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

q

_{conv}= φ . AWhere:

A = Area of the heated surface (m

^{2}). In the pipe, cross-sectional area which is heated is π.D.zφ = Heat flux on the surface of pipe (Watt/m

^{2})q

_{conv}= Convection heat transfer (Watt)z = length of pipe (m)

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

q

_{conv}= φ . π . D . zWhile the heat transfer on the fluid inside pipe is:

q

_{conv}= W_{f}. c_{pf}. (T_{f}(z) – T_{fi})Where:

W

_{f}= mass flow rate in the liquid phase (kg/s)c

_{pf}= coefficient of heat convection in the liquid phase (J/kg^{0}C]T

_{f}(z) = local fluid temperature in the pipe (^{0}C)T

_{fi}= temperature of fluid enter pipe [^{0}C ]So the heat balance on pipe is by combining equations above to be following equation:

φ . π . D . z = W

_{f}. c_{pf}. (T_{f}(z) – T_{fi})Mass flow rate (W

_{f}) is often made in mass velocity (G) the relationship between both of them is as following equation:G = (4. W

_{f}) / (π . D^{2})So by rearranging the equation above and combine them can be obtained equation below to calculate distribution the local heat fluid of along pipe.

T

_{f}(z) = T_{fi}+ ((4 . φ . z) / (G . C_{pf}. D))Pipe wall surface temperature is the temperature of local fluid coupled with the difference of wall temperature and the local temperature:

T

_{w}= (T_{f}(z) + ΔT_{f})Where:

ΔT

_{f}= φ / h_{fo}So the equation will be:

T

_{w}= (T_{f}(z) + (φ / h_{fo}))h

_{fo}is calculated from Nusselt number as following equation:Nu

_{D}= (h_{fo}. D) / k_{f}Where:

Nu

_{D}= Nusselt numberh

_{fo}= coefficient of convection fluid (W/m^{2 0}C)k

_{f}= thermal fluid conductivity (W/m^{ 0}C)D = pipe diameter (m)

Nusselt number for laminar flow in pipe:

Nu

_{D}= 0.17 Re^{0.33}Pr_{f}^{0.43}(Pr_{f}/Pr_{w})^{0.25}((D^{3}ρ_{f}^{3}gβΔT)/(μ_{f}^{2}))^{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.

Nu

_{D}= 0.023 Re^{0.28}Pr_{f}^{0.4}
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