083442d3-9ea6-4f62-a1f8-23b7b54cb9aa 16 Javier Ochoa 4 5 false false 0 0 decimal

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Optimize thermal perfomance of spiral coils. Author: K.N. Murty. Chemical Engineering, April 17, 1987. Spiral coils are used to heat or cool liquids in various process equipment. For example, when the spiral coil is inmersed in a tank with a liquid sorounded it. The system is designed so that flow inside of the coils is laminar. Although the process is simple, the steps to find the optimum size is not so easy. The complex computations can be avoided with the help of a graph, derived from the fundamental equations involved. The author of the article explained the equations in full detail, which are briefly presented below.

For laminar flow, the friction factor in spiral coils is given by:

K 0.262 0.326 d.i R / (3.5^* + :

f.c f.s φ.s * :

f.s 64 R.e / :

φ.s 1 1.73 R.e 0.2^* d.i R / (* K * + :

For laminar flow, the heat-transfer coefficient for straight tubes is given by an equation found in the "Heat Exchanger Design Handbook", Ernst U. Schlunder ed. , Vol. 2, pp. 2.5.1-2. Hemisphere Publishing Corp., NY, 1983.

For spiral coils, the spirality correction factor the Nusselt number , Nu, and for heat transfer is:

Nu 3.66 3^1.61 3^Pe * d.i R / (13 /^* + :

C 1 1.77 d.i R / (* + :

The ratio of friction factor to Nusselt number is an index of the operational efficiency of the system.

Optimize thermal perfomance of spiral coils to heat or cool liquids in various process equipment are designed so that flow inside the coils is laminar. While the setup is simple, the computation of the equations can be avoided because the system has maximum efficiency when the minimum of the relation (fc / Nu) versus (di / R) is found.

y a.1 1 a.2 x * + a.3 x 4.5^* + (a.4 1 a.5 x * + (* / * :

The equation derived by the autor after arrangments is the following:

y f.c Nu / :

x d.i R / :

a.4 3.66 3^1.61 3^P.e * d.i L / * + (13 /^:

a.1 64 R.e / :

a.2 0.4533 R.e 0.2^* :

a3 0.564 R.e 0.2^* :

a5 1.77 :

Pe Re Pr * :

When dy / dx = 0, the maximum efficiency is achived and the resulting equation to find the optimum ratio (di/R) versus the Reynolds number which is the following:

x NRE f 0.4533 2.538 x 3.5^* + 3.494 x 4.5^* + 1.77 NRE 0.2^/ - :

We can specify a range for NRe between 0.1 and 900, solve the equation and plot the results.

NRE 0.1 0.5 1251020304070100150160200250300350400450500550600650700750800850900950291 mat :

k 1 NRE length range res k el x NRE k 1 el f x solve : for

NRE length 29

res 0.7925 0.7176 0.6856 0.6534 0.6103 0.5768 0.5418 0.5205 0.5047 0.4724 0.45 0.4223 0.4175 0.4005 0.3819 0.3653 0.3498 0.335 0.3206 0.3063 0.2918 0.2768 221 mat

y NRE res augment :

The graph obtained here is the same as the one presented in the article.