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Prediction of friction factor and non dimensions numbers in force convection
 

Prediction of friction factor and non dimensions numbers in force convection

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    Prediction of friction factor and non dimensions numbers in force convection Prediction of friction factor and non dimensions numbers in force convection Document Transcript

    • International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 259 PREDICTION OF FRICTION FACTOR AND NON DIMENSIONS NUMBERS IN FORCE CONVECTION HEAT TRANSFER ANALYSIS OF INSULATED CYLINDRICAL PIPE S.K. Dhakad1 , Pankaj Sonkusare2 , Pravin Kumar Singh3 , Dr. Lokesh Bajpai 4 1 Assistant Professor Department of mechanical Engg. S.A.T.I, Engineering College Vidisha M.P India 2 Lecturer in Department of mechanical Engg. S.A.T.I Engineering College Vidisha M.P. India 3 Assistant Professor Department of mechanical Engg. BUIT, Bhopal M.P. India 4 Professor and Head of Mechanical Engg. Deptt., S.A.T.I. Engineering College Vidisha M.P. India ABSTRACT The heat transfer through convection mode is very important in the thermal engineering and industrial application. In the present work force convection heat transfer analysis has been done for 40 mm diameter and 400 mm length of pipe subjected to insulated thickness of 5mm on outer span. The experimental analysis has been done for the 1/3, 2/3, 1 opening positions of the flow control valve, and along with bypass valve fully opened. This present work an experimental study on the Nusselt number (Nu), Reynold number (Re), Frictional factor (Ff) has been done with short length 30 mm diameter pipe insert under uniform wall heat flux boundary condition. In the experiment measured Reynolds number with air as a test fluid. The analysis has been done in steady state condition and regulated the flow of water so as to obtained temperature rise up-to 3-40 C limits. The Experimental results are cross validated with analytical results using the open literature as design data book. The experimental results are also validated with standard references available in open literature. The experimental results are well compare with analytical results also with standard open literature results. KEY WORDS: Force convection, experiment, convective heat transfer coefficient, Frictional Factor. 1. INTRODUCTION Heat transfer from a solid surface/ wall in the fluid in contact takes place by conduction to a very small extent because fluid particles are no more confined to their position as in solid. Convection involving macroscopic motion of fluids is thus the prominent mode responsible for heat INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 4, Issue 4, July - August (2013), pp. 259-265 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com IJMET © I A E M E
    • International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 260 transfer in such cases. If motion of fluid is made faster, with the help of pump or fan or blower, for rapid heat transfer then it is termed as forced convection heat transfer on the other hand if no external agency is involved to increase the flow velocity then heat transfer continues to takes place at a slow rate, only due to setting-up of natural convection currents and is called natural or free convection heat transfer. Rate of heat transfer in both these cases, as per Newton’s law of cooling. 2. EXPERIMENTAL DETAILED The apparatus consists of a test section surrounded by water jacket complete test rig shown in figure 1. Air supplied from a blower, regulate with the help of a bypass valve & a flow control valve, is passed through an orifice, fitted with a manometer for measurement of pressure difference across it, and a heating section before entering the test section detailed components are shown in figure 2. Power input to the heater of heating section is regulated by a dimmer & measured by a wattmeter (or a voltmeter & ammeter). Thermocouples with a selector switch an installed for measurement of temperature of:- 1. Air before entrance to the test section (at exit of the air heating section). 2. Pipe wall at seven positions in the test section. 3. Air at exit from the test section. Figure 1 Position of thermocouple in test section
    • International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 261 Figure 2 Experimental set up 3. PROPOSED METHODOLOGY Rate of heat transfer in both these cases, as per Newton’s law of cooling, is expressed as: q = h A (Ts - T∞)………………………………………. (1) it is evident from this expression that for given surface temperature (Ts), fluid temperature (T∞), and surface area (A) the rate of heat transfer depends only on the value of heat transfer coefficient (h) ‘h’ in turn depends on a number of parameters including the thermo physical properties of fluid, the surface dimensions and roughness and velocity of flow. ‘h’ is thus not as simple as it seems to be in the above mentioned equation. Investigations have arrived at various empirical equations on the basis of wide range of experiments conducted. A well known and widely accepted relationship for forced convection heat transfer between the walls of a circular or non-circular duct or annular passage and the fluid flowing through it in the fully developed turbulent flow mode (found applicable for constant wall flux as well as constant wall temperature) named as “Dittus Boelter Equation” is: Nu = h L / Kf = 0.023 (Re)0.8 (Pr)n …………………………(2) for 0.7 < Pr < 100 Where n is a constant having value 0.3 for cooling and 0.4 for heating, L is characterstic dimension of the body (L = inner dia. of a circular duct or equivalent dia. of a noncircular duct) and kf is thermal conductivity of the fluid, Nu, Re and Pr are Nusselt number, Reynold number and Prandtl number respectively. All thermophysical properties are evaluated at average of temperatures of bulk of the fluid at inlet and exit. In fully developed laminar flow inside a smooth tube where, Re Pr (d/1) > 10, average value of nusselt number can be obtained from the equation. Nu = 1.86 [ Re Pr/(1/d)]0.33 (µ/µs)0.25 ……………………….