Analyzing Heat Transfer Properties in Various Food Materials

Every time you pasteurise milk, freeze a batch of vegetables, or sterilise a canned product, the outcome depends on how heat moves through that food. The rate of heat penetration, the uniformity of temperature change, and the energy required for the entire process are all governed by a set of measurable thermal properties. Understanding these properties – thermal conductivity, specific heat, thermal diffusivity, and the behaviour of food during phase transitions – is essential for designing efficient, safe, and quality-preserving food processes.

Why thermal properties matter in food processing 🔗

Food processing operations such as blanching, cooking, drying, pasteurisation, sterilisation, freezing, and thawing all revolve around adding or removing heat from a product. The success of any thermal treatment depends on how a product’s materials respond to an influx of temperature, and thermal conductivity is one of the key characteristics that can influence heat treatment outcomes. Without accurate data on thermal properties, engineers cannot calculate how long a canning process must run, what temperature a freezer should reach, or how thick a product layer can be before the centre remains under-processed.

Thermal properties data are required in engineering and process design – an energy balance for a heating or cooling process simply cannot be performed, and the temperature profile within the material cannot be determined, without knowing the thermal properties of the material. In practical terms, this means that getting these numbers wrong can lead to either under-processing (a food safety hazard) or over-processing (a quality loss).

Thermal conductivity 🔗

Thermal conductivity (k) describes how readily heat passes through a material. It is expressed in watts per metre per degree Kelvin (W/m·K). Thermal conductivity is defined as the quantity of heat transmitted through a unit thickness in a direction normal to a surface of unit area, due to a unit temperature gradient under steady-state conditions.

In equation form:

k = (Q × L) / (A × ΔT)

where Q is the heat flow rate, L is the thickness, A is the area, and ΔT is the temperature difference.

What affects thermal conductivity in foods? 🔗

The thermal conductivity of a food product depends mainly on its chemical composition, molecular structure, and the temperature at which it is processed. Water has a relatively high thermal conductivity (~0.60 W/m·K at room temperature), so foods with high moisture content – fruits, vegetables, lean meats – tend to conduct heat more easily than dry or fatty foods. Fats and oils, by contrast, have low thermal conductivity values (around 0.15-0.18 W/m·K), which is why oil-rich products heat and cool more slowly.

Although stainless steel conducts heat ten times less effectively than aluminium, this difference is small compared with the low thermal conductivity of foods, which is 20 to 30 times lower than steel. This is precisely why the internal resistance of the food – rather than the equipment wall – usually limits how fast a product heats up.

Foods are generally non-homogeneous, varying in composition and structure not only between products, but also within a single product. For instance, the thermal conductivity of meat measured along the muscle fibres can be 15-30% higher than measurements taken across the fibres. Similarly, a layered vegetable like an onion will show variation depending on growing conditions and post-harvest treatment.

Prediction models for thermal conductivity 🔗

Because it is impractical to experimentally measure thermal conductivity for every food formulation, prediction models are widely used. The Choi and Okos model estimates thermal conductivity using the mass fractions of a food’s major components :

k = 0.58X_w + 0.155X_p + 0.25X_c + 0.16X_f + 0.135X_a (W/m·K)

Here, X_w, X_p, X_c, X_f, and X_a represent the mass fractions of water, protein, carbohydrate, fat, and ash, respectively. More advanced structural models like the Maxwell-Eucken equation also account for how these components are physically arranged within the food matrix – whether in parallel layers, in series, or as dispersed particles in a continuous phase.

Specific heat 🔗

Specific heat (c_p) is the amount of energy required to raise the temperature of one kilogram of a substance by one degree Celsius. It is expressed in J/kg·°C or kJ/kg·K. Specific heat is the amount of heat needed to raise the temperature of 1 kg of a material by 1 °C, and is found using the equation: Q = m × c_p × ΔT.

Water has the highest specific heat among common food components at about 4.18 kJ/kg·K. This means that water-rich foods need more energy to heat – and release more energy when cooled – than dry foods. The specific heat of ice is only about 2.1 kJ/kg·K, roughly half that of liquid water, so when a food freezes, its specific heat decreases significantly.

