Answer:
68.4 seconds
Step-by-step 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