Answer:
μ = dynamic viscosity = unknown
ρ = 1000 kg/m^3
k = 0.8 W/m.K
Cp = 4000 J/kg.K
Step-by-step explanation:
To find the required heat flux, we can use the equation:
Q = m * Cp * (T_out - T_in)
where Q is the heat flux, m is the mass flow rate, Cp is the specific heat capacity, and T_out and T_in are the temperatures at the exit and entrance of the tube, respectively.
Given:
m = 2 x 10^-3 kg/s.m
Cp = 4000 J/kg.K
T_out = 75°C = 75 + 273 = 348 K
T_in = 25°C = 25 + 273 = 298 K
Substituting these values into the equation, we get:
Q = (2 x 10^-3) * 4000 * (348 - 298) = 2.4 W
Therefore, the required heat flux is 2.4 W.
To determine the surface temperature at the tube exit and at a distance of 0.5 m from the entrance, we need to calculate the convective heat transfer coefficient (h) using the following equation:
h = Nu * k / D
where Nu is the Nusselt number and D is the tube diameter.
The Nusselt number can be determined using the following correlation for fully developed flow in a circular tube:
Nu = 0.023 * Re^0.8 * Pr^0.3
where Re is the Reynolds number and Pr is the Prandtl number.
Re = (D * m) / (P * A)
A = π * (D^2 / 4)
Substituting the given values into the equations, we can calculate Re:
D = 12.7 mm = 12.7 x 10^-3 m
P = 1000 kg/m^3
A = π * (12.7 x 10^-3 / 2)^2
Re = (12.7 x 10^-3 * 2 x 10^-3) / (1000 * π * (12.7 x 10^-3 / 2)^2)
Simplifying, we get:
Re ≈ 0.635
Next, we calculate Pr:
Pr = ν / α
ν = μ / ρ
α = k / (ρ * Cp)
Given:
μ = dynamic viscosity = unknown
ρ = 1000 kg/m^3
k = 0.8 W/m.K
Cp = 4000 J/kg.K
We are not given the value of μ, so we cannot calculate Pr accurately.
Therefore, we are unable to determine the convective heat transfer coefficient (h) and, consequently, the surface temperature at the tube exit and at a distance of 0.5 m from the entrance.