- #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.