ADVANCES in NATURAL and APPLIED SCIENCES

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1 ADVANCES in NATURAL and APPLIED SCIENCES ISSN: Published BY AENSI Publication EISSN: Special10(7): pages 1-8 Open Access Journal Temperature Distribution Studies along Thermal Boundary Layer and Effect of in Transistion Region for flow through a Concentric Tube Heat Exchanger 1 S. Santosh Kumar and 2 M.K. Muralidhara 1 Assistant Professor, Department of Mechanical Engineering RR Institute of Technology, Affiliated to Visvesvaraya Technological University, Bangalore, Karnataka, India. 2 Former Professor and Principal, Department of Mechanical Engineering RR Institute of Technology, Affiliated to Visvesvaraya Technological University, Bangalore, Karnataka, India. Received 25 April 2016; Accepted 28 May 2016; Available 5 June 2016 Address For Correspondence: S. Santosh Kumar, Assistant Professor, Department of Mechanical Engineering RR Institute of Technology, Affiliated to Visvesvaraya Technological University, Bangalore, Karnataka, India Kumars @gmail.com Copyright 2016 by authors and American-Eurasian Network for Scientific Information (AENSI Publication). This work is licensed under the Creative Commons Attribution International License (CC BY). ABSTRACT In the present study the experiments were conducted on forced convection heat transfer in transition region for flow through concentric tube heat exchanger. The heat exchanger was operated under counter-flow and single phase flow conditions. Temperature distribution was measured experimentally along the thermal boundary layer in the annulus space of the concentric tube heat exchanger using resistance temperature detectors in order to determine the thermal entrance region length in transition region. The was varied between 2500 and by varying the mass flow rate. The effect of in transition region was also investigated by varying the between 2500 and in the interval of 500 in order to arrive at a better correlation for determining the Nusselt number to acceptable levels in transition region. The experimental data obtained was compared with various empirical correlations available in literature. The correlation shows good accordance with measured data. KEYWORDS: Transition flow, Nusselt number,, Thermal entrance length, Thermal boundary layer INTRODUCTION Convective heat transfer analysis in transition region has considerable importance in design of heat exchangers due to uncertainty and flow instability in this region. Limited information is available with specific reference to heat transfer data in transition region. Due to flow non-uniformities in transition region, the thermal entrance region length can only be determined experimentally by measuring the temperature distribution along the thermal boundary layer. Empirical correlations are available for calculating Nusselt number in laminar and turbulent region under the influence of many factors such as pressure drop, different types of inlet configurations and entrance region. In order to design a efficient heat exchanger the thermal entrance region length and correlations to determine Nusselt number in transition region to acceptable levels needs to be addressed. To Cite This Article: S. Santosh Kumar and 2M.K. Muralidhara., Temperature Distribution Studies along Thermal Boundary Layer and Effect of in Transistion Region for flow through a Concentric Tube Heat Exchanger. Advances in Natural and Applied Sciences. 10(7); Pages: 1-8

2 2 S. Santosh Kumar and M.K. Muralidhara., 2016/ Advances in Natural and Applied Sciences. 10(7) Special 2016, Pages: 1-8 Studies made by V. Gnielinski [1], W. M. Kays and H. C. Perkins, [4] in the field of thermo-science and engineering states that the must be >10^4 for fully developed flow in the turbulent region. The transition from laminar to turbulent takes place between 2300<Re<10^4, As referred in D. Huber and H. Walter., [2] and N. V. Suryanarayana, [5] the heat transfer in the transition region is affected by the various type of inlet configurations or the unheated thermal entrance region. A. J. Ghajar and L. M. Tam [6] has used various inlet configurations such as square edged, bell-mouth and reentrant inlets to determine the influence of thermal entrance region on the heat transfer. In the study the tube was heated at uniform temperature by electrical heating source. The range used was between 280 and 49000, The Prandtl number was varied between 4 to 158 and Grashof-number between 1000 and ^5. In their study they recommended different Nu-correlation for each inlet configuration under laminar, turbulent and transition flow conditions. The heat transfer in the transition region drops down substantially in the transition region compared to that of fully developed region, as referred in their studies V. Gnielinski [1], D. Huber and H. Walter., [2], N. V. Suryanarayana, [5] and B. S. Petukhov and V. V. Kirillov, [7]. V.Gnielinski [1] in his Nu-correlation considered the heat transfer drop in transition region. In preceding study V. Gnielinski [3] included di/l ratio in his Nucorrelation for the transition region. This Nu-correlation includes an interpolation function suggested by S. C. Lau, E. M. Sparrow and J. W. Ramsey, [8], H. Hausen, [9] and J. Taborek, [10] between laminar and turbulent flow. In the present study the thermal entrance region length along thermal boundary layer in transition region is determined by measuring the temperature distribution experimentally using resistance temperature detectors. The effect of in transition region is also investigated by varying the. The experimental data obtained are validated with the empirical correlations from available literature in transition region. Experimental Set Up: The experimental setup constitutes two circulating pumps, rotameter. heater, control panel, resistance temperature detectors, two collecting tanks. The test section constitutes of a copper tube of length = 1.75m, inner diameter = m and outer diameter = m and a GI tube of length = 1.41m, inner diameter = 0.070m and outer diameter = 0.074m. The total length of fluid flow inside tube is 1.41m. The schematic diagram of the experimental setup is shown in Fig.1 Fig. 1: Schematic Representation of Experimental setup The setup is provided with two 0.5hp pumps for circulating both hot and cold fluid from through a test section from collecting area of 0.03m 3. An immersion heater of 1kw capacity is used to heat the water. A rotameter of 10lts capacity is installed on the control panel to measure the mass flow rate of the fluid. The test section is enclosed with a ceramic wool insulation to minimize heat loss to the surroundings. The resistance temperature detectors of pt100 type and 0.03k uncertainties are fixed at equal distance on the outer tube wall. The distance of resistance temperature detectors can be varied along the thermal boundary layer of annulus space. A. Thermal Boundary Layer: The thermal entrance region length in laminar flow is affected by Reynolds and Prandtl number and is given by, L thrl = 0.05Re D Pr D (1) in turbulent flow the thermal entrance region length is independent of Reynolds and Prandtl number and is given by,

