3. CALCULATION OF CONCENTRIC TUBES HEAT EXCHANGERS

3.2. Mathematical model counter configuration

The configuration of the two fluids would be as follows:

With the corresponding graph of temperature distribution:

This proposed the thermal balance equations for each flow: q = W1 · Cp1 · (T1i -T10) q = W2 · Cp2 · (T20 - T2i) * If any fluid has a phase change: q = W· ∆Hphase change (3) Where (in units of the International System (SI)): q = heat a fluid that is transmitted to another (J/s) W1 = mass flow of hot fluid (1) (Kg/s) W2 = mass flow of cold fluid (2) (Kg/s) Cp1= heat capacity of the hot fluid (1) (J/Kg·K) Cp2 = heat capacity of the cold fluid (2) (J/Kg·K) T1i= initial temperature of the hot fluid (1) (K) T10 = final temperature of the hot fluid (1) (K) T 2i = initial temperature of the cold fluid (2) (K) T20 = final temperature of the cold fluid (2) (K) ∆Hphase change = enthalpy of the fluid to phase change (J/Kg)	(1) (2)   (3)
Then it raises the general equation of heat pass : q = U0·A0·∆Tlog (if referred to the outer tube inside) (4) q = Ui·Ai·∆Tlog (if referred to the inner tube inside) (5) Where is ∆Tlog:	(4) (5)   (6)
n the picture below you can see the section of a double tube:
The global coefficient of heat transmission referred to the area outside the inner tube, U0, has the expression:	(7)
And the coefficient referred to the internal area:	(8)
Ri and Ro are the resistances due to fouling occurring inside and outside the inner tube, which hinder the transmission of heat.	(9)
Where: Ao: Area outside the inner tube (m2) Ai: Area inside the inner tube (m2) hi: Convection coefficient inside of the fluid 1 (W/m2K) ho: Convection coefficient outside of the fluid 2 (W/m2K) K: Thermal conductivity of tube material (W/m·K) K' : Thermal conductivity of the resistance (W/m·K) L: Pipe length (m) Ro: resistance due to fouling of the outer fluid 2 (m2K/W) Ri: internal resistance due to fouling of the fluid 1 (m2K/W) X: Thickness of the resistance (m)