Convection Section Design:

In the convection section, heat is transferred by both radiation and convection. The convection transfer coefficients for fin and stud tubes are explored here as well as bare tube transfer. The short beam radiation is treated separately from the convection transfer below.
This section of Fired Heater Design is divided into five main areas, which can be selected from the subject drop down box above or you may use the jump links below to go to a section. You may also use your browser "back button" to return to where you were.

Overall Heat Transfer Coefficient, U_o:

Where,

And,

And the resistances are computed as,

Where,

Inside film heat transfer coefficient, hi:
The inside heat transfer coefficient calculation procedure is covered in detail, elsewhere in this course.

Effective outside heat transfer coefficient, he

Where,

Outside film heat transfer coefficient, hc:
The bare tube heat transfer film coefficient, h_c, can be described by the following equations.
For a staggered tube arrangement,

And for an inline tube arrangement,

Where,

We can describe a sample bare tube bank as follows:

Gas Properties
For the gas properties, we can use the script we used in the radiant section design to get the properties of the gas at the average temperature.

From this program, we get the following properties,
k_b, Btu/hr-ft-F = 0.0315
c_p, Btu/lb-F = 0.2909
m_b, cp = 0.0340 = 0.0340*2.42 = 0.0823 lb/hr-ft
To calculate the mass velocity, G_n, we need to first calculate the net free area of the tube bank. For these calculations, we are going to assume the tube rows are corbelled, so the net free area, NFA:
NFA = N_wide*t_spc/12*t_lgth-N_wide*t_Od/12*t_lgth = 8*8/12*13-8*4.5/12*13 = 30.333 ft²
Therefore,
G_n = W_gas / NFA = 100000/30.333 = 3296.739
And using our formula for h_c,

To get a feel for the values of the coeffcient, use the following script to run various designs.

The radiation transfer coefficient, h_r is described later in this section. Fouling resistances, R_fi and R_fo are allowances that depend upon the process or service of the heater and the fuels that are being burned.

You will notice that the heat transfer equations for the fin tubes are basically the same as for the bare tubes untill you reach the h_e factor, where a new concept is introduced to account for the fin or extended surface. The procedure presented herein are taken from the Escoa manual which can be downloaded in full from the internet.

Overall Heat Transfer Coefficient, U_o:

Where,

And,

And the resistances are computed as,

Where,

Inside film heat transfer coefficient, hi:
The inside heat transfer coefficient calculation procedure is covered in detail, elsewhere in this course.
Effective outside heat transfer coefficient, h_e:

Where,

And,
Average outside heat transfer coefficient, h_o:

Where,

Outside film heat transfer coefficient, hc:

Where,

Colburn heat transfer factor, j:

Where,

Reynolds number correction, C₁:

Where,

Geometry correction, C₃:
For segmented fin tubes arranged in, a staggered pattern

an inline pattern,

For solid fin tubes arranged in, a staggered pattern

an inline pattern

Where,

Non-equilateral & row correction, C₅:
For fin tubes arranged in, a staggered pattern

an inline pattern

Where,

Mass Velocity, G_n:

Where,

Net Free Area, A_n:

Where,

Surface Area Calculations:
For the prime tube,

And for solid fins,

And for segmented fins,

And then,

Where,

We can describe a sample fin tube bank as follows:

Gas Properties
For the gas properties, we can use the script we used in the radiant section design to get the properties of the gas at the average temperature. From this program, we get the following properties,
k_b, Btu/hr-ft-F = 0.0290
c_p, Btu/lb-F = 0.2858
m_b, cp = 0.0317 = 0.0317*2.42 = 0.0767 lb/hr-ft
To calculate the mass velocity, G_n, we need to first calculate the net free area of the tube bank. For these calculations, we are going to assume the tube rows are corbelled, so the net free area, A_n:
A_d = 8*13*8/12 = 69.333
A_c = (4.5+2*0.75*0.05*6)/12 = 0.4125 So,

And,

Now we can calculate the reynolds number, R_e,

And,

For, s_f = 1/6-.05=0.1167

And,
P_l = (8²-8/2²)^0.5=6.9282

Now we can calculate the Colburn factor,

And finally,

To get a feel for the values of the coeffcient, use the following script to run various designs.

The radiation transfer coefficient, h_r is described later in this section. Fouling resistances, R_fi and R_fo are allowances that depend upon the process or service of the heater and the fuels that are being burned.

Fin Efficiency, E:
For segmented fins,

And for solid fins,

Where,

And,

Where,

For segmented fins,

And for solid fins,

Fin Tip Temperature, T_s:
The average fin tip temperature is calculated as follows,

Maximum Fin Tip Temperature, T_fm:
The maximum fin tip temperature is calculated as follows,

Where,

And, The value for theta, q, can be described by the following curve.

The gas radiation factor, h_r, can be calculated from the following correlations. This factor is used in calculating the overall heat transfer coefficient for bare tubes and fin tubes. The formulas for the stud tubes has this factor built into the equations. For bare tubes,

And for fin tubes,

Where,

Outside radiation factor, g _r: The outside radiation factor can be described by the following curves:

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