(3) Suggested by Sieder and Tate, which is applicable to the constant wall temperature situation. Flow rate of water through the cooling water jacket around the test section & temperature of water at inlet to & exit from it are measured by a measuring flask & mercury in glass thermometer. Pressure difference across orifice in mm of air column h = hm×ρ/ρa …………….. (4)
    • International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 262 Flow rate of air, ma = C × A √ [2 h / (1-β4 )] …………………….. (5) Velocity of air in flow sections V = M /ρ×At …………………… (6) Where, Ao = π/4 do 2 , At = π/ 4 dt 2 , Ats = π .dt . Lt ……………. (7) Bulk mean (average) temperature of air in test section Tst = (Tst + Tse)/2 ………………………. (8) Mean temperature of tube surface Tt = (T1 + T2 + T3 + T4 + T5 + T6 + T7)/7 ………………... (9) Heat lost by air in the test section q = ma Cpa (Tai - Tae) ……………………………………… (10) Also, q = hexp Ats (Tat - Tt) ……………………………… (11) Experimental value of heat transfer coefficient is thus: hexp = q/[Ats (Tat - Tt)] ………………………………………(12) Note down properties of air at average temperature of air Tat Reynold number, Re = ρa Va dt / µa …….. ………….. (13) Prandtl number, Pr = µa Cpa / ka ………………………….. (14) The relationship between Reynold number and frictional factor as [1] f=0.758Re-0.331 ………………………………………………. (15) Theoretical value of heat transfer coefficient hth can be calculated using appropriate equation as per the type of flow/ value or Re. 4. EXPERIMENTAL RESULTS AND ANALYSIS The Table 1 has shown the experimental measurement of convective heat transfer coefficient and Nusselt number, (Nu) Reynold number (Re) corresponding to three flow rate of air by regulating the bypass valve of the blower. Table1: Experimental measurement of convective heat transfer coefficient, Nusselt number, Reynold number Flow rate of air Heat transfer rate Q (w) Convective heat transfer h (w/m2 °C) Nusselt number (Nu) Reynold number (Re) 1/3, Opening of bypass valve 1840 287.50 3194.44 2245.48 2/3, Opening of bypass valve 2050 340.03 3778.11 2568.11 Full Opening of bypass valve 2295 351.39 3904.3 2636.5 5. ANALYTICAL RESULTS AND ANALYSIS: The analytical results of convective heat transfer coefficient, Nusselt number (Nu), Reynold number (Re) corresponding and frictional factor are shown in the tables 2, 3 & 4corresponding to three flow rate of air by regulating the bypass valve of the blower.
    • International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 263 Table 2 shown Analytical results corresponding to 1/3 opening of bypass valve Test section Length L(mm) Heat transfer rate Q (w) Convective heat transfer h (w/m2 °C) Temp . (°C) Mass flow rate of air (ma)kg/sec Velocity of air (Va) M/s Nusselt number Nu. Reynold number Re Friction Factor (Ff) 1 50 1840 162.774 39 0.000061 0.048 226.075 270.58 0.118 2 80 1840 195.329 37.5 0.000061 0.048 434.06 455.98 0.099 3 140 1840 219.965 36.6 0.000061 0.048 855.42 784.60 0.083 4 200 1840 254.77 35.7 0.000061 0.048 1415.4 1173.84 0.073 5 260 1840 271.290 35.4 0.000061 0.048 1959.3 1522.6 0.066 6 320 1840 283.542 35.16 0.000061 0.048 2520.3 1862.42 0.062 7 400 1840 284.85 35.14 0.000061 0.048 3165.05 2234.65 0.059 Table 3: shown Analytical results corresponding to 2/3opening of bypass valve Test section Length L(mm) Heat transfer rate Q (w) Convective heat transfer h (W/m2 °C) Temp. (°C) Mass flow rate of air (ma) kg/sec Velociy of air (Va) M/s Nusselt number Nu. Reynold number Re Friction Factor (Ff) 1 50 2050 204.020 38 0.000061 0.048 283.36 324.175 0.111 2 80 2050 233.166 37 0.000061 0.048 518.14 525.37 0.095 3 140 2050 272.027 36 0.000061 0.048 1057.8 929.94 0.078 4 200 2050 310.888 35.25 0.000061 0.048 1727.1 1376.48 0.069 5 260 2050 326.43 35 0.000061 0.048 2357.57 1765.54 0.063 6 320 2050 337.689 34.8 0.000061 0.048 3001.68 2141.89 0.059 7 400 2050 336.034 34.8 0.000061 0.048 3733.7 2550.4 0.056 Table 4: shown Analytical results corresponding to full opening of bypass valve. Test section Length L(mm) Heat transfer rate Q (w) Convective heat transfer h (W/m2 °C) Temp.(°C) Mass flow rate of air (ma) kg/sec Velociy of air (Va) M/s Nusselt number Nu. Reynold number Re Friction Factor (Ff) 1 50 2295 228.403 38 0.000063 0.050 317.22 354.80 0.108 2 80 2295 261.03 37 0.000063 0.050 580.07 575.032 0.092 3 140 2295 288.509 36.33 0.000063 0.050 1121.982 974.75 0.077 4 200 2295 317.779 35.75 0.000063 0.050 1765.43 1400.83 0.068 5 260 2295 338.375 35.4 0.000063 0.050 2443.8 1817.03 0.063 6 320 2295 351.390 35.2 0.000063 0.050 3123.4 2211.1 0.059 7 400 2295 358.280 35.1 0.000063 0.050 3980.8 2684.6 0.055 6. RESULTS AND DISCUSSION The variation of Nusselt number and Reynold number with three different opening of bypass valve have been shown in figure 3. The analytical as well experimental results are comparing well with each other. The results are also well comparing along with standard references [1].
