How to calculate the heating temperature of iron-chromium-aluminum heating wire

The calculation of the heating temperature of the iron-chromium-aluminum heating wire is relatively complicated and involves multiple factors. The following is a step-by-step introduction to the calculation method:
1. Basic Principle
The iron-chromium-aluminum heating wire generates heat through current passing through resistance, following Joule's law, where (Q) is the heat generated (joule), (I) is the current (ampere), (R) is the resistance (ohm), and (t) is the time (second). This heat will be transferred to the surrounding medium, causing its temperature to rise, and the temperature of the heating wire itself will also rise.
2. Calculation steps
(1) Determine the parameters of the heating wire
Resistance value (R): The resistance of the iron-chromium-aluminum heating wire can be calculated based on its material properties and size. The resistance calculation formula is, where is the resistivity of the iron-chromium-aluminum material at a specific temperature (unit:), which will change with temperature. Generally, the values ​​corresponding to different temperatures can be found in the manual; (L) is the length of the heating wire (meters); (S) is the cross-sectional area of ​​the heating wire (square meters).
 Rated power (P): If the rated voltage (U) and rated current (I) of the heating wire are known, the rated power can be obtained according to ; it can also be calculated by the resistance value and the rated voltage.
(2) Calculation of heat dissipation
 Convective heat dissipation: It is mainly related to the temperature difference between the surface of the heating wire and the surrounding air, the air flow rate, the surface area of ​​the heating wire, etc. Convective heat dissipation formula, where (h) is the convection heat transfer coefficient (), when the air is naturally convection, (h) is approximately in the range of, and when forced convection, (h) will be larger; (A) is the surface area of ​​the heating wire (); is the difference between the surface temperature of the heating wire and the surrounding air temperature ((K) or).
 Radiative heat dissipation: It is related to the blackness of the surface of the heating wire, the absolute temperature, the ambient temperature, etc. Radiation heat dissipation formula, where is the Stefan-Boltzmann constant; is the blackness of the heating wire surface. Generally, the blackness of the iron-chromium-aluminum heating wire in the oxidized state is ; (A) is the surface area of ​​the heating wire (); (T) is the absolute temperature of the heating wire surface ((K)), is the absolute temperature of the surrounding environment ((K)).
(3) Establish a heat balance equation
When the heating wire reaches a stable working state, the heat generated is equal to the heat lost, that is. Substitute the previously calculated convection heat dissipation and radiation heat dissipation formulas into the heat balance equation:

At this time, (U), (R), (h), (A),,, are known quantities (or can be measured or calculated), (T) is an unknown quantity (that is, the heating temperature of the heating wire we require). By solving the above equation, the heating temperature of the heating wire (T) can be obtained. Generally, this equation is a nonlinear equation and may need to be solved by numerical methods (such as iteration method). In practical applications, it can also be estimated by empirical formulas or experimental data to simplify the calculation process.

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