Respuesta :
The solidification time for a slab shaped casting is 161.1min and for a sphere with 10cm diameter is 4.475min
Data;
- ρ(m) = Density of metal (kg/m^3) = 7850kg/m^3
- T(o)= Initial temperature of mold = 28 + 273 = 301K
- Tm = melting or freezing temperature of liquid = 1540 degree
- ΔT(s) = T(p) - T(m) = 0 (No superheat)
- L = latent heat of fusion (JKg^-1) = 273*10^3 Jkg^-1
- K = Thermal conductivity of mold = 0.8655 w/mK
- ρ = density of mold = 1600 kg/m^3
- c = specific heat of mold = 1.17 kJ/kg K
- Cm = specific heat of metal = 0.45 kJ/kg K
Solidification Time
Using the formula
[tex]\gamma = [\frac{\rho m L}{(T_m - T_o)}]^R[\frac{\pi}{4k\rho c} ][1+(\frac{C_m\delta T_s}{L})][/tex]
Substituting the values into the equation;
[tex]\gamma = [\frac{7850*272*10^3}{(1540-28)}]^2[\frac{\pi}{4*0.8655*1600*1170}][1+0]\\ \gamma= 9.66697*10^5 s/m^2\\ \gamma = 1.611 min/cm^2[/tex]
The formula for solidification time is given as
[tex]T_s = \gamma (\frac{v}{A})^2[/tex]
i) The casting of 10cm thickness
For slab shape casting,
[tex](v/A)= \frac{A*t}{A} = t\\ (\frac{v}{A})^2 = A^2 = (0.1)^2 = 0.01\\ t = 16111.6*0.01 = 161.1min[/tex]
ii) For a sphere of 10cm diameter
[tex](\frac{v}{A}) =(\frac{R}{3})\\ (\frac{v}{A})^2 = (\frac{0.05}{3})^2\\ t_s = 16111.6*(\frac{0.05}{3})^2\\ t_s= 4.475min[/tex]
From the calculations above, the solidification time for a slab shaped casting is 161.1min and for a sphere with 10cm diameter is 4.475min
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