Reference ID: MET-8FA7 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Ohmic heating, also known as Joule heating or electrical resistance heating, is a process where an alternating electric current is passed through a conductive food product or fluid; the resulting internal electrical resistance generates thermal energy directly within the product, providing rapid and uniform heating that minimizes thermal degradation. Understanding the lethality distribution during ohmic heating is essential for optimizing pasteurization and sterilization outcomes in both food and chemical processing applications.
Methodology & Formulas
The calculation of the required electrical parameters follows a systematic approach based on the physical properties of the fluid and the desired thermal outcome. The process is governed by the following fundamental relationships:
1. Electrical Resistance: The resistance of the fluid column is determined by its geometry and electrical conductivity:
\[ R = \frac{L}{A \cdot \sigma} \]
2. Required Thermal Power: The power required to achieve a specific temperature rise is calculated using the mass flow rate, specific heat capacity, and the target temperature differential, adjusted by a safety factor to account for environmental heat losses:
3. Required Voltage: Based on the relationship between power, voltage, and resistance, the necessary operating voltage is derived as follows:
\[ E = \sqrt{Q \cdot R} \]
Parameter
Symbol
Constraint/Threshold
Description
Electrical Conductivity
σ
0.01 S/m ≤ σ ≤ 10.0 S/m
Typical range for food-grade conductive fluids.
Operating Voltage
E
E ≤ 1000 V
Safety threshold for industrial equipment insulation.
Physical Inputs
L, A, ṁ
> 0
Geometric and flow parameters must be positive.
Where:
R is the electrical resistance (Ω)
L is the length of the heating zone (m)
A is the cross-sectional area (m2)
σ is the electrical conductivity (S/m)
Q is the required power (W)
ṁ is the mass flow rate (kg/s)
Cp is the specific heat capacity (J/kg·°C)
ΔT is the temperature increase (°C)
Sf is the safety factor (dimensionless)
E is the required voltage (V)
The power density in an ohmic heating process is determined by the electrical conductivity of the food product and the applied electric field strength. To calculate the volumetric power generation, use the following parameters:
Identify the electrical conductivity (σ) of the product in Siemens per meter (S/m).
Determine the electric field strength (E) in Volts per meter (V/m), calculated as the voltage gradient across the electrodes.
Apply the formula: P = σ · E2, where P represents the power density in Watts per cubic meter (W/m3).
Electrical conductivity is not a constant value and will fluctuate based on several process variables. Engineers must account for:
Temperature: Conductivity typically increases linearly with temperature for most liquid and semi-solid food products.
Ionic concentration: The presence of dissolved salts and acids significantly enhances the ability of the product to conduct current.
Phase changes: Structural changes, such as starch gelatinization or protein denaturation, can alter the effective conductivity of the matrix.
To size the power supply for a continuous system, you must balance the energy required to raise the product temperature with the system throughput. Follow these steps:
Calculate the mass flow rate (ṁ) of the product in kilograms per second (kg/s).
Determine the specific heat capacity (Cp) of the product in Joules per kilogram-Kelvin (J/kg·K).
Define the required temperature rise (ΔT) in Kelvin.
Use the energy balance equation: Q = ṁ · Cp · ΔT, where Q is the total power in Watts.
Adjust the final value by the system efficiency factor to account for heat losses to the environment.
Worked Example: Ohmic Heating Power Calculation
In a pilot-scale food processing facility, a continuous flow ohmic heater is utilized to pasteurize a viscous liquid product. To ensure microbial safety, the system must achieve a specific temperature rise while accounting for heat losses and electrical resistance of the medium. The following calculation determines the required electric field strength to meet the thermal demand.
Knowns:
Length of the heating chamber (L): 0.5 m
Cross-sectional area (A): 0.005 m2
Mass flow rate (ṁ): 0.1 kg/s
Specific heat capacity (Cp): 4000 J/kg·K
Required temperature increase (ΔT): 20 K
Electrical resistance (R): 100.0 Ω
Safety factor: 1.1
Step-by-Step Calculation:
Calculate the required thermal power (Qrequired) to achieve the temperature rise:
\[ Q_{required} = \dot{m} \cdot C_p \cdot \Delta T \cdot \text{Safety Factor} \]
\[ Q_{required} = 0.1 \cdot 4000 \cdot 20 \cdot 1.1 = 8800.0 \text{ W} \]
Determine the required voltage (V) using the relationship between power and resistance:
\[ P = \frac{V^2}{R} \implies V = \sqrt{Q_{required} \cdot R} \]
\[ V = \sqrt{8800.0 \cdot 100.0} = 938.083 \text{ V} \]
Calculate the electric field strength (E) applied across the chamber length:
\[ E = \frac{V}{L} \]
\[ E = \frac{938.083}{0.5} = 1876.166 \text{ V/m} \]
Final Answer:
The required electric field strength to achieve the target heating is 1876.166 V/m.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
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