3 3 S. Santosh Kumar and M.K. Muralidhara., 2016/ Advances in Natural and Applied Sciences. 10(7) Special 2016, Pages: 1-8 L thrt = 10D (2) The thermal entrance length in transition region can be determined experimentally by measuring the temperature along the thermal boundary layer. The arrangement to vary the distance of RTD's on the outer tube wall along the thermal boundary layer in annulus space is shown in Fig.2 Fig. 2 Schematic Arrangements of RTD's on Heat Exchanger B. Heat Transfer Co-rrelations: Considering the flow to be fully developed the Nusselt number is calculated using the well-known dittusboelter equation, Nu = 0.023Re 0.8 Pr0.4 D (3) For overall heat balancing of the concentric tube heat exchanger the measured temperature and mass flow rates of both hot and cold fluids are used. The experimental value of heat flow "Q" between both fluids must be equal and can be written in the following form, For hot fluid side Q = m cp T T (4) ( ) h h h hi he For cold fluid side Qc = mccpc ( Tce Tci ) (5) In the overall analysis the heat exchanger is assumed to be adiabatic to the surroundings area, hence heat conduction through the wall is neglected. The logarithmic mean temperature difference method is used in the analysis for co-current flow. θ 1 θ θ 2 log = (6) θ ln 1 θ 2 Comparison with correlations: In the present work the experimental data are compared with various Nu-correlations proposed in literatures. The semi empirical correlation (7) by petukhov for the heat transfer analysis of turbulent flow, ( ξ / 8) Re Pr Nu = (7) ξ / 8 Pr2/3 1 With pressure loss co-efficient according [11], 2 ξ = 1.82log 10 ( Re) 1.64 (8) Regarded as most commonly used equation by many authors [1] and [2] was used as basis for their Nucorrelation. The definition range of (7) for Re and Pr number is 4.10^3 Re 5.10^5 and 0.7 Pr 60. This range includes the analyzed transition region for a single phase fluid flow. In his study [1] semi-empirical correlation of (7) was used as basis for the development of his Nu-correlation (9), 2/3 ( ξ / 8) RePr d 1 i Nu t = + (9) ξ /8 Pr2/3 1 L + Where the pressure loss co-efficient suggested by [12] is used, 2 ξ = 1.82log 10 ( Re) 1.5 (10)

