Answer:
Average surface temperature = 11.4 C
Explanation:
Temperature of the surface = Incoming Temperature + (Heat generated by the Average person's head/ Coefficient of heat transfer x Surface Area of head)
Area = πD² = π(0.2)² = 0.1256 m²
h = (Thermal Conductivity/Diameter of Surface)(Nusselt Number)
Nu = 2 + [0.4Re^0.5 + 0.06Re^2/3] x Pr^0.4 x [μ∞/μs]^1/4
where Re is the Reynold Number, Pr = 0.7336 is the Prandtl Number, μ∞ = 1.778 x 10^-5 is the dynamic viscosity and μs = 1.802 x 10^-5 is the Dynamic Viscosity at 15 C
Re = VD/v where V is the velocity of wind, D is the diameter of the sphere and v is the kinematic viscosity
Re = (8.056 x 0.2)/(1.426 x 10^-5) = 1.13 x 10^6
Substituting value of Re into Nu equation
Nu = 2 + [0.4(1.13 x 10^6)^0.5 + 0.06(1.13 x 10^6)2/3] (0.7336 ^0.4){(1.778 x 10^-5)/(1.802 x 10^-5)^1/4}
Nu = 2 + [1076.1](0.8835)(0.9967) = 949.5
Putting Nu values in h
h = (0.02439/0.2)(949.5) = 115.8 W/m² C
putting h value in Ts equation
Ts = 10 + [(84/4)/(115.8 x 0.1256)] = 11.4 C
