A long pipe Di=75 cm Do=10 cm and kpipe=35 Wm-K is covered with insulation The insulation ki=5 Wm-K has a thickness of t=125cm The temperature of a fluid flowing inside of the pipe is T∞i=20°C and th

The convection coefficient governing the heat transfer from the fluid flowing inside of the pipe to the inside wall of the pipe can be calculated using the Dittus-Boelter equation:

Nu = 0.023Re^0.8Pr^0.4

where Nu is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number. The Reynolds number can be calculated as:

Re = (ρvD_i)/μ

where ρ is the density of the fluid, v is the velocity of the fluid, D_i is the inner diameter of the pipe, and μ is the viscosity of the fluid. The Prandtl number can be calculated as:

Pr = μC_p/k

where C_p is the specific heat of the fluid and k is the thermal conductivity of the fluid. The Nusselt number can then be used to calculate the convection coefficient using the equation:

h_i = (Nu*k)/D_i

where h_i is the convection coefficient.

First, we need to calculate the Reynolds number. Assuming the fluid is water:

ρ = 1000 kg/m3 v = Q/A = (0.2 m3/h)/(π*(0.075 m)2/4) = 0.56 m/s μ = 0.00089 Pa-s

Re = (ρvD_i)/μ = (1000 kg/m3)(0.56 m/s)(0.075 m)/(0.00089 Pa-s) = 5272

Next, we need to calculate the Prandtl number. Again, assuming the fluid is water:

C_p = 4181 J/(kg-K) k = 0.606 W/(m-K)

Pr = μC_p/k = (0.00089 Pa-s)(4181 J/(kg-K))/(0.606 W/(m-K)) = 6.12

Using the Dittus-Boelter equation, we can calculate the Nusselt number:

Nu = 0.023Re^0.8Pr^0.4 = 0.023(5272)^0.8(6.12)^0.4 = 101.3

Finally, we can calculate the convection coefficient:

h_i = (Nu*k)/D_i = (101.3)(0.606 W/(m-K))/(0.075 m) = 814.8 W/(m2-K)

Therefore, the convection coefficient governing the heat transfer from the fluid flowing inside of the pipe to the inside wall of the pipe is 814.8 W/m2-K