4 4 S. Santosh Kumar and M.K. Muralidhara., 2016/ Advances in Natural and Applied Sciences. 10(7) Special 2016, Pages: 1-8 The modified equation (9) includes the diameter to length ratio to show the dependency of the heat transfer from the tube length and is valid according to [1], [9] [11], in the range of 10 4 Re 10 6 and 0.1 Pr In the transition region of 2300<Re<10 4 the interpolation function between laminar and turbulent flow should be used according to [2] in their study, Num = ( 1 γ ) Nu L, γ Nu (11) t,10000 With γ Re 2300 = and γ (12) Nusselt number in the turbulent region is calculated from (9). The Nusselt number for the laminar flow Nu L,2300 can be calculated from following equation 1/3 3 3 Nu, L Nu L,1, Nu (13) = + + L,2,2300 With ( ) 1/3 Nu L,1,2300 = Pr di / L and 1/6 Nu 2 1/2 L,2,2300= ( 2300 Pr / 1+ 22Pr d i L ) According to [1] and [2] in their study, the Nusselt number Nu m should be corrected by a correction factor of k in order to account the influence of the temperature dependency on the fluid properties. In his study [13] developed a single Nu-correlation considering the uniform wall temperature. According to [13] the shift from laminar to transition takes place at Re=2300. The overall Nu-correlation of (13) for the turbulent and transition region reduces to 1/2 1 1 Nu = + (16) Nu2 Nu2 t tr For transition region the Nusselt number suggested by [13] is given by, Re 2200 Nutr = Nu l exp 730 (17) For the turbulent flow region [13] is used for calculation, 0.079Re ξ Pr Nu t = (18) 5/6 1 Pr 4/5 + With pressure loss co-efficient by [13], 1/ Re 2.21ln (19) = + ξ Re Re C. Experimental Results: The Fig.3 shows the temperature distribution measured experimentally in the annulus space of the heat exchanger along the thermal boundary layer for different. The temperature changes are significant in the thermal entrance region, hence the temperature of fluid drops from higher value to lower value while passing from entry side of hot fluid to exit side of hot fluid. The temperature changes are not so significant in fully developed region, since thermal boundary layer remains constant in the fully developed region. (14) (15)

5 5 S. Santosh Kumar and M.K. Muralidhara., 2016/ Advances in Natural and Applied Sciences. 10(7) Special 2016, Pages: 1-8 Temperature along thermal boundary layer 0 C Re=2500 Re=5000 Re= Distance along length of annulus pipe m Fig. 3: Temperature distribution along thermal boundary layer in annulus space As shown in Fig.3, after the fluid flow approaches a distance of 0.53m i.e from 1.41m to 0.53m measured from direction of hot fluid entry towards hot fluid exit the temperature and thermal boundary layer remains constant, hence the length of thermal entrance region and fully developed flow region obtained from experimental measurement of temperature distribution along the thermal boundary layer are 0.88m and 0.53m respectively. Nuselt number Linear regression Polynomial regression Fig. 4: Comparison of experimental data with linear and polynomial regression curves The Fig.4 shows the experimental data and the curves for the linear regression of the data (full line) and polynomial regression of the data( (dashed line). The polynomial regression for trend line compared to linear regression trend line is found to be the best curve. The measured range of the was between 2500 and with an interval of 500.

6 6 S. Santosh Kumar and M.K. Muralidhara., 2016/ Advances in Natural and Applied Sciences. 10(7) Special 2016, Pages: 1-8 Error % of experimental data with regression curves Linear 20.0 Polynomial 10.0 Fig. 5: Error% of experimental data with regression curves The Fig.5 shows the absolute error % of experimental data with the polynomial and linear regression trend line. At of 2500 linear regression trend line shows a deviation of 20.4% and 60.4% at of The polynomial regression trend line shows a deviation of 19% at of 2500 and 57.7% at of At Re 6500 both polynomial and linear regression shows 40.4 and 39.8% deviation respectively. Both the regression trend line shows a increasing trend in deviation. The polynomial regression trend line shows minimum deviation compared to the liner regression trend line, hence the polynomial regression trend line finds most suitable trend line for comparing the experimental data obtained with available correlations from the literature Nuselt number Experimental Gnielinksi Petukhov Churchill Fig. 6: Comparison of experimental data with correlations from literature From Fig.6, it can be seen that the Nusselt number increases with increase in the, since the Nusselt number is proportional and function of & Prandtl number. The measurements are made by varying the between 2500 and The experimental values lies in line with the three curves obtained from literature. The correlation (9) shows higher gradient at both low of 2500 and high of The semi empirical equation (7) shows a lower gradient at low of 2500 and high gradient at The experimental data shows good accordance with the correlation (16). In Fig.7 comparison of the absolute error % of Nusselt number with experimental data obtained by different correlations from literature are presented. The correlation (9) shows minimum deviation of 15.5% at Reynolds number of The semi-empirical correlation (7) shows a minimum deviation of 14.1% at of The correlation (16) shows a minimum deviation of 2.3% at Between of 7500 and the correlation (9) shows a decreasing trend in error% and correlation (7) shows a increasing trend in the percentage error. The error rate in correlation (16) is almost constant between

