Actual Heat Conduction between Molten Metal and Metallic Mold

Abstract

  To explain cooling of metal poured in a metallic mold, the solution of the equation of heat conduction between molten metal and metallic mold in ideal contact condition is used in general. But in practical casting, the surface of mold is very rough and even coated. Accordingly, molten metal does not contact with mold ideally. It can be considered that actual contact condition has heat resistance between metal and mold when heat flows from metal to mold. In this case, the boundary condition of the equation is as follows,
    U₁(0, t)−U₂(0, t)=−R_H d⁄(dx) U₁(0, t)
  Using this condition, when metal and mold have infinite length from the surface of contact, we get the following solution.
  Concerning metal,
    U₁(x, t)=θ₁ − k₁⁄(μλ₁) (θ₁−θ₂){erfc(−x⁄(2k₁√t)) − e^{−μx⁄(R_Hk₁) + (μ⁄(R_H))2t} • erfc(μ⁄(R_H)√t + −x⁄(2k₁√t))}
  Concerning mold,
    U₂(x, t)=θ₂ + k₂⁄(μλ₂) (θ₁−θ₂){erfc(x⁄(2k₂√t))−e^{μx⁄(R_Hk₂) + (μ⁄(R_H))2t} • erfc(μ/R_H)√t + x⁄(2k₂√t))}
          t : time after pouring
          x : distance from the surface of contact, x≦0 for metal, x≧0 for mold
        U₁(x, t) : temperature of metal
        U₂(x, t) : temperature of mold
          k?? : thermal diffusivility of metal
          k?? : thermal diffusivility of mold
          λ₁ : thermal conductivity of metal
          λ₂ : thermal conductivity of mold
          θ₁ : pouring tempemperature
          θ₂ : initial tempepature of mold
    μ=(λ₁k₂+λ₂k₁)/λ₁λ₂
        [Written in non-displayable characters.]
  In this solution, the term involving contact heat resistance R_H is the complementary one. When R_H decreases, the term tends to zero and the solution agrees with that in ideal contact condition. Therefore, this solution is more general for heat conduction between metal and mold.
  In this experiment, measurements of contact heat resiststance were carried out in steady state at comparatively low temperature using solid metal instead of molten metal.
  It became clear that heat resistance changes by thickness of coating, roughness of the surface of mold and the pressure which is applied to metal, and that its value in practical aluminum casting lies approximately between 10 and 100cm²•s• °C/cal.