Question

A 2 in schedule 40 pipe insulated with 1 in of 85% magnesia is carrying a fluid at 800°F. The insulated pipe passes through a room at 80°F, and the outside surface of the magnesia is at 100°F. Please calculate

The total heat loss per linear foot of pipe (in Btu/h),

The temperature of the inside wall of the pipe (in *F), and

The heat transfer coefficient between the fluid inside the pipe and the inside pipe wall (in Btu/h?ft²?F°).

The outside heat transfer coefficient is 10 Btu/h?ft²?F°.

Answer 1

Given,

2 in schedule 40 pipe

Therefore

D_o = 2.375 in

D_i = 2.067 in

t = 0.154 in

Insulation thickness, t_i = 1 in

For 85% magnesia, thermal conductivity, k_m = 0.07 W/mK

We will use notations with respect to figure.

r₁ = 1.0335 in = 0.0262509 m

r₂ = 1.1875 in = 0.0301625 m

r₃ = 2.1875 in = 0.0555625 m

k_m = 0.07 W/mK

h_o = 10 Btu/h ft^2oF = 56.744 W/m²K

T1	800 F	426.667 C
T2	Unknown (to be found out 'T')	-
T3	Unknown	-
T4	100 F	37.7778 C
T5	80 F	26.6667 C

Considering only the surface exposed to atmosphere,

For unit length,

Assuming the material of pipe as steel

k_s = 19 W/mK

Now to find the temperature of inner surface of pipe,

For the inner surface of pipe,