What Is the Specific Heat of Beef

FREEZING | Principles

B.R. Becker , B.A. Fricke , in Encyclopedia of Food Sciences and Nutrition (Second Edition), 2003

Thermal Properties of Foods

The thermal properties of foods are important in the design of food storage and refrigeration equipment as well as in the estimation of process times for refrigerating, freezing, heating, or drying of foods. Because the thermal properties of foods are strongly dependent upon chemical composition and temperature, the most viable option is to predict these thermal properties using mathematical models that account for the effects of chemical composition and temperature.

Composition data for foods are readily available in the literature. These data consist of the mass fractions of the major food components: water, protein, fat, carbohydrate, fiber, and ash. Food thermal properties can be predicted by using these composition data in conjunction with temperature-dependent mathematical models of the thermal properties of the individual food components.

Equations for predicting the thermal properties of these food components have been developed as functions of temperature in the range of −   40 to 150   °C. These equations are presented in Table 1. Because water is the predominant constituent in most food items, the water content of food items significantly influences the thermophysical properties of foods. Therefore, equations for predicting the thermal properties of water and ice have also been developed. These equations are presented in Table 2.

Table 1. Thermal property equations for food components (−40   °C ≤ t ≤ 150   °C)

Thermal property	Food component	Thermal property model
Thermal conductivity (W   m−1  K−1)	Protein	k  =   1.7881   ×   10−1  +   1.1958   ×   10−3 t  −   2.7178   ×   10−6 t 2
	Fat	k  =   1.8071   ×   10−1  −   2.7604   ×   10−3 t  −   1.7749   ×   10−7 t 2
	Carbohydrate	k  =   2.0141   ×   10−1  +   1.3874   ×   10−3 t  −   4.3312   ×   10−6 t 2
	Fiber	k  =   1.8331   ×   10−1  +   1.2497   ×   10−3 t  −   3.1683   ×   10−6 t 2
	Ash	k  =   3.2962   ×   10−1  +   1.4011   ×   10−3 t  −   2.9069   ×   10−6 t 2
Density (kg   m−3)	Protein	ρ  =   1.3299   ×   103 −   5.1840   ×   10−1 t
	Fat	ρ  =   9.2559   ×   102 −   4.1757   ×   10−1 t
	Carbohydrate	ρ  =   1.5991   ×   103  −   3.1046   ×   10−1 t
	Fiber	ρ  =   1.3115   ×   103  −   3.6589   ×   10−1 t
	Ash	ρ  =   2.4238   ×   103  −   2.8063   ×   10−1 t
Specific heat (J   kg−1  K−1)	Protein	c p  =   2.0082   ×   103  +   1.2089t  −   1.3129   ×   10−3 t 2
	Fat	c p  =   1.9842   ×   103  +   1.4733t  −   4.8008   ×   10−3 t 2
	Carbohydrate	c p  =   1.5488   ×   103  +   1.9625t  −   5.9399   ×   10−3 t 2
	Fiber	c p  =   1.8459   ×   103  +   1.8306t  −   4.6509   ×   10−3 t 2
	Ash	c p =   1.0926 × 103  +   1.8896t  −   3.6817   ×   10−3 t 2

Table 2. Thermal property equations for water and ice (−   40   °C ≤ t ≤ 150   °C)

	Thermal property	Thermal property model
Water	Thermal conductivity (W   m−1  K−1)	k w  =   5.7109   ×   10−1  +   1.7625   ×   10−3 t  −   6.7036   ×   10−6 t 2
	Density (kg   m−3)	ρ w  =   9.9718   ×   102  +   3.1439   ×   10−3 t  − 3.7574   ×   10−3 t 2
	Specific heat (J   kg−1  K−1) a	c w  =   4.0817   ×   103  −   5.3062t  +   9.9516   ×   10−1 t 2
	Specific heat (J   kg−1  K−1) b	c w  =   4.1762   ×   103  −   9.0864   ×   10−2 t  +   5.4731   ×   10−3 t 2
Ice	Thermal conductivity (W   m−1  K−1)	k ice  =   2.2196   −   6.2489   ×   10−3 t  +   1.0154   ×   10−4 t 2
	Density (kg   m−3)	ρ ice  =   9.1689   ×   102  −   1.3071   ×   10−1 t
	Specific heat (J   kg−1  K−1)	c ice  =   2.0623   ×   103  +   6.0769t

a

For the temperature range of −40 to 0   °C.

b

For the temperature range of 0 to 150   °C.

In general, the thermophysical properties of a food item are well behaved when the temperature of the food item is above its initial freezing point. However, below the initial freezing point, the thermophysical properties of a food item vary dramatically with temperature.