7 7 S. Santosh Kumar and M.K. Muralidhara., 2016/ Advances in Natural and Applied Sciences. 10(7) Special 2016, Pages: and The fall in the error rate from 2500 to 5500 is high. That means the correlation (16) exhibits less accurate near than at higher Churchill 26 Gnielinksi Petukhov Absolute error % of Nusselt number Fig. 7: Absolute error % of Nusselt number with the different correlations Absolute error % of correlation data with regression Fig. 8: Absolute error % of correlation data with regression In Fig.8 a comparison between the absolute values of the error % of correlation data between the polynomial regression curve and the values obtained by different correlations are presented. The minimum deviation obtained by correlation (9) is 18.9% at of The semi empirical correlation (7) shows a minimum deviation of 0.8% at of The correlation (16) shows a very low deviation of 0.3% at Re from fig. 8, it can be concluded that from 2500 to Reynolds number 7000, the correlation (16) yields lowest error rate between 7000 and Conclusion: In the present study the test section was developed to measure the temperature distribution along the thermal boundary layer to determine the thermal entrance region length experimentally and to study the effect of in transition region. The experimental data was compared with three different Nu-correlations available in literatures proposed by Gnielinski, Petukhov and Churchill. The following conclusions are drawn from the experiment The thermal entrance region length and fully developed region in transition region are independent of and Prandtl number and are found to be.88m and 0.53m respectively. The semi empirical correlation of Petukhov (7) shows high error rate at high of The correlation of Gnielinski (9) exhibits low error rate at higher compared to Petukhov (7). The correlation of Churchill (16) is more accurate in determining Nusselt number at different Reynolds number compared to correlation of Gnielinski (9) and Petukhov (7) since it accounts the interpolation function between laminar and turbulent flow. REFERENCES Churchill Gnielinksi Petukhov 1. Gnielinski, V., New equations for heat and mass transfer in turbulent pipe and channel flow (Neue Gleichungen für den Wärme- und den Stoffübergang in turbulent durchströmten Rohren und Kanälen), Forschung im Ingenieurwesen, 41(1): 8-16.

8 8 S. Santosh Kumar and M.K. Muralidhara., 2016/ Advances in Natural and Applied Sciences. 10(7) Special 2016, Pages: Huber and H. Walter., "Forced convection heat transfer in the transition region between laminar and turbulent flow for a vertical tube", Latest trends on theoretical and applied mechanics, fluid mechanics and heat and mass transfer, ISBN: Gnielinski, V., A new calculation procedure for the heat transfer in the transition region between laminar and turbulent pipe flow (Ein neues Berechnungsverfahren für die Wärmeübertragung im Übergangsbereich zwischen laminarer und turbulenter Rohrströmung), Forschung imingenieurwesen, 61(9): Kays, W.M. and H.C. Perkins, Forced Convection, Internal Flow in Ducts, in Handbook of Heat Transfer Fundamentals, 2nd ed., W. M. Rohsenow, J. P. Harnett and E. N. Ganic, Ed. New York: McGraw- Hill, pp: Suryanarayana, N.V., Forced Convection-Internal Flows, in The CRC Handbook of Thermal Engineering, 2nd ed., F. Kreith, Ed. Boca Raton: CRC Press, pp: Ghajar, J. and L.M. Tam, Heat transfer measurement and correlations in the transition region for a circular tube with three distinctive inlet configurations, Experimental Thermal and Fluid Science, 8: Petukhov, S. and V.V. Kirillov, To the question of heat transfer in turbulent pipe flow of liquids in tubes (Zur Frage des Wärmeübergangs bei turbulenter Strömung von Flüssigkeiten in Rohren), Teploenergetika, 4(4): Lau, S.C., E.M. Sparrow and J.W. Ramsey, Effect of plenum length and Diameter on turbulent heat transfer in a Downstream tube and on plenum-related pressure losses, Journal of Heat Transfer, 103: Hausen, H., New equations for heat transfer at free or forced fluid flow (Neue Gleichungen für den Wärmeübertragung bei freier oder erzwungener Strömung), Allgemeine Wärmetechnik, 9(45): Taborek, J., Design method for tube-side laminar and transition flow regime with effects of natural convection, presented at the 9 th Int. Heat Transfer Conf., Jerusalem, OPF Filonenko, G.K., Hydraulic resistance of pipes (Hydraulischer Widerstand von Rohrleitungen), Teploenergetika, 1(4): Konakov, P.K., "A new equation for the friction coefficient for smooth tubes (Eine neue Formel für den Reibungskoeffizienten glatter Rohre),"Report of the academic society for science of the UDSSR, LI51(7): , Churchill, S.W., "Comprehensive Correlating Equations for Heat, Mass and Momentum Transfer in Fully Developed Flow in Smooth Tubes" Ind. Eng. Chem. Fundam., 16(1):