Composition-based prediction of specific heat 🔗

The basic expressions for predicting food properties from food composition were proposed by Choi and Okos (1986), and their research was among the first to incorporate the influence of temperature on the thermophysical properties of foods. The general specific heat model is:

c_p = 4.180X_w + 1.711X_p + 1.98X_f + 1.547X_c + 0.908X_a (kJ/kg·°C)

This equation shows clearly that water dominates the specific heat of most foods. A tomato with ~94% water will have a specific heat close to 4.0 kJ/kg·°C, while a dry grain at ~12% moisture will be much lower, around 1.5-1.8 kJ/kg·°C. Choi and Okos correlations are more accurate at low moisture contents and for a wider range of product composition compared to simpler models like Siebel’s equations.

Thermal diffusivity 🔗

Thermal diffusivity (α) combines thermal conductivity, density, and specific heat into a single parameter that indicates how quickly a temperature change will propagate through a material. Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure, and it measures the rate of heat transfer inside a material.

The equation is:

α = k / (ρ × c_p)

where k is thermal conductivity (W/m·K), ρ is density (kg/m³), and c_p is specific heat (J/kg·K). The SI unit is m²/s.

Practical significance of thermal diffusivity 🔗

Materials with a high thermal diffusivity will heat or cool quickly; conversely, substances with a low thermal diffusivity will heat or cool slowly, making thermal diffusivity an important property in unsteady-state heat transfer situations. Most food processing operations – heating a can in a retort, chilling a carcass in a cold room, baking bread – are unsteady-state processes where temperatures change continuously with time. This makes thermal diffusivity arguably the most practically useful single thermal property for process calculations.

Typical thermal diffusivity values for unfrozen foods range from about 1.0 × 10⁻⁷ to 1.8 × 10⁻⁷ m²/s. Frozen foods can have thermal diffusivity values nine to ten times higher than unfrozen ones because ice has roughly four times the thermal conductivity and half the specific heat of liquid water. This is why a frozen block of fish heats more unevenly than a thawed fillet – heat races through the frozen zone but slows dramatically once thawing begins.

The Biot and Fourier numbers 🔗

Two dimensionless numbers help engineers decide how to approach heat transfer calculations for food. The Biot number (Bi) relates the internal resistance of the food to the surface film resistance, and at small Bi values (below 0.2) the surface film is the main resistance to heat flow. When the Biot number is larger (0.2-40), which covers most food processing situations, internal conduction limits the rate of heating or cooling, and thermal diffusivity becomes the controlling property.

The Fourier number (Fo) relates thermal diffusivity, the size of the food piece, and the duration of heating or cooling. Together, the Biot and Fourier numbers are used with Heisler and Gurney-Lurie charts to solve unsteady-state heat transfer problems for simple food geometries like slabs, cylinders, and spheres.

Phase transitions and latent heat 🔗

Unlike sensible heating (where temperature changes), phase transitions involve energy exchange without a temperature change. Sensible heat is the energy added or removed to change a material’s temperature to a target value, while latent heat is the energy that must be removed or added in order to change the phase of water in the material – and during the phase change, the temperature remains constant.

Freezing and latent heat of fusion 🔗

For pure water, the latent heat of fusion is approximately 334 kJ per kg. For food products, the actual latent heat depends on the water content and can be estimated by multiplying 334 kJ/kg by the mass fraction of water in the food. A lean beef cut with 75% moisture, for example, would require roughly 250 kJ/kg just for the phase change – a substantial energy load that must be handled by the freezing equipment.

Unlike pure water, which freezes sharply at 0°C, foods contain dissolved sugars, salts, and other solutes that depress the freezing point. Freezing preserves food by converting most of the water to ice at −18°C ± 3°C or lower, which reduces the availability of liquid water for chemical and microbiological reactions. Because the water in food freezes over a range of temperatures rather than at a single point, the apparent specific heat rises dramatically near the initial freezing point, making energy calculations more complex.

Evaporation and latent heat of vaporisation 🔗

On the heating side, converting liquid water to steam requires approximately 2,257 kJ/kg – nearly seven times the energy of fusion. Phase changes in water are important in many types of food processing, including steam generation, evaporation by boiling, water loss during dehydration, baking, and frying. In processes like spray drying and evaporation, the latent heat of vaporisation dominates the energy budget, and engineers must design equipment capable of supplying or removing this large energy load efficiently.

How food type affects thermal properties 🔗

Different categories of food materials behave very differently during thermal processing due to variations in composition, structure, and moisture content.

