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
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