thumb|A coiled [[heating element from an electric toaster, showing red to yellow incandescence]]
Joule heating (also known as resistive heating, resistance heating, or Ohmic heating) is the process by which the passage of an electric current through a conductor produces heat.
Joule's first law (also just Joule's law), also known in countries of the former USSR as the Joule–Lenz law, states that the power of heating generated by an electrical conductor equals the product of its resistance and the square of the current. Joule heating affects the whole electric conductor, unlike the Peltier effect which transfers heat from one electrical junction to another.
Joule-heating or resistive-heating is used in many devices and industrial processes. The part that converts electricity into heat is called a heating element.
Practical applications of joule heating include, but are not limited to:
- Buildings are often heated with electric heaters where grid power is available.
- Electric stoves and ovens use Joule heating to cook food.
- Soldering irons generate heat to melt conductive solder and make electrical connections.
- Cartridge heaters are used in various manufacturing processes.
- Electric fuses are used as a safety device, breaking a circuit by melting if enough current flows to heat them to the melting point.
- Electronic cigarettes vaporize liquid by Joule heating.
- Food processing equipment may make use of Joule heating: running a current through food material (which behave as an electrical resistor) causes heat release inside the food. The alternating electrical current coupled with the resistance of the food causes the generation of heat. A higher resistance increases the heat generated. Joule heating allows for fast and uniform heating of food products, which maintains quality. Products with particulates heat up faster (compared to conventional heat processing) due to higher resistance.
History
James Prescott Joule first published in December 1840, an abstract in the Proceedings of the Royal Society, suggesting that heat could be generated by an electrical current. Joule immersed a length of wire in a fixed mass of water and measured the temperature rise due to a known current flowing through the wire for a 30 minute period. By varying the current and the length of the wire he deduced that the heat produced was proportional to the square of the current multiplied by the electrical resistance of the immersed wire.
In 1841 and 1842, subsequent experiments showed that the amount of heat generated was proportional to the chemical energy used in the voltaic pile that generated the template. This led Joule to reject the caloric theory (at that time the dominant theory) in favor of the mechanical theory of heat (according to which heat is another form of energy).
Assuming the element behaves as a perfect resistor and that the power is completely converted into heat, the formula can be re-written by substituting Ohm's law, <math>V = I R </math>, into the generalized power equation:
<math display="block">P = IV = I^2R = V^2/R</math>
where R is the resistance.
Alternating current
When current varies, as it does in AC circuits,
<math display="block">P(t) = U(t) I(t)</math>
where t is time and P is the instantaneous active power being converted from electrical energy to heat. Far more often, the average power is of more interest than the instantaneous power. For an ideal resistor, with zero reactance, the average joule-heating power is
<math display="block">P_{\rm avg} = U_\text{rms} I_\text{rms} = (I_\text{rms})^2 R = (U_\text{rms})^2 / R</math>
where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square.
If the reactance is nonzero, the formulas are modified. The average joule-heating power is
<math display="block">P_{\rm avg} = U_\text{rms}I_\text{rms}\cos\phi = (I_\text{rms})^2 \operatorname{Re}(Z) = (U_\text{rms})^2 \operatorname{Re}(Y^*)</math>
where <math>\phi</math> is phase difference between current and voltage, <math>\operatorname{Re}</math> means real part, Z is the complex impedance, and Y* is the complex conjugate of the admittance (equal to 1/Z*).
Note that <math>\operatorname{Re}(Z) = R</math>, and
<math display="block">\operatorname{Re}(Y^*) = \operatorname{Re} \frac{1}{Z^*} = \operatorname{Re} \frac{Z}{|Z|^2} = \frac{R}{|Z|^2}</math>.
For more details in the reactive case, see AC power.
Differential form
Joule heating can also be calculated at a particular location in space. The differential form of the Joule heating equation gives the power per unit volume.
<math display="block">\frac{\mathrm{d}P}{\mathrm{d}V} = \mathbf{J} \cdot \mathbf{E}</math>
Here, <math>\mathbf{J}</math> is the current density, and <math>\mathbf{E}</math> is the electric field. For a material with a conductivity <math>\sigma</math>, <math>\mathbf{J}=\sigma \mathbf{E}</math> and therefore
<math display="block">\frac{\mathrm{d}P}{\mathrm{d}V} = \mathbf{J} \cdot \mathbf{E} = \mathbf{J} \cdot \mathbf{J}\frac{1}{\sigma} = J^2\rho</math>
where <math>\rho = 1/\sigma</math> is the resistivity. This directly resembles the "<math>I^2R</math>" term of the macroscopic form.