    • International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 264 Figure 3: The variation of Nusselt number and Reynold number with three different opening of bypass valve The variation of frictional factor with respect to different flow rate has been shown in the figure 4.The experimental as well analytical validation of friction factor compare well with each other along with references [1]. Figure 4: the variation of frictional factor with respect to different flow rate CONCLUSION The experimental analysis of convective heat transfer coefficient at the different flow rate of air has been analyzed in this paper. The validation of non dimension numbers and friction factor with analytical results has been done, using the standard properties of air available in the open literature, corresponding steady state temperature of the fluid (air).The both the results (experimental and analytical) are well compared with the standard references [1]. 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Nusseltnumber Reynolds number 1/3 Opening of blower valve[Experimental results] 2/3 Opening of blower valve [Experimental results] Full opening of blower valve [Experimental results] 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 500 1000 1500 2000 2500 3000 3500 Frictionfactor Reynolds number Experimental Results Analytical Results reference results
    • International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 265 ABRASION: Re - Reynold number Pr - Prandtl number Nu - Nusselt number D - Diameter of pipe Lp - length of pipe h - convective heat transfer coefficient (W/m2 °C) ma - mass flow rate of air (kg/sec.) Va - velocity of air (m/s) F f - friction factor T - temperature (°C) L - length of test section (in mm) Q - heat transfer rate (W) Tai - inlet air of temperature Tae - exhaust air of temperature hexp - experimental value of heat transfer coefficient ρa - density of air µa - dynamic viscosity of air Ats - area of test section h - pressure difference Tt - Mean temperature of tube surface REFERENCES [1] Smith Eiamsa-ard et al., “Convective heat transfer in a circular tube with short-length twisted tape insert” International Communications in Heat and Mass Transfer, Vol. 36, (2009), PP. 365–371. [2] T.S. Zhao et al., “Forced convection in a porous medium heated by a permeable wall perpendicular to flow direction: analyses and measurements” International Journal of Heat and Mass Transfer, vol. 44, (2001), pp. 1031-1037 [3] W. L. Pu et al., “an experimental study of mixed convection heat transferin verticalpacked channel” AIAA Journal of Thermophysics and Heat Transfer, Vol.13 (4), 1999, pp. 517-521. [4] Zhai, Z. and Chen, Q., “Numerical determination and treatment of convective heat transfer coefficient in the coupled building energy and CFD simulation,” Building and Environment, Vol. 36(8), 2004, pp. 1000-1009. [5] P. Promvonge et al., “Heat transfer behaviors in a tube with combined conical-ring and twisted-tape insert” International Communications in Heat and Mass Transfer, Vol. 34, (2007), PP. 849–859. [6] C.V. Herman, F. Mayinger, “Experimental Analysis of forced convection heat transfer in a grooved channel” Advances in Heat Transfer, 1992, PP. 900-913. [7] G. Refai Ahmed and M.M. Yovanovich, “Analytical Method for Forced Convection from Flat plates, Circular Cylinders and Spheres”, Journal of Thermophysics and Heat Transfer, Vol. 9, No. 3, (July-September 1995), PP. 516-523. [8] Pankajsonkusare, s.k. dhakad et al., “Force convection heat transfer analysis through different channel (Review of work)” Indian Journal of Applied Research Vol.3 Issue 8 august2013 p.p.256-258. [9] Sudhanshu Dogra, Nitin Chauhan and Gaurav Bhardwaj, “Effect of Artificial Roughness on Heat Transfer and Friction Factor Characteristics in Rectangular Duct of a Double Pass Solar Air Heater”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 4, Issue 3, 2013, pp. 289 - 298, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359.