Here, we give values of parameters and coefficients in the dependences of thermal physical characteristics on temperature T, given in Kelvin, and their modification for the relative temperature θ = T/Twork in two operating ranges, Twork = 293 K and Twork = 1300 K < Tmelt = 1356.55 K, based on data [21–24]

Copper density: ρ0 = 8890 [kg m–3],

ρ1 = 0.362 [kg m–3 K–1],

ρ(T) = 8890 – (8890 – 8680)(T – Tn)/(600 – 20) for Tn = 293 K, ρ(T) = ρ0 + ρ1(T – Tn) = ρ0[1 + \(\rho _^}\)(θ – θп)], \(\rho _^}\) = 0.012 (0.0529) for Twork = 293 (1300) K.

Heat capacity: cp = 0.381 [kJ/(kg K)],

\(c_}^}\) = 1.419 × 10–4 [kJ/(kg K2)],

\(_}}\)(T) = 0.374 + (0.414 – 0.374)(T – Tn)/(573 – 293),

\(_}}\) = cp/1.02 = 0.374 [kJ/(kg K)],

\(_}}\)(T) = \(_}}\) + \(c_}^}\)(T – Tn) = \(_}}\)[1 + \(c_^}\)(θ – θп)],

\(c_^}\) = 0.1115.

Thermal conductivity coefficient:

κ(T) = k(θ) = κ0–κ1T + κ2T2 – κ3T3,

ki = (–1)iκi\(T_}}}^\), [kj] = W m–1 K–1, κ0 = 427,

κ1 = 0.147, κ2 = 1.14 × 10–4, κ3 = 4.7 × 10–8,

[κj] = W m–1 K–(j+1), k(θ) = κ0(1 + k1θ + k2θ2 + k3θ3),

k1 = –0.101, k2 = 0.0229, k3 = –0.00276 for Twork = 293 K and k1 = –0.448, k2 = 0.4508,

k3 = –0.241 for Twork = 1300 K.

Convective (Newtonian) heat transfer:

Heat transfer with gas,

αg(T) = h0– h1T + h2T2 – h3T3,

[\(_}}_}\)] = Jm–3 K–1, h0 = 0, h1 = 0.003, h2 = 10–6,

h3 = 10–9, [hj] = W m–2 K–(j+1), [CN] = W m–2 K–1,

cN(T) = 1 + c1θ + c2θ2 + c3θ3, c1 = –0.11,

c2 = 0.0107, c3 = –0.00314 for Twork = 293 K, and c1 = –0.488, c2 = 0.0475, c3 = –0.0139 for Twork = 1300 K. cN(Tamb = 293 K) = 0.898.

Heat exchange with a steel substrate

αsub = \(_}\;}}}}_}}}}\) = const, CFe = 30 [W m–2 K–1].

Radiation heat transfer:

αR = 4.54 × 10–8 [W m–2 K–4], βR = 0.143.

Absorption coefficient:

1 – R(T) = B0b(θ) = B0 + B1T + B2T2, B0 = 0.028, B1 = 1.5 × 10–5, |B2| < 10-8,

[Bj] = K–j, b(θ) = 1 + b1(θ) + b2(θ)2, b1 = 0.157,

|b2| < 0.031.