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1 Miss M Hallquist Prof JP Meyer
2 Laminar Turbulent Re < Re > 3 Less insulation needed Good energy balances High pressure drop High insulation requirements Insufficient energy balance Low heat transfer coefficients Low p pressure drop p???? Transitional
3 4 Re Pr d.7 Nu x.4. Gr Pr x / 3 b w.4 x 9 D Nusselt Num mber [Nu] 3 8 Re 38 4 Pr 6 8 Gr.8 4. b 3.8 w 6 Petukhov et al. (969) ESDU () Ghajar j and Tam ((994)) Chilton and Colburn (933) Dittus and Boelter (93) Petukhov (99) Gnielinski (976) Churchill (977) C Constant UHF Reynolds Number [Re] 3
4 Applications Energy transfer in chillers Heat rejection in condensers Steam generation in power stations System efficiency & capacity Best of both worlds Accurate correlation 4
5 Experimental Set up 4 3 Data Acquisition System 6 Test Section 7 C Cold water tank Positive displacement pump Accumulator Bypass valve Flow meter (low flow rate) Flow meter (high flow rate) DC inverter welder MPC controller 8
6 Measurement Procedure Reynolds number: 4 3 Prandtl number: 4 7 Nusselt number: Grashoff number: 6 6 Heat H t flux: fl W/
7 Data Reduction hqd hnu s i Ts k Tb Q q s elec d i L Qelec i R l R R T T R L Ac mm Integrate wall temperatures Average of inlet & outlet temperature T f ( x ) T f,i q( x) d i x. m Cp ( x) 7
8 System Validation Temperature [[ C] Lo ocal Nusselt Nu umber, Nu Lo ocal Nusselt Nu umber, Nu Measured Wall Temperature Bulk Fluid Temperature Fluid Temperature Ghajar andcalculated Tam (994) Ghajar andlinear Tam (994) (Measured Wall Temperature) Measurements M t Measurements 3 3 3Length[m] Tube [m] Tube Length Tube Length [m]
9 System Validation 6 Measurements Ghajar j and Tam ((994)) Gnielinski (976) Average e Nusselt numb ber, Nu Reynolds Number, Re 9
10 Data Reduction f Pd i L v Measured Average fluid bulk temperature
11 System Validation..6 Poiseulle Measurements Blasius Ghajar and Tam (994) AllenMeasurements and Eckert (964).4.. r, f Facto or, f Reynolds Number, Re Reynolds Number, Re 8 6 7
12 Heat Transfer io, h(x) t /h(x) b Local Hea at Transfer Rati Rey ynolds Number r, Re.E+.E+4.E Re = Re = 8 6mm 6 mm Tube Tube - 78 Re = - 68 Re = mm Tube - Re 83 = mm Tube - 4 Re 78 = 3 Re = mm Tube Re = mm Tube mm Tube mm Tube mm Tube mm Tube mm Tube mm Tube mm Tube E+.E+.E+ 3 4.E+3 6.E+47 8.E+ 9.E+6 Reynolds number, Raleigh Number, Re Ra -6 Temperature [ C]
13 Heat Transfer Nu usselt Number [Nu] Reynolds Number [Re] 3
14 r, f Facto or, f Reynolds Number, Re Reynolds Number, Re
15 and Frictio on Facto and rccorrected 3 3 Predicted P Nuss selt Number Prredicted Nusse elt Nnumber Measurements Series Measurements 33 Series 33 of 4.7) 4473 Nu = factor jprediction 73 Series 4(k 73 Nu prediction (k4 =73 factor of 4.7) Series F i ti F t 4 W/ St Pr / 3 f k.... Number, Reynolds Re Reynolds Number, Re Measured Nusselt Number Measured Nusselt Number 3 3
16 Calculated Nus sselt Number Grashoff.8 Pr(L/ Num mber /d i ).87 [Gr] Gr.4Pr.( (L/d i ).6 3 E.E E E Series Measurements Series4 Nu prediction D E C y =.7393x.4 AR² =.997 B b Re y = 7.97xs Nu.664 R² = L. 393 e Gr Pr x b. 87 Re Pr 3. 8 L s 4 73 Gr Pr x Nu Measured Re Re.8.4 Pr Nusselt. Pr.4 (µ. (µ b /µ b /µ Number s ).4 s ).4 Nu E+ 3.E+.E+.E
17 Consistent data for all test cases Smooth transition between laminar and turbulent flow regimes Transition is dependent on heat flux of the system Secondary flow effects.? Development of a correlation Improvements Data logger Power supply Calibration methods 7
18 [stpr.6] Ghajar & Tam (994). Reynolds Number [Re] 8
19 Uncertainties.6 Av verage Nusseltt Number Unce ertainty [%] Reynolds Number [Re]
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