Convective heat exchange within a compact heat exchanger EGEE 520 Instructor: Dr. Derek Elsworth Student: Ana Nedeljkovic-Davidovic 2005

1. Introduction  Characterised mainly by a high heat transfer area per unit volume;  Optimization between heat exchange and pressure drop;  Parallel flow compact heat exchangers mm

2.1 Governing Equations  Analytical expression describing parabolic velocity distribution u=16Umax(y-y0) (y1-y) (x-x0) (x1-x0) / [(y1-y0) 2 (x1-x0) 2 ]  Energy balance equation  Boundary condition Twall=500[K] T inlet=300[K]; Convective flow-outlet;

2.2 Solution using FEMLAB Temperature distribution  Air: k= (w/m K) c= 1529 (J/kg K) ρ= (kg/m3) Velocity: U max = 2.2 (m/s) Twall=500[K] Tinlet=300[K]  Aluminum: k=155 (w/m K) c= 895 (J/kg K) ρ= 2730 (kg/m3)

3.1 Validation FEMLAB results: ∫T 2 dA= [Km 2 ]; ∫WdA=3.168e-6 [m/s m 2 ] Mass and heat flow rate :   =89.21 [W/m2K] Average value of the Nusselt number: Nu= D/k=3.18 Thermally fully developed flow with constant wall temperature Nu=2.976( A.F. Mills, 1999, Heat transfer) Average heat transfer coefficient:

3.2 Validation  Re= 68 <2300  Tm=400[K]  Thermally developing, hydraulically developed flow for Re <2300 and constant wall temperature (Housen)

4. Parametric study Table1: Parametric study with variable velocity vTzT inT o   hot [m/s][K] [W/m 2 K] Table2: Parametric study with variable wall temperature vTwTinT o   hot [m/s][K] [W/m 2 K]

5.Section of the heat exchanger

6. Conclusion  Average value of the Nusselt number Nu= D/k=3.18  Convective heat transfer coefficient increases with an increase in velocity and with an increase in wall temperature  To calculate more precise value of  and Nu, local heat transfer coefficient is necessary to be determined.