Convection Heat Transfer in Liquid Phase

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

q_conv = 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)

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 . z

While 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/kg⁰C]

T_f(z)     = local fluid temperature in the pipe (⁰C)

T_fi        = 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 = 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 . 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.

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 number

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

k_f         = thermal fluid conductivity (W/m ⁰C)

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 ((D³ρ_f³gβΔT)/(μ_f²))^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