- #1
Tiberious
- 73
- 3
Homework Statement
An appropriate correlation for heat transfer by natural convection from a horizontal pipe to the atmosphere is Nu=0.53Gr^0.25 Pr^0.25
Where,
Gr= (αp^2 d^3 (T_1-T_f )g)/μ^2
And
Pr〖= (C_p μ)/k〗
Show the above correlation can be simplified to
h ≈1.34((T_s-T_f)/d)^0.25 Wm^(-2) K^(-1)
When air has the values listed below
α=3.077∙10^(-3 ) K^(-1)
p=1.086 kg m^(-3)
C_p=1.0063 kj kg^(-1) K^(-1)
k=2.816∙10^(-5) kWm^(-1) K^(-1)
μ=1.962∙10^(-5) kg m^(-1) s^(-1)
The Attempt at a Solution
Inputting the Grashof and Prandtl number equations:Nu=0.53〖(αp^2 d^3 (T_1-T_f )g)/μ^2 〗^0.25 〖(C_p μ)/k〗^0.25
As,
N_u= hd/k
Replacing this into our equation,
hd/k=0.53〖(αp^2 d^3 (T_1-T_f )g)/μ^2 〗^0.25 〖(C_p μ)/k〗^0.25
Rearranging,
h=k/d 0.53〖(αp^2 d^3 (T_1-T_f )g)/μ^2 〗^0.25 〖(C_p μ)/k〗^0.25
Distributing through the exponents,
Struggling to figure this one out. Any assistance is appreciated.
I know I have to Distribute though the terms. Just a little unsure in what order to carry our the operations.