Heat transfer gradient through the reactor

Yan & Vasudha

EGEE 520 project presentation

Dec 1 2005

Introduction2

Steel

Fuel

Glass reactor

Al2O3

Air

1

2

3

4

7 5

68

9

12

10

11

3

Governing equations

Conduction: dn

dTkAq

k: thermal conductivity (Wm-1K-1) A: cross-sectional area (m2)dT/dn: temperature gradient (Km-1)

Convection: )( fluidsolid TThAq h: heat transfer coefficient (Wm-2K-1) Tsolid: temperature at the surface of the solid body (K)Tfluid: ambient or remote temperature of the fluid (K)

Radiation: ])()[( 44 TTAq solidSB

εSB: Stefan-Boltzman constant (Wm-2K-4) σ: emissivity of the surface Tsolid: temperature at the boundary of the solid body (K) T∞: ambient temperature (K)

Partial differential equation for heat conduction:

dt

dTcq

z

Tk

zy

Tk

yx

Tk

x pzyx

)()()(

4

Formulation Initial assumptions: Steady-state process; Axial symmetry (2D); Modes: Convection and Conduction & Incompressible Navier-Stokers

Material ρ

(kg/m3)

η

(Pa•s)

k

(W/(m•K))

Cp

(J/(kg•K))

u(t0)

(m/s)

v(t0)

(m/s)

p(t0)

(Pa)

T(t0)

(K)

Gasoline Rho(p,T)a Eta(T)a k(T)a Cp(T)a 0 0 0 298

Silica glass 2203 1000 1.38 703 0 0 0 298

Air, 1 atm Rho(p,T)a Eta(T)a k(T)a Cp(T)a 0 0 0 298

Al2O3 3965 35 730 0 0 0 298

Steel AISI 4340 7850 44.5 475 0 0 0 298

Subdomain and Boundary settings in FEMlab

1 2 3 4, 5 6, 7 8, 9 10, 11 12

30 cm 1 cm 1 cm 0.2 cm 10 cm 9 cm 0.5 cm 30 cm

Thermal

insulation

293 K

vz (m/s)

Convective

flux 773 K 773 K 600 K 400 K 298 K

5

Solution

Temperature distribution with flow rate 0.01mL/s

])(1[2

])(1[2])(1[ 222max R

r

Area

Q

R

rV

R

rVV aver

6

ValidationHeat gained by fluid when it passes through the reactor:

TCQq pfuelfuelfuel

9.10439113.0 Tfuel 3293, /8891.776 mkgKfuel

64.5412459.5 TCpfuel)/(6887.2078293, KkgJC Kpfuel

smsmLQ fuel /10/01.0 38

Heat transfer through radial conduction in cylindrical wall:

dr

dTkAqr

2

1

2

12

r

r

T

Tr kdTrl

drq

)/ln(

)(2

12

12

rr

TTlkqr

q = 7.895 W/m3

q = 9.7596 W/m3

7

Parametric Study

Temperature distribution with flow rate 0.001mL/s

8

Parametric Study

Temperature distribution with flow rate 0.1mL/s

9

Conclusion

When the flow rate of fuel is high, temperature distribution is roughl

y symmetric with z = 0. The temperature of fuel is almost constant

(293 K) except in two bottoms.

When the flow rate of fuel is decreased, the temperature of fuel incre

ases.

Temperature distributions within Al2O3 and steel almost maintain the

same no matter what the flow rate is. However, the temperature distr

ibution within air changes with changing flow rate.

FEMlab is a useful tool for simulation of heat transfer process, and t

he results of our modeling are reasonable.

Questions?