How Do You Calculate Pipe Temperature with Uniform Heating Over Length?

[wasaimal]

is anyone help to solve this problem?

Water at a temperature of 20degree C and a pressure 8 bar enters a pipe of dia.0.2 cm.The Pipe uniformly heated with 5.0kW/m². Calculate the Temperature along the pipe for the pipe length of 20m. plot temperatuer as a function of the pipe length. m=0.5 kg/s

wasaimal@hotmail.com

 

[Mech_Engineer]

This is obviously homework, what are your thoughts on how it needs to be solved?

 

[wasaimal]

I have no clue

 

[wasaimal]

Given
T_in = 20 C^0 Heat Flux = 5.0 kW/m^2
D = 0.2 cm X = Length = 20 m
Pressure = 8 bar Area = (πD^2)/4 = (3.14〖(0.002)〗^2)/4 = 3.14E-〖10〗^6 〖 m〗^2
Calculate
Calculate the Temperature along the pipe for the pipe length.
Plot Temperature as a function of the pipe length.
Energy balanced equation is valid for ant pipe length.
q’ (X) = m ̇ C_p (T_x - T_in)
T_x = T_in + (q’)/(mC_p ) ̇ X
= 20 + 0.0157/(0.5)4180 X = 20 + 7.511E-〖10〗^6 X (It’s a linear distribution along the pipe).

any one check and if i am on correct path?

 

[Chestermiller]

is anyone help to solve this problem?

Water at a temperature of 20degree C and a pressure 8 bar enters a pipe of dia.0.2 cm.The Pipe uniformly heated with 5.0kW/m². Calculate the Temperature along the pipe for the pipe length of 20m. plot temperatuer as a function of the pipe length. m=0.5 kg/s

wasaimal@hotmail.com

It looks like the problem is overspecified. You can't specify the mass flow rate if you give the pressure drop (presumably 7 bars).

You first need to get a handle on whether the flow is turbulent or laminar by approximating the Reynolds number. If the flow is laminar, Bird, Stewart, and Lightfoot gives the solution for constant flux laminar flow heating of fluid flow in a tube. If the flow is turbulent, they give the equation for the Nussult Number (dimensionless heat transfer coefficient) as a function of the Reynolds Number and Prantdl number.