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HỘI THẢO QUỐC TẾ ATiGB LẦN THỨ CHÍN - The 9 ATiGB 2024 9
Q + Q P
Q = h c , W (6) f = c (13)
2 L
2 c 1 .V .
According to heat transfer theory, ratio between 2 c c D
actual and maximum achievable heat transfer rates Here, ΔPc is pressure drop of the cold fluid flow
represents effectiveness, which is calculated as: (Pa), Vc is fluid velocity at inlet of the annulus side
Q (m/s) and ρc is fluid density of the cold fluid flow
= (7) (kg/m ).
3
Q max
Reynolds numbers of the hot fluid flow and the
Here, Q = (m.C ) (T − T ) cold fluid flow are defined as
max p min h,in c,in
.V .d
in which (mCp)min indicates the smaller value Re = h h 3 (14)
between mcCp,c and mhCp,h. h h
And, mean convective heat transfer coefficients of .V .D
the hot fluid flow and the cold fluid flow can be Re = c c (15)
c
obtained as c
Here, μh and μc are dynamic viscosity of the hot
q
= w , W/m .K (8) fluid flow and the cold fluid flow (kg/m.s).
2
h
−
0,5 (T h,in + T h,out ) T w C. Boundary conditions
q Hot fluid enters the inner pipe at constant
= w , W/m .K (9)
2
c temperature of 333K and velocity of
T − 0,5 (T + T )
w c,in c,out Re .
Here, T is mean temperature of the inner pipe V = h h , m/s (16)
h
w h .d 3
wall (K), and q is mean thermal flux on the inner Cold fluid enters the annulus with constant flow
w
2
pipe wall (W/m ). rate of 0.1 kg/s and temperature of 293K in the
Thus, mean Nusselt numbers of the hot fluid flow opposite direction.
and the cold fluid flow are Static pressure is assumed to be atmospheric at
.d both outlets. Moreover, mass balance is used. Same
Nu = h 3 (10) turbulent intensity and hydraulic diameter as those at
h h the inlets were used as turbulence conditions at the
.D outlets.
Nu = c (11) Non-slip condition for the fluid flow applies to all
c
c
walls of the heat exchanger. Moreover, thermal
Here, d3 is inner diameter of the inner pipe (m), insulation was assumed for the outer pipe of the heat
D is hydraulic diameter of the annulus (m); λh, λc is exchanger.
thermal conductivity of the hot fluid flow and the cold D. Computational Mesh
fluid flow (W/m.K).
Structured finite volume meshs with a high
Friction coefficient is evaluated using pressure resolution of case 1, 2 and 3 are created.
difference at the inlet and outlet on each side. Friction A mesh sensitivity study is conducted both
coefficient of the hot fluid flow is obtained as
quantitatively and qualitatively. Fig. 3 shows the
P variation in Th, Tc with different mesh resolutions. As
f = 1 h 2 L (12) can be seen, with the resolution larger than 792600,
h
h
2 h .V . d 766320, 825995 elements (corresponding to cases 1, 2,
3
3), the temperature at outlet of the hot fluid flow and
Here, ΔPh is pressure drop of the hot fluid flow the cold fluid flow is unchanged. This mesh resolution
(Pa), Vh is fluid velocity at inlet of the inner pipe is considered the most optimal and hence employed
(m/s), L is pipe length (m) and ρh is fluid density of for our simulations.
3
the hot fluid flow (kg/m ).
Similarly, friction coefficient of the cold fluid flow
is obtained as
ISBN: 978-604-80-9779-0