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68.4 seconds

Explanation:

Assume that the temperature of the stainless steel rod will reach 120 C in t seconds. According to lumped – capacity analysis use the following expression to determine the value of t

T- T∞/T₀ – T∞ = e^-(hA/ρcV)t, where T is the required temperature, T∞ is the surface temperature, T₀ is initial temperature of the rod, h is the convection heat transfer coefficient, A is surface are, ρ is density of stainless steel, c is specific head and V is the volume of the rod.

Area of rod = π x d x L and Volume of rod is (π/4) x d² L

T - T∞/T₀ – T∞ = e^-(h x π x d x L/ρc(π/4 x d² x L))t

T - T∞/T₀ – T∞ = e^-(4h/(ρ x c x d))t, d is the radius of the log and L is the length of rod

The value of c and ρ for stainless steel can be obtained from the table of properties of metals

Substitute 120 C for T, 150 C for T∞, 25 C for T₀, 7817 kg/m³ for ρ, 460 J/kg.C for c, 6.4 x 10⁻³ m for d, 120 W/m².C for h in the above equation

T - T∞/T₀ – T∞ = e^-(4h/ρ x c x d))t

120 – 150/25 – 150 = e ^ -(4 x 120/7817 x 460 x 6.4 x 10⁻³)t

0.24 = e^-0.02086t

Take natural log on both sides

㏑0.24 = -0.02086t

T = 68.4 seconds

Thus, the temperature of the stainless steel will reach 120 C in 68.4s