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Operating Frequency Formula

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Frequency of induction furnace is the operating frequency of coreless induction furnace. Check FAQs

f furnace = \frac{ρ \cdot 10^{9}}{4 \cdot π^{2} \cdot {t c}^{2} \cdot μ r}

f_furnace - Frequency of Induction Furnace?ρ - Specific Resistance?t_c - Thickness of Cylinder?μ_r - Relative Permeability?π - Archimedes' constant?

Operating Frequency Example

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With units

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Here is how the Operating Frequency equation looks like with Values.

Here is how the Operating Frequency equation looks like with Units.

Here is how the Operating Frequency equation looks like.

2.8453 = \frac{113.59 \cdot 10^{9}}{4 \cdot {3.1416}^{2} \cdot {10.6}^{2} \cdot 0.9}

2.8453kHz = \frac{113.59μΩ*cm \cdot 10^{9}}{4 \cdot {3.1416}^{2} \cdot {10.6cm}^{2} \cdot 0.9}

2.8453 = \frac{113.59 \cdot 10^{9}}{4 \cdot {3.1416}^{2} \cdot {10.6}^{2} \cdot 0.9}

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Operating Frequency Solution

Follow our step by step solution on how to calculate Operating Frequency?

FIRST Step Consider the formula

f furnace = \frac{ρ \cdot 10^{9}}{4 \cdot π^{2} \cdot {t c}^{2} \cdot μ r}

Next Step Substitute values of Variables

∴

f furnace = \frac{113.59μΩ*cm \cdot 10^{9}}{4 \cdot π^{2} \cdot {10.6cm}^{2} \cdot 0.9}

Next Step Substitute values of Constants

∴

f furnace = \frac{113.59μΩ*cm \cdot 10^{9}}{4 \cdot {3.1416}^{2} \cdot {10.6cm}^{2} \cdot 0.9}

Next Step Convert Units

∴

f furnace = \frac{1.1E-6Ω*m \cdot 10^{9}}{4 \cdot {3.1416}^{2} \cdot {0.106m}^{2} \cdot 0.9}

Next Step Prepare to Evaluate

∴

f furnace = \frac{1.1E-6 \cdot 10^{9}}{4 \cdot {3.1416}^{2} \cdot {0.106}^{2} \cdot 0.9}

Next Step Evaluate

∴

f furnace = 2845.28728341767Hz

Next Step Convert to Output's Unit

∴

f furnace = 2.84528728341767kHz

LAST Step Rounding Answer

∴

f furnace = 2.8453kHz

Operating Frequency Formula Elements

Variables

Constants

Frequency of Induction Furnace

Frequency of induction furnace is the operating frequency of coreless induction furnace.

Symbol: f_furnace

Measurement: FrequencyUnit: kHz

Note: Value should be greater than 0.

Formulas to find Frequency of Induction Furnace

Specific Resistance

Specific resistance is also known as resisitivity. The resistivity of a material is the resistance of a wire of that material of unit length and unit area of cross-section.

Symbol: ρ

Measurement: Electric ResistivityUnit: μΩ*cm

Note: Value should be greater than 0.

Formulas to find Specific Resistance

Thickness of Cylinder

Thickness Of Cylinder is the length of the cylinder used.

Symbol: t_c

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Thickness of Cylinder

Relative Permeability

Relative permeability is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum.

Symbol: μ_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Relative Permeability

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Furnace Heating category

Go Heat Conduction

Q = \frac{k \cdot A furnace \cdot T total \cdot (T 1 - T 2)}{t w}

Go Heat Radiation

H = 5.72 \cdot e \cdot K \cdot ({(\frac{T 1}{100})}^{4} - {(\frac{T 2}{100})}^{4})

Go Energy Required by Furnace to Melt Steel

E = (m \cdot S heat \cdot (T 2 - T 1)) + (m \cdot L heat)

Go Energy Efficiency

η = \frac{E t}{E a}

How to Evaluate Operating Frequency?

Operating Frequency evaluator uses Frequency of Induction Furnace = (Specific Resistance*10^9)/(4*pi^2*Thickness of Cylinder^2*Relative Permeability) to evaluate the Frequency of Induction Furnace, The Operating Frequency formula is defined as the frequency used to drive the coreless induction furnace. Frequency of Induction Furnace is denoted by f_furnace symbol.

How to evaluate Operating Frequency using this online evaluator? To use this online evaluator for Operating Frequency, enter Specific Resistance (ρ), Thickness of Cylinder (t_c) & Relative Permeability (μ_r) and hit the calculate button.

FAQs on Operating Frequency

What is the formula to find Operating Frequency?

The formula of Operating Frequency is expressed as Frequency of Induction Furnace = (Specific Resistance*10^9)/(4*pi^2*Thickness of Cylinder^2*Relative Permeability). Here is an example- 0.002845 = (1.1359E-06*10^9)/(4*pi^2*0.106^2*0.9).

How to calculate Operating Frequency?

With Specific Resistance (ρ), Thickness of Cylinder (t_c) & Relative Permeability (μ_r) we can find Operating Frequency using the formula - Frequency of Induction Furnace = (Specific Resistance*10^9)/(4*pi^2*Thickness of Cylinder^2*Relative Permeability). This formula also uses Archimedes' constant .

Can the Operating Frequency be negative?

No, the Operating Frequency, measured in Frequency cannot be negative.

Which unit is used to measure Operating Frequency?

Operating Frequency is usually measured using the Kilohertz[kHz] for Frequency. Hertz[kHz], Petahertz[kHz], Terahertz[kHz] are the few other units in which Operating Frequency can be measured.

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Operating Frequency Formula

Operating Frequency Example

Operating Frequency Solution

Operating Frequency Formula Elements

Other formulas in Furnace Heating category

How to Evaluate Operating Frequency?

FAQs on Operating Frequency

Variable Name