Fruits and vegetables 🔗

With moisture contents often above 80%, fruits and vegetables have thermal properties close to those of water. Their thermal conductivity typically falls between 0.4 and 0.6 W/m·K, and their specific heat is in the range of 3.5-4.0 kJ/kg·°C. However, their porous structure – air pockets in apples, fibrous layers in celery – can lower effective thermal conductivity and create uneven heating.

Meat and fish 🔗

These products have moderate-to-high moisture (60-80%) and contain significant protein and fat. Thermal conductivity measured along the fibres is 15-30% higher than that measured across the fibres in meats. This anisotropy means that the orientation of a meat piece inside processing equipment can affect how quickly it heats through.

Dairy products 🔗

Milk, with about 87% water, has a thermal conductivity of around 0.55 W/m·K. As dairy products become more concentrated (cream, cheese, butter), the increasing fat fraction lowers both thermal conductivity and specific heat. Butter, at ~80% fat, has a thermal conductivity of only about 0.20 W/m·K.

Dry and powdered foods 🔗

Grains, flour, and milk powder have low moisture content and contain trapped air, which is an excellent insulator (k ≈ 0.025 W/m·K). As a result, their effective thermal conductivity can be very low (0.07-0.20 W/m·K), and they heat or cool much more slowly than their dense, moist counterparts.

Measuring thermal properties 🔗

There are two broad approaches to determining the thermal properties of food: direct experimental measurement and composition-based prediction.

Experimental methods 🔗

The dual-needle probe method is widely used for simultaneously measuring thermal conductivity and diffusivity. A heated probe is inserted into the food sample, and the temperature response of a nearby sensor is recorded over time. This approach has been used to determine thermal properties of materials like tomato puree, soy protein, soybean oil, guacamole, honey, cream cheese, and sucrose solutions under various conditions.

Differential Scanning Calorimetry (DSC) is the standard method for measuring specific heat and tracking phase transitions in food, including glass transition temperatures, ice melting, and protein denaturation. It can operate over a wide temperature range and requires only a small sample.

Prediction models 🔗

Prediction of temperature-dependent thermophysical properties is an important component of process design for food manufacturing. The Choi and Okos (1986) models remain the most widely cited. They express thermal conductivity, specific heat, density, and thermal diffusivity as functions of both temperature (−40°C to 150°C) and the mass fractions of six major food components: water, protein, fat, carbohydrate, fibre, and ash. These models were developed as mathematical functions of temperature and have been used extensively in the ASHRAE Handbook of Refrigeration for food property estimation.

Implications for process design 🔗

Getting thermal property data right has direct consequences for several critical processing decisions:

Retort sterilisation: The slowest-heating point in a can (the “cold spot”) must reach a target temperature for a minimum duration to ensure commercial sterility. Thermal diffusivity of the food determines where this cold spot is and how long the process must run.

Freezing time estimation: Plank’s equation, though based on simplified assumptions, is commonly used as a starting point for estimating freezing times and helps engineers understand the effects of product size, heat transfer coefficient, and thermal properties on freezing rates. More accurate modified equations require inputs of thermal conductivity, density, and specific heat both above and below the freezing point.

Pasteurisation and continuous-flow heating: In plate heat exchangers and tubular heaters, the residence time needed to achieve pasteurisation depends on how quickly heat penetrates from the heated wall to the centre of the food stream. For viscous foods with low thermal diffusivity, longer holding tubes or higher wall temperatures are needed.

Energy budgeting: Calculating the total refrigeration load for a freezing operation requires summing the sensible heat removal (above freezing), the latent heat of phase change, and the sensible heat removal (below freezing). Errors in specific heat or latent heat estimates directly translate into under-sized or over-sized equipment.

What do you think? How might advances in rapid thermal property measurement change the way food manufacturers optimise their processing lines? And could real-time monitoring of thermal properties during processing help reduce energy waste while still ensuring food safety?

References

1. https://link.springer.com/chapter/10.1007/0-387-30808-3_3
2. https://www.sciencedirect.com/topics/food-science/thermal-property-of-food
3. https://www.tandfonline.com/doi/full/10.1080/10942911003754726
4. https://link.springer.com/article/10.1007/s12393-016-9157-z
5. https://www.researchgate.net/publication/327690409_Review_of_the_Thermo-physical_properties_models_of_foods
6. https://eng.libretexts.org/Bookshelves/Biological_Engineering/Introduction_to_Biosystems_Engineering_(Holden_et_al.)/06:_Processing_Systems/6.01:_Freezing_of_Food