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Food Freezing Technology

Chenchaiah Marella , Kasiviswanathan Muthukumarappan , in Handbook of Farm, Dairy and Food Machinery Engineering, 2013

8.3 Effect of Freezing on Food Thermal Properties

Knowledge of thermal properties of food products is needed in design of cooling, freezing processes, and equipment, as well as cooling load calculations. Data on thermal properties of some foods are given in Table 13.3. Thermal conductivity of ice (k=2.24   W/m K) is around four times that of water (k=0.56   W/m K). Consequently, thermal conductivity of frozen foods will be three to four times higher than that of unfrozen foods. During the initial stages of freezing, increase in thermal conductivity is rapid. For high fat foods the variation in thermal conductivity with temperature is negligible. For meats, orientation of fibers greatly influences thermal conductivity. Thermal conductivity measured along the fibers is 15–30% higher than that measured across the fibers in meats (Dickerson, 1968). Thermal conductivities of several food products at different temperatures are available in the literature (Lentz, 1961; Smith et al., 1952; Woodams and Nowrey, 1968).

Table 13.3. Thermal Properties of Frozen Foods (Earle, 1983)

Food	Water Content, %	Specific Heat, kJ/kg K	Latent Heat, kJ/kg
Apple	84	1.88	280
Banana	75	1.76	255
Watermelon	92	2.0	305.1
Peaches	87	1.92	288.4
Green beans	89	1.96	296.8
Cabbage	92	1.96	305.1
Carrot	88	1.88	292.6
Beef	75	1.67	255
Fish	70	1.67	275.9
Pork	60	1.59	196.5
Bread	32–37	1.42	108.7–221.2
Egg	--	1.67	275.9
Milk	87.5	2.05	288.4

Specific heat of ice (2.1   kJ/kg K) is only half of the specific heat of water (4.218   kJ/kg K). On freezing, specific heat of foods decreases. Measurement of specific heat is complicated because there is continuous phase change from water to ice. Latent heat of fusion for any food product can be estimated from the water fraction of the food (Fennema, 1973). Solute concentration in foods is so small that latent heat of freezing of solutes is generally ignored while estimating the cooling loads. Thermal diffusivity of frozen foods can be calculated from density, specific heat, and thermal conductivity data. The thermal conductivity of ice is around four times higher than that of water and its specific heat is half that of water. This leads to an increase of around nine to ten times in thermal diffusivity values of frozen foods when compared to unfrozen ones (Desrosier and Desrosier, 1982).

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Heat processing

P.J. Fellows , in Food Processing Technology (Third Edition), 2009

10.1.1 Thermal properties of foods

Three important thermal properties of foods are specific heat, thermal conductivity and thermal diffusivity. Specific heat is the amount of heat needed to raise the temperature of 1   kg of a material by 1   °C. It is found using Equation10.1 and specific heat values for selected foods and other materials are given in Table 10.1.

Table 10.1. Specific heat of selected foods and other materials

Material	Specific heat (kJ   kg −   1  °C −   1)	Temperature (°C)
Foods – solid
Apples	3.59	Ambient
Apples	1.88	Frozen
Bacon	2.85	Ambient
Beef	3.44	Ambient
Bread	2.72	–
Butter	2.04	Ambient
Carrots	3.86	Ambient
Cod	3.76	Ambient
Cod	2.05	Frozen
Cottage cheese	3.21	Ambient
Cucumber	4.06	Ambient
Flour	1.80	–
Lamb	2.80	Ambient
Lamb	1.25	Frozen
Mango	3.77	Ambient
Milk – dry	1.52	Ambient
Milk – skim	3.93	Ambient
Potatoes	3.48	Ambient
Potatoes	1.80	Frozen
Sardines	3.00	Ambient
Shrimps	3.40	Ambient
Foods – liquid
Acetic acid	2.20	20
Ethanol	2.30	20
Milk – whole	3.83	Ambient
Oil – maize	1.73	20
Oil – sunflower	1.93	20
Orange juice	3.89	Ambient
Water
Water	4.18	15
Water vapour	2.09	100
Ice	2.04	0
Non-foods – solid
Aluminium	0.89	20
Brick	0.84	20
Copper	0.38	20
Glass	0.84	20
Glass wool	0.7	20
Iron	0.45	20
Stainless steel	0.46	20
Stone	0.71-0.90	20
Tin	0.23	20
Wood	2.4–2.8	20
Non-foods – gases
Air	1.005	Ambient
Carbon dioxide	0.80	0
Oxygen	0.92	20
Nitrogen	1.05	0

Adapted from Anon (2005c, 2007a), Singh and Heldman (2001a) and Polley et al. (1980)

10.1 ${\mathit{c}}_{\mathrm{p}}=\frac{\mathit{Q}}{\mathit{m}\left({\mathit{\theta }}_1-{\mathit{\theta }}_2\right)}$

where c _p (J   kg^{−   1}  °C^{−   1})   =   specific heat of food at constant pressure, Q (J)   =   heat gained or lost, m (kg)   =   mass and θ ₁ – θ ₂ (°C)   =   temperature difference.

