BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 3, 2012 81
The mathematical model chosen is based on pressure based, since heat
transfer modeling is done in incompressible fluids. Formulating the
mathematical model is of default type which makes solver stable and
convergent, although the number of equations and complexity of calculations
increases. Moreover, the default scheme, unlike the explicit one, is
recommended for heat transfer processes with phase change, by providing
freedom of choice of time step within a wide range of values.
The type of solver adopted was Solidification and Mellting. This type of
solver is intended to solve the problems of heat transfer with phase change. For
a better analysis of the thermal field in certain areas of the computing range a
number of surfaces have been introduced to monitor the evolution of
temperature in the course of the process (Fig. 1).
At the same time to follow the surface temperature evolution was
monitored , namely, water surface temperature, track foundation board surface
temperature and pipe surface temperature. Equations underlying the
mathematical model and the initial and limit conditions are
∂ ρ + ∇ =
∂τ
( ρV ) 0,
(1)
( )
∂ ρu ∂p μ
+∇ =− − +∇ ∇
∂τ ∂x k
( ρuV ) u ( μ u),
(2)
( )
∂ ρv ∂p μ
+∇ ( ρvV ) =− − v +∇( μ∇ v) + ( ρm
−ρ)
g, (3)
∂τ ∂y k
( ρh)
( ρβL)
∂
⎛k
⎞ ∂
+∇ ( ρhV ) =∇⎜
∇h ⎟− −∇( ρβLV ),
∂τ ⎝c ⎠ ∂t
(4)
⎛
K = K
⎜
⎝
β
3
( 1−
β)
0 2
⎞
, (5)
⎟
⎠
where: τ – time, ρ – density, p – pressure, V – velocity vector, u, v – velocity
components on x and y axes, μ – dynamic viscosity, β – liquid fraction, L –
latent heat, K – permeability, K 0 – Kozeny-Karman constant and