Reference ID: MET-4633 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Ohmic (a.k.a. Joule or resistance) heating is a volumetric technique in which an alternating electric field is applied directly to a conductive product. Because heat is generated inside the material, there are no hot surfaces and the temperature rise is nearly instantaneous. The calculation below is used to size heaters, set flow rates, and verify that the outlet temperature remains within product-quality limits for:
Food sterilisation (milk, juices, soups)
Polymer melt pre-heating before extrusion
Continuous-flow chemical reactors
Sludge or biomass pasteurisation
Process engineers apply the energy balance to relate the volumetric power density to the convective enthalpy rise of the moving fluid.
Methodology & Formulas
Convert the quoted electric-field strength to SI units
\( E\ [\mathrm{V\ m^{-1}}] = E_{\text{kV cm}^{-1}} \times 10^{5} \)
Apply an energy balance on the steady-flow heater
\[ \dot{Q} = \dot{m}\,c_{p}\,\Delta T \]
Solve for the temperature rise and outlet temperature
\[ \Delta T = \frac{\dot{Q}}{\dot{m}\,c_{p}} \qquad [\mathrm{K}] \]
\( T_{\text{out}} = T_{\text{in}} + \Delta T \)
Typical safety & operating limits
Parameter
Threshold
Comment
Electric field, E
≤ 0.5 kV cm⁻¹
Higher values risk arcing or product overheating
Outlet temperature
≤ 200 °C
Exceeds normal food/polymer processing range
Mass flow rate
> 0 kg s⁻¹
Must be positive for physical consistency
Heater volume
> 0 cm³
Must be positive for physical consistency
Use the steady-state energy balance: ΔT = (σ E² t) / (ρ cp), where σ is electrical conductivity (S m⁻¹), E is electric field strength (V m⁻¹), t is residence time (s), ρ is density (kg m⁻³), and cp is specific heat (J kg⁻¹ K⁻¹). For most pumpable foods, assume ρ ≈ 1,000 kg m⁻³ and cp ≈ 3,900 J kg⁻¹ K⁻¹. Example: σ = 0.8 S m⁻¹, E = 1,000 V m⁻¹, t = 5 s gives ΔT ≈ 10 °C.
Electrical conductivity σ increases with temperature, so the same voltage delivers more power (P = σ E²). However, the specific heat cp also rises slightly and the denominator in the energy balance grows, while heat losses to the surroundings increase exponentially via convection and radiation. The net effect is a diminishing ΔT per unit time once the product exceeds ~80 °C.
Electrical conductivity σ versus temperature curve (20–100 °C) using a conductivity cell on a 5 °C interval.
Specific heat cp by DSC or calculated from composition using Siebel’s equation.
Density ρ with a pycnometer or assuming 950–1,050 kg m⁻³ for most juices and soups.
Viscosity if the flow is non-Newtonian, because residence time distribution widens and some zones overheat.
Gradually reduce electric field strength along the heater length by tapering electrode gap or using segmented electrodes with lower voltage on the last 20% of the column. Alternatively, inject a small stream of cold feed to mix with the hot product just before the outlet, or operate under slight back-pressure to raise boiling point and avoid vapor formation.
Worked Example – Ohmic Heating of a Fruit Purée
A small-scale aseptic processing line heats a 500 cm³ batch of low-acid fruit purée from 20 °C to the required sterilisation temperature using direct ohmic (resistive) heating. The purée is pumped through a cylindrical heater at 0.5 kg s⁻¹ while an electric field of 0.2 kV cm⁻¹ is maintained across the product. Determine the steady-state temperature rise produced by the ohmic power.
Knowns
Electric field strength, \(E\) = 0.2 kV cm⁻¹ = 20,000 V m⁻¹
