In most heat exchangers some scale formation will take place on both sides of the heat transfer surface after the heat exchanger has been in use for some time (unless scale inhibition mechanism is in place). This introduces two additional resistances in the heat flow path. Thus the total thermal resistance becomes:

ΣR        = R_i + R_si +R_w + R_so + R_o                         (eq. 1.27)

Where R_si = thermal resistance due to scale formation on inside surface of inner pipe, m² C/W

        R_so = thermal resistance due to scale formation on outside surface of inner pipe, m² C/W

(We can here consider no scaling on outside surface of inner pipe)

Since it is difficult to ascertain accurately the thickness and thermal conductivity of the scale formed, the effect of scale deposit on heat flow is generally taken into account by specifying an equivalent scale heat transfer coefficient, hs.
 
The reciprocal of the scale heat transfer coefficient is called the fouling factor. If hsi and hso denote the heat transfer coefficient for the scale formed on the inside and outside surface of he inner pipe, then:

R_si        =   1/A_ih_si                                                           (eq. 1.29)

R_so        =   1/A_oh_so                                                         (eq. 1.30)

And q = .                          (t_i - t_o)                                     (eq. 1.31)

               1/A_ih_i + 1/A_ih_si + ln (r_o/r_i) +1/A_oh_so + 1/A_oh_o

                                           2πLK_w

U_i  = .                                          1                                                (eq. 1.32)

                 1/h_i + 1/h_si + A_i ln (r_o/r_i) + [A_i/A_o]. 1/h_so + [A_i/A_o]. 1/h_o

                                                  2πLK_w 

or

U_i  =                                             1                                            (eq. 1.33)  

            1/h_i + 1/h_si + [r_i/k_w] ln (r_o/r_i) + [r_i/r_o]. 1/h_so + [r_i/r_o]. 1/h_o

The fouling factor (1/h_s) for some representative applications are listed in following table:

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Introduction | Combined heat transfer process | Heat transfer in cooling tower | Variables affecting performance of CT heat transfer | Heat transfer within cooling system (heat exchanger) | Types of heat exchanger | Basic design procedure and theory | Designing a test heat exchanger | Log Mean Temperature difference | L.M.T.D. Correction factors | Overall heat transfer coefficient | Elaborated method for calculating U values | Effect of scale formation | Condensation of steam | Condenser, where the hot fluid temperature varies | Significance of pressure | Significance of flow rate | Methods of checking steam condenser performance | Common conversion factors