In the harmonic case, where all field quantities vary with the angular frequency <math>\omega</math> as <math>e^{-\mathrm{i} \omega t}</math>, complex valued phasors <math>\hat\mathbf{J}</math> and <math>\hat\mathbf{E}</math> are usually introduced for the current density and the electric field intensity, respectively. The Joule heating then reads
<math display="block">\frac{\mathrm{d}P}{\mathrm{d}V} = \frac{1}{2}\hat\mathbf{J} \cdot \hat\mathbf{E}^* = \frac{1}{2}\hat\mathbf{J} \cdot \hat\mathbf{J}^*/\sigma = \frac{1}{2}J^2\rho,</math>
where <math>\bullet^*</math> denotes the complex conjugate.
Electricity transmission
Overhead power lines transfer electrical energy from electricity producers to consumers. Those power lines have a nonzero resistance and therefore are subject to Joule heating, which causes transmission losses.
The split of power between transmission losses (Joule heating in transmission lines) and load (useful energy delivered to the consumer) can be approximated by a voltage divider. In order to minimize transmission losses, the resistance of the lines has to be as small as possible compared to the load (resistance of consumer appliances). Line resistance is minimized by the use of copper conductors, but the resistance and power supply specifications of consumer appliances are fixed.
Usually, a transformer is placed between the lines and consumption. When a high-voltage, low-intensity current in the primary circuit (before the transformer) is converted into a low-voltage, high-intensity current in the secondary circuit (after the transformer), the equivalent resistance of the secondary circuit becomes higher and transmission losses are reduced in proportion.
During the war of currents, AC installations could use transformers to reduce line losses by Joule heating, at the cost of higher voltage in the transmission lines, compared to DC installations.
Applications
Food processing
thumb|General process for joule heating in food
Joule heating is a flash pasteurization (also called "high-temperature short-time" (HTST)) aseptic process that runs an alternating current of 50–60 Hz through food. Heat is generated through the food's electrical resistance. As the product heats, electrical conductivity increases linearly.
Electrical energy is linearly translated to thermal energy as electrical conductivity increases, and this is the key process parameter that affects heating uniformity and heating rate.
This method can also inactivate antinutritional factors thereby maintaining nutritional and sensory properties.
Ohmic heating is limited by viscosity, electrical conductivity, and fouling deposits. Additionally, a successful 12D reduction for C. botulinum prevention has yet to be validated. FJH has also been used to recover rare-earth elements used in modern electronics from industrial wastes<!-- with practical potential to reduce environmental/health impacts from mining, waste-generation and imports if it can be scaled up-->. Beginning from a fluorinated carbon source, fluorinated activated carbon, fluorinated nanodiamond, concentric carbon (carbon shell around a nanodiamond core), and fluorinated flash graphene can be synthesized.
Gallery
Heating efficiency
Heat is not to be confused with internal energy or synonymously thermal energy. While intimately connected to heat, they are distinct physical quantities.
As a heating technology, Joule heating has a coefficient of performance of 1.0, meaning that every joule of electrical energy supplied produces one joule of heat. In contrast, a heat pump can have a coefficient of more than 1.0 since it moves additional thermal energy from the environment to the heated item.
The definition of the efficiency of a heating process requires defining the boundaries of the system to be considered. When heating a building, the overall efficiency is different when considering heating effect per unit of electric energy delivered on the customer's side of the meter, compared to the overall efficiency when also considering the losses in the power plant and transmission of power.
Hydraulic equivalent
In the energy balance of groundwater flow a hydraulic equivalent of Joule's law is used:
<math display="block"> \frac{dE}{dx} = \frac{(v_x)^2}{K} </math>
where:
- <math>dE/dt</math> = loss of hydraulic energy (<math>E</math>) due to friction of flow in <math>x</math>-direction per unit of time (m/day), comparable to <math>P</math>
- <math>v_x</math> = flow velocity in <math>x</math>-direction (m/day), comparable to <math>I</math>
- <math>K</math> = hydraulic conductivity of the soil (m/day), the hydraulic conductivity is inversely proportional to the hydraulic resistance which compares to <math>R</math>