The Cowles electric furnace uses a conducting granular charge between opposing electrodes. Electrical resistance produces heat within that charge. Use the calculator to compare electrical power, equivalent resistance and average electrode-shank current density, with a section showing the electrodes, packing, enclosure and complete circuit.
Cowles Electric Furnace Interactive Calculator
Explore electrical power, equivalent bed resistance and average current density in an assumed round electrode shank. The section shows the continuous current path through a granular core inside the furnace enclosure.
Equation Used
- DC operating point; lead and contact losses omitted.
- Circular electrode shank with uniform average current density.
- Bed resistance inferred from V/I, not from material properties.
- Illustrated enclosure and carbon plates follow the historical arrangement but are not dimensioned design drawings.
- No thermal, chemical, electrode-life or permissible-loading calculation.
Current and voltage define an entered operating point. The model does not predict bed resistivity from composition, temperature or electrode spacing. The 300 kW comparison is not an operating limit.
A continuous resistance-heating path
The section follows the box-furnace arrangement in the Cowles patent. Carbon plates contact opposite ends of a granular core. Packing surrounds that core inside a firebrick enclosure, with a vented removable cover above.
Blue leads connect the illustrated DC source to the electrode shanks. Yellow markers indicate conventional-current direction through the circuit; they are not pieces of charge or a prediction of electron drift. The solid material stays in place.
The diameter control changes the assumed round shank thickness and its calculated average current density. The patent arrangement supplies the visual structure; it does not specify the user-entered circular diameter.
Understanding direct electrical heating
This historical arrangement illustrates heat generation within a conducting charge. The calculator compares electrical quantities at an entered voltage and current. It does not calculate smelting yield, reaction time or a furnace operating schedule.
Electrical calculations
Power is P = VI. Equivalent resistance is R = V/I. For the assumed circular shank, area in square centimetres is π(d/10)²/4 when diameter is entered in millimetres. Average current density is I divided by that area.
The percentage tile is 100P/300,000 with P in watts. The 300 kW value is a comparison reference, not a furnace rating. A result above 100% does not independently establish overload, and a result below it does not establish suitability.
Example operating point
At 5,000 A and 60 V, electrical power is 300 kW and equivalent resistance is 12 mΩ. A 300 mm round shank has about 706.86 cm² area, giving average current density of 7.07 A/cm².
Halving shank diameter quarters its area and makes the average current density four times larger at unchanged current. Changing the current or voltage changes electrical power. None of those calculations alone determines furnace temperature.
What the picture and calculator establish
The illustration distinguishes the core from its surrounding packing and completes the external electrical path. Geometry is explanatory. Animated marker speed and core color are visual cues, not transport or thermal measurements.
Material properties, temperature-dependent resistance, contacts, geometry, heat losses and chemical reactions are outside the model. The controls are exploration ranges rather than operating recommendations.
Reference
E. H. and A. H. Cowles, US319945A, Electric Smelting-Furnace, 1885, figures III–V.
Calculator questions
Why does diameter change current density but not power?
The calculator treats current and voltage as independent entered values. Diameter changes only the cross-sectional area used for current density.
Is the colored core a temperature prediction?
No. Color responds to electrical power. A thermal calculation would require additional material, geometry and heat-transfer inputs.
What does the 300 kW percentage mean?
It compares the entered electrical power with a fixed reference. It is not an equipment rating.
Why do the yellow markers circulate?
They identify a continuous electrical path through the leads, electrodes and charge. Their motion is illustrative.
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