The specific heat of compressible gases is usually quoted at constant pressure, but in some applications where the pressure changes (e.g. vacuum evaporation (Chapter 14, section 14.1) or high-pressure processing (Chapter 8) it is quoted at constant volume (C _v). The specific heat of foods depends on their composition, especially the moisture content (Equation10.2). Equation10.3 is used to estimate specific heat and takes account of the mass fraction of the solids contained in the food:

10.2 ${\mathit{c}}_{\mathrm{p}}=0.837+3.348\mathit{M}$

where M  =   moisture content (wet-weight basis, expressed as a fraction not percentage),

10.3 ${\mathit{c}}_{\mathrm{p}}=4.180{\mathit{X}}_{\mathrm{w}}+1.711{\mathit{X}}_{\mathrm{p}}+1.928{\mathit{X}}_{\mathrm{f}}+1.547{\mathit{X}}_{\mathrm{c}}+0.908{\mathit{X}}_{\mathrm{a}}$

where X  =   mass fraction and subscripts w   =   water, p   =   protein, f   =   fat, c   =   carbohydrate and a   =   ash.

Thermal conductivity is a measure of how well a material conducts heat. It is the amount of heat that is conducted through unit thickness of a material per second at a constant temperature difference across the material and is found using Equation10.4.

10.4 $\begin{array}{l}\mathit{k}=\frac{\mathit{Q}}{\mathit{t\theta }}\\ \end{array}$

where k (J   s^{−   1}  m^{−   1}  °C^{−   1} or W m^{−   1}  °C^{−   1})   =   thermal conductivity and t (s)   =   time.

Thermal conductivity is influenced by a number of factors concerned with the nature of the food (e.g. cell structure, the amount of air trapped between cells, moisture content), and the temperature and pressure of the surroundings. A formula to predict thermal conductivity based on the composition of foods is shown in Equation10.5:

10.5 $\mathit{k}={\mathit{k}}_{\mathrm{w}}{\mathit{X}}_{\mathrm{w}}+{\mathit{k}}_{\mathrm{s}}\left(1-{\mathit{X}}_{\mathrm{w}}\right)$

where k _W (W   m^{−   1}  °C^{−   1})   =   thermal conductivity of water, X _w  =   mass fraction of water, k _s  =   (W   m^{−   1}  °C^{−   1})   =   thermal conductivity of solids (assumed to be 0.259   W   m^{−   1}  °C^{−   1}).

A reduction in moisture content causes a substantial reduction in thermal conductivity. This has important implications in unit operations which involve conduction of heat through food to remove water (e.g. drying (Chapter 16), frying (Chapter 19) and freeze drying (Chapter 23)). In freeze drying the reduction in atmospheric pressure also influences the thermal conductivity of the food.

Ice has a higher thermal conductivity than water and this is important in determining the rate of freezing and thawing (Chapter 22). The importance of thermal conductivity is shown in sample problem 10.1 and sample problem 11.1 (Chapter 11). The thermal conductivities of some materials found in food processing are shown in Table 10.2.

Sample problem 10.1

Part 1: In a bakery oven, combustion gases heat one side of a 2.5   cm steel plate at 300   °C and the temperature in the oven is 285   °C. Assuming steady state conditions, and a thermal conductivity for steel of 17   W   m^{−   2}  °C^{−   1}, calculate the rate of heat transfer per m² through the plate.

Part 2: The internal surface of the oven is 285   °C and air enters the oven at 18   °C. Calculate the surface heat transfer coefficient per m², assuming the rate of heat transfer is 10.2   kW.

Solution to sample problem 10.1

Part 1:

From Equation10.11,

$\begin{array}{l}\mathit{Q}=-\frac{17\times 1\times \left(300-285\right)}{0.025}\\ =10200\mathrm{W}\end{array}$

Part 2:

From Equation10.13,

$\begin{array}{l}\mathit{h}=\frac{10200}{\left(285-18\right)}\\ =38.2\mathrm{W}{\mathrm{m}}^{-1}°{\mathrm{C}}^{-1}\end{array}$

This value indicates that natural convection is taking place in the oven.

