 4 278