Heat irradiation at current of gas in the channel

calculation of liquid or gas heating during flow in the heat exchanger pipe
(with external heat supply)

Scheme of the nomogram system for calculating the heat transfer of a liquid (gas) from the channel walls

Systems of nomograms to calculate the heating parameters of a liquid (gas) flow in a pipe (with an external heat supply). The method for calculating the heat transfer process is formed on the basis of the condition for obtaining the length (section) of a channel (for example, a heat exchanger), under which the gas (liquid) flowing through it is heated by a conditionally accepted temperature value - 3.14 K. When carrying out a graphic-analytical calculation of heat transfer during gas flow in a channel (pipeline), the values of the following parameters are determined (set or selected): Th [K] - temperature of a heater (wall of the channel), Tg [K] - temperature of gas, Cp [kJoule/(kg·K)] - thermal capacity at constant pressure, alfa [kWatt/(m2·K)] - heat transfer coefficient, G [mg/s] - gas discharge, d  [mm]  - diameter of the channel, L  [mm] -  length of a part of the channel. We segment the channel (range of temperatures, - the temperature of each part is constant Tg- middle). Parameters are set - d, G, alfa/Cp. Calculation of length of the channel at change of temperature of gas on  3,14 К. Calculate - how many such segments on 3.14 K in one range of temperatures. Calculate The total length of segments. The calculation formula, nomogram systems for graphic-analytical calculation of the heat transfer coefficient, as well as approximate values of the heat transfer coefficient for different conditions are given on the page "Graphic-analytical calculation of the heat transfer coefficient - α"

The following method for estimating graphic-analytical calculation of gas (liquid) heating in a pipe with an external heat source (for example, an electric heater) is proposed.

1.We divide the channel into several sections (according to the gas temperature), assuming that the gas temperature Tg is constant in each section (average over the section).
For example, when flowing through a hot pipe, the gas must be heated from ten degrees Celsius to ninety: eighty degrees. We divide the channel into ten sections, assuming that in each section the gas temperature should change by eight degrees, and the average temperature in the section is the temperature at the outlet of the previous section plus 8/2 = 4 K (average temperature change in the section), i.e. . the first section: the temperature will change from ten to eighteen degrees, the average temperature - fourteen, the second section: the temperature will change from eighteen to twenty-six degrees, the average - twenty-two degrees, etc. The resulting average temperature is used in the calculation - this is Tg. Only for the calculation of nomograms you need to convert it to Kelvin.

2. With the accepted (in the first approximation) values of the channel diameter d, gas flow rate G, ratio alfa/Cp, as well as the obtained average temperature in the section (on the first - fourteen ...) using systems of nomograms, we determine the length of the minimum segment in the channel section under consideration (corresponds to a temperature change of 3.14 K). The resulting length of an elementary segment must be multiplied by the number of elementary segments in the area under consideration.
In our example, in each section, the gas temperature should increase by eight degrees. Therefore, elementary segments in this section: 8 / 3.14 = 2.55, therefore, the length of an elementary segment obtained using nomograms must be multiplied by 2.55 - we get the length of one section.

3. This procedure must be performed for each of the sections. Then sum the obtained lengths of all sections and, as a result, find the total length of the channel.
In our example, there are ten segments, so we need to search the elementary length ten times in each of the segments and calculate the length of each segment. Then sum the lengths of the segments.

EXAMPLE
CALCULATION OF HEAT TRANSFER WITH A GAS FLOW IN A CAPILLARY

Capillary with internal  diameter d = 1 mm and maintained wall temperature Th = 800 K.
The gas at the entrance to the capillary has a temperature Tg1 = 300 K, at the exit - Tg2 = 700 K.
We accept constant - alfa = 6 kWatt/(kg*K), Cp=2 kJoule/(kg*K).
Gas consumption G = 120 mg/s. Find the length of the capillary.

We divide the channel of the pipeline (capillary) into ten sections. The difference in gas temperature values in each section will be 40 K.
Nom-s # is the number of the main complex of nomograms, the ranges of parameter values of which are suitable for us. Nom-s add # is the number of an additional nomogram with suitable parameter ranges.
The calculation is based on the average gas temperature in each section of the capillary.

So, the total length of the capillary is 20.4 mm.

As you can see, on some  sections (5 - 7) it is necessary to use two systems of nomograms, since some of the parameters go beyond the area of one system of nomograms.
As you can see, it is more convenient to work with the program itself that generates nomogram systems than with its screenshots. This program works with the calculation method itself (a set of methods) and generates an extensive field of options, on which you can move along the axes of the nomograms, increasing or decreasing the required zones of options, as if from a satellite considering the necessary areas of the territory.

A variant of this calculation with the construction of a system of nomograms using an applet (a simplified version of the program for calculating the field of options and constructing a complex of nomograms) is shown on the page "Heat transfer due to fluid movement in a pipe"

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