Convective heat exchange within a compact heat exchanger

EGEE 520Instructor: Dr. Derek ElsworthStudent: 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 exchangersmm

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;

QTCTkt

TC upp

)(

2.2 Solution using FEMLABTemperature distribution

Air:k=0.0505 (w/m K) c= 1529 (J/kg K) ρ= 0.8824 (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 ValidationFEMLAB results:

∫T2dA=0.001528 [Km2]; ∫WdA=3.168e-6 [m/s m2]

Mass and heat flow rate:

[kg/m3] 6-e79.2 WAm

[W] 3-e48.733 inop TTcmQ

meanwall TTA

Q1 =89.21 [W/m2K]

Average value of the Nusselt number:Nu= D/k=3.18Thermally 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)

65.3)Pr(Re117.01

)Pr(Re19.0657.3

467.0

8.0

LDLD

Nu

4. Parametric study

Table1: Parametric study with variable velocity

v Tz T in T o hot

[m/s] [K] [K] [K] [W/m2K]

2.2 500 300 471.6 89.2

2 500 300 475.3 84.21

1.8 500 300 479.0 78.69

1.6 500 300 482.7 72.61

1.4 500 300 484.8 64.93

Table2: Parametric study with variable wall temperature

v Tw Tin T o hot

[m/s] [K] [K] [K] [W/m2K]

2 400 300 386.4 82.124

2 500 300 475.3 84.213

2 600 300 564.8 85.274

2 700 300 657.4 87.161

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.