### Convection Heat Transfer in Liquid Phase

Convection heat transfer with heat flux (φ) constant is calculated using the following equation:

qconv = φ . A

Where:
A = Area of ​​the heated surface (m2). In the pipe, cross-sectional area which is heated is π.D.z
φ = Heat flux on the surface of pipe (Watt/m2)
qconv = Convection heat transfer (Watt)
z = length of pipe (m)

So for a pipe with diameter D, The value of heat transfer that occurs is:

qconv = φ . π . D . z

While the heat transfer on the fluid inside pipe is:

qconv = Wf . cpf . (Tf (z) – Tfi)

Where:
Wf        = mass flow rate in the liquid phase (kg/s)
cpf        = coefficient of heat convection in the liquid phase (J/kg0C]
Tf(z)     = local fluid temperature in the pipe (0C)
Tfi        = temperature of fluid enter pipe [0C ]

So the heat balance on pipe is by combining equations above to be following equation:

φ . π . D . z = Wf . cpf . (Tf (z) – Tfi)

Mass flow rate (Wf) is often made ​​in mass velocity (G) the relationship between both of them is as following equation:

G = (4. Wf) / (π . D2)

So by rearranging the equation above and combine them can be obtained equation below to calculate distribution the local heat fluid of along pipe.

Tf (z) = Tfi + ((4 . φ . z) / (G . Cpf . D))

Pipe wall surface temperature is the temperature of local fluid coupled with the difference of wall temperature and the local temperature:

Tw = (Tf (z) + ΔTf )

Where:
ΔTf = φ / hfo
So the equation will be:
Tw = (Tf (z) + (φ / hfo))

hfo is calculated from Nusselt number as following equation:

NuD = (hfo . D) / kf
Where:
NuD     = Nusselt number
hfo        = coefficient of convection fluid (W/m2 0C)
kf         = thermal fluid conductivity (W/m 0C)
D         = pipe diameter (m)

Nusselt number for laminar flow in pipe:

NuD = 0.17 Re0.33 Prf0.43 (Prf/Prw)0.25 ((D3ρf3gβΔT)/(μf2))0.1

applies to z/D > 50 and Re < 2000, while for turbulent flow in a pipe used Dittus-Boelter equation, which applies to z/D > 10 and Re > 3000.

NuD = 0.023 Re0.28 Prf0.4