In subsea oil and natural gas production, hydrocarbon fluids may leave the reservoir with a temperature of 70°C and flow in subsea surrounding of 5°C. As a result of the temperature difference between the reservoir and the subsea surrounding, the knowledge of heat transfer is critical to prevent gas hydrate and wax deposition blockages. Consider a subsea pipeline with inner diameter of 0.5 m and wall thickness of 8 mm is used for transporting liquid hydrocarbon at an average temperature of 70°C, and the average convection heat transfer coefficient on the inner pipeline surface is estimated to be 250 W/m^2·K. The subsea surrounding has a temperature of 5°C and the average convection heat transfer coefficient on the outer pipeline surface is estimated to be 105 W/m^2·K. The pipeline is made of a material with thermal conductivity of 60 W/m·K, by using the heat conduction equation.

a. Obtain the temperature variation in the pipeline wall.
b. Determine the inner surface temperature of the pipeline.
c. Determine the heat flux through the outer pipeline surface.

A specific thermal energy correlation was established inability to forecast the heat transfer in two-phase flow irrespective of flow, gas-liquid combination, or pipe traverse speed:

It's variable of flow (Fp) as well as the factor of tendency (I *) are provided as follows:

Its l and g superscript apply only to the liquid state as well as the gas phase.

D = diameter tube, m

G = Acceleration of gravity, [tex]\frac{m}{s^2}[/tex]

[tex]H_l[/tex]= coefficient of liquid-phase convection[tex]= \frac{W}{m^2 \times K}[/tex]

[tex]H_{tp}[/tex]= heat transfer of two phase flow, [tex]\frac{W}{m^2\times K}[/tex]

k = thermophysical properties,[tex]\frac{W}{m \times K}[/tex] = volumetric flow rates, [tex]\frac{kg}{s}[/tex]

Pr = number of Prandtl

[tex]Re_{l}[/tex]= Liquid Reynolds number in situ =

V = velocity, [tex]\frac{m}{s}[/tex],

x = standard of flow = /(+)

A = fraction void

r = density, \frac{kg}{m^3}

M = complex viscosity (subscripts b or s for both the conductivity evaluation refer to a bulk average and temperature increases),[tex]\frac{Kg}{m \times s}[/tex]

S = air pressure, [tex]\frac{N}{m}[/tex]

q = angle of inclination, rad

In which the device or environment concentrations in \frac{N}{m^2} respectively is Psys while Patm, and the surface fluid and gas speeds in \frac{m}{s} are Vsl and Vsg respective. Similarity of convection equation 1 were built through a list of observational information point for various flowing patterns, axes of inclination, including variations of gas-liquid and applies to a specific set of parameters:

700 £ Resl £ 127,000, 14 £ Resg £ 209,000, 9.99 '10-3 £ Prg / Prl £ 148' 10-3, and 3.64 '10-3 £ mg/ml £ 26.3' 10-3, while Resl and Resg were the Reynolds substrate liquid and gas amounts, respectively.

Definition of outcomes ii The total of 986 observational information points 176 for horizontal flow, 555 data sets for inclination flow or 255 data sets upward sedimentation tanks) confirmed the specific two-phase heat transfer correlation equation.

It's 986 research data sets with distinctive testing facilities that were collected by various sources. Equation 1 accurately predicted three-quarters of the information option within ±25 percent and 94 percent of the calculated data within an uncertainty range of ±30 percent, as seen in fig.1, across all 986 observational data sets. All in all, there is indeed a root-mean-square variance of 18.4% from the experimental results throughout the prediction of a general two-phase heat transfer relation. Respond to links 7 and 8 for just a comprehensive description of this work.