Table 10.2. Thermal conductivity of selected foods and other materials

Material	Thermal conductivity (Wm−   1 oC−   1)	Temperature (°C)
Food
Acetic acid	0.17	20
Apple juice	0.56	20
Avocado	0.43	28
Beef, frozen	1.30	–10
Bread	0.16	25
Carrot	0.56	40
Cauliflower, frozen	0.80	–8
Cod, frozen	1.66	–10
Egg, frozen liquid	0.96	–8
Ethanol	0.18	20
Freeze dried foods	0.01–0.04	0
Green beans, frozen	0.80	–12
Ice	2.25	0
Milk, whole	0.56	20
Oil, olive	0.17	20
Orange	0.41	15
Parsnip	0.39	40
Peach	0.58	28
Pear	0.59	28
Pork	0.48	3.8
Potato	0.55	40
Strawberry	0.46	28
Turnip	0.48	40
Water	0.57	20
Gases
Air	0.024	0
Air	0.031	100
Carbon dioxide	0.015	0
Nitrogen	0.024	0
Packaging materials
Cardboard	0.07	20
Glass	0.52	20
Polyethylene	0.55	20
Poly(vinylchloride)	0.29	20
Metals
Aluminium	220	0
Copper	388	0
Stainless steel	17–21	20
Other materials
Brick	0.69	20
Concrete	0.87	20
Insulation	0.026–0.052	30
Polystyrene foam	0.036	0
Polyurethane foam	0.026	0

Adapted from Anon (2007a,b), Choi and Okos (2003), Singh and Heldman (2001a) and Lewis (1990)

Although, for example, stainless steel conducts heat ten times less well than aluminium (Table 10.2), the difference is small compared with the low thermal conductivity of foods (20 to 30 times lower than steel) and does not limit the rate of heat transfer. Stainless steel is much less reactive than other metals, and is therefore used in most food processing equipment that comes into contact with foods.

Thermal diffusivity is a measure of a material's ability to conduct heat relative to its ability to store heat. It is a ratio involving thermal conductivity, density and specific heat, and is found using Equation10.6:

10.6 $\mathit{\alpha }=\frac{\mathit{k}}{\mathit{\rho }{\mathit{c}}_{\mathrm{p}}}$

where α (m²s^{−   1})   =   thermal diffusivity and ρ (kg   m^{−   3})   =   density. Thermal diffusivity is used to calculate time-temperature distribution in materials undergoing heating or cooling and selected examples are given in Table 10.3.

Table 10.3. Thermal diffusivity of selected foods

Food	Thermal diffusivity (×   l0−   7  m2  s−   1)	Temperature (°C)
Apples	1.37	0–30
Avocado	1.24	41
Banana	1.18	5
Beef	1.33	40
Cod	1.22	5
Ham, smoked	1.18	5
Lemon	1.07	0
Peach	1.39	4
Potato	1.70	25
Strawberry	1.27	5
Sweet potato	1.06	35
Tomato	1.48	4
Water	1.48	30
Water	1.60	65
Ice	11.82	0

Adapted from Singh and Heldman (2001a) and Murakami (2003)

The thermal diffusivity of foods is influenced by their composition, especially their moisture content, and it can be estimated using Equation10.7:

10.7 $\mathit{\alpha }=0.146\times {10}^{-6}{\mathit{X}}_{\mathrm{w}}+0.100\times {10}^{-6}{\mathit{X}}_{\mathrm{f}}+0.075\times {10}^{-6}{\mathit{X}}_{\mathrm{p}}+0.082\times {10}^{-6}{\mathit{X}}_{\mathrm{c}}$

where X  =   mass fraction and subscripts w   =   water, f   =   fat, p   =   protein and c   =   carbohydrate. For example, every 1% increase in the moisture content of vegetables corresponds to a 1–3% increase in their thermal diffusivity (Murakami 2003). Changes in the volume fraction of air can also significantly alter the thermal diffusivity of foods. During heating, the temperature does not have a substantial effect on thermal diffusivity, but in freezing the temperature is important because of the different thermal diffusivities of ice and water.

'Sensible' heat is the heat needed to raise the temperature of a food and is found using Equation10.4, rearranged from Equation10.1:

10.8 $\mathit{Q}=\mathit{m}\times {\mathit{c}}_{\mathrm{p}}\left({\mathit{\theta }}_1-{\mathit{\theta }}_2\right)$

where Q (J)   =   sensible heat, m (kg)   =   mass, c _p (J   kg^{−   1}  °C^{−   1} or K^{−   1})   =   specific heat of food at constant pressure and θ (°C)   =   temