4. GENERAL METHODS OF CALCULATION OF HEAT EXCHANGERS

4.1. Method of factor F

This method uses a correction value F:

Proposing the general equation of heat step:

Insulating Δtm the first equation:

It proposed the 2 thermal balance equations:

Where:

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 = cold fluid heat capacity (2) (J / kg · K)

T_1i = initial temperature of the hot fluid (1) (K)

T₁₀ = final temperature of hot fluid (1) (K)

T_2i = initial temperature of cold fluid (2) (K)

T₂₀ = cold end temperature of the fluid (2) (K)

U = convection coefficient (KJ / h · m 2 K)

A = area of the passage of heat (m 2)

∆Tm = logarithmic mean temperature difference

With equations 1, 2 and 16 can find the variables necessary to find the value of F graphically.

This correction value F is a function of R, P and configuration (2:1, 1:1, 2:4, etc.)

Where:

With equations 17 and 18, and the configuration of heat exchanger can go to the chart and find
the value of F.

We can find two types of problems:

- DESIGN PROBLEM.

INFORMATION:

With this information you must be find the area (A₀ or A_i).

The steps to follow in order to find this area are:

 

1) Proposed the two heat balance equations to find q:

2) Proposed the general equation of heat step:

 

Insolate area (A₀):

Insolate area (A_i):

3) Make diagram of temperature distribution and calculate Δtlog.

4) Calculate R and P:

 

5) Go to the graph and found the two values of R and Q, find F, as shown below
( calculated value of P = 0.6 and R = 1.0):

6) Finally, using the general equation of heat step through the area is calculated
(A₀ o A_i):

- HEAT PROBLEM.

INFORMATION:

With this information and using different equations have to find the final temperature
(T₁₀ and T₂₀).

These problems can be solved by groping along the following steps:

-Rough estimate temperature (assume T'₁₀ T'₂₀).

1) Proposed the general equation of heat step:

2) Make the diagram of distribution temperatures and calculate ∆Tlog.

3) Calculate R and P:

 

4) Go to the graph and found the two values of R and P, find F, as shown below ( calculated value of P = 0.6 and R = 1.0):

5) In general equation of heat step, is the value of heat flux (q):

6) Proposed the two equations of thermal balance to find the temperatures:

7) Check the values found are equal to those alleged. Otherwise, they must assume new initial values and repeat the process explained.

- Rough estimate heat flow (we assume q').

1) Proposed the two equations of thermal balance to find the temperatures:

2) Proposed the general equation of heat step:

3) Make the diagram of distribution temperatures and calculate ∆Tlog.

4) Calculate R and P:

5) Go to the graph and with values of R and P, found F.

6) In general equation of heat step, is the value of heat flux (q):

7) Check the values found are equal to those alleged. Otherwise, they must assume new initial values and repeat the process explained.