Numerical prediction of phase-change heat conduction of injection-molded high density polyethylene thick-walled parts via the enthalpy transforming model with mushy zone

Polymer Engineering and Science, Sept, 2008 by Bin Yang, Xiao-Rong Fu, Wei Yang, Li Huang, Ming-Bo Yang, Jian-Min Feng

NOMENCLATURE

a             Coefficient in Eq. 17

b             Reference length, m; coefficient in Eq. 17

e             Control-volume face between P and E

w             Control-volume face between P and W

n             Control-volume face between P and N

s             Control-volume face between P and S

[C.sub.p]     Heat capacity, J [kg.sup.-1]
              [degrees][C.sup.-1]

H             Enthalpy, J [kg.sup.-1]

k             Thermal conductivity, W [m.sup.-1]
              [degrees][C.sup.-1]

L             Latent heat, J [kg.sup.-1]

S             Coefficient in Eq. 12

[S.sub.1](t)  Lower moving boundary of the mushy zone, m

[S.sub.2](t)  Upper moving boundary of the mushy zone, m

T             Temperature, [degrees]C

[T.sub.kir.]  Kirchhoff temperature, W/m

[T.sub.0]     Initial temperature, [degrees]C

[T.sub.w]     Mold temperature, [degrees]C

[T.sub.1]     Lower boundary temperature of the mushy zone,
              [degrees]C

[T.sub.2]     Upper boundary temperature of the mushy zone,
              [degrees]C

[T.sub.f]     Reference temperature, defined by [T.sub.f] =
              ([T.sub.1]   [T.sub.2])/2, [degrees]C

t             Time, sec

x             Distance along x-axis direction, m

y             Distance along y-axis direction, m

[DELTA]t      Time increment, sec

[DELTA]x      Space step along x-axis direction, m

[DELTA]y      Space step along y-axis direction, m

[alpha]       Thermal diffusivity, defined by [alpha] = k/([rho]
              [C.sub.p),

              [m.sup.2] [s.sup.-1]

P             Material density, kg [m.sup.-3]

[GAMMA]       Coefficient in Eq. 12

[tau]         Fourier number (Fo) or dimensionless time,

              defined by Eq. 25

[zeta]        Coefficient, defined by Eq. 19

X             Dimensionless distance along the x-axis, defined
              by Eq. 23

[xi]          Dimensionless distance along the y-aixs, defined
              by Eq. 23

[theta]       Dimensionless temperature, defined by Eq. 24

Subscripts

s             Solid phase
l             Liquid phase
P             Mush region
P             Grid point
E             East neighboring point of grid P
W             West neighboring point of grid P
N             Norst neighboring point of grid P
S             South neighboring point of grid P

REFERENCES

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(5.) K. W. Westerberg, C. Wiklof, and B.A. Finlayson, Numer. Heat Transf. Part B: Fund., 25, 119 (1994).

(6.) C.K. Hsieh, Trans. ASME, 117e, 1076 (1995).

(7.) A. Aziz, A. Jaleel, and M. Haneef, Chem. Eng. J. Biochem. Eng. J., 19, 171 (1980).

(8.) M. Parang, D.S. Crocker, and B.D. Haynes, Int. J. Heat. Fluid. FL, 11, 142 (1999).

(9.) P. Lin and Y. Jaluria, Polym. Eng. Sci., 37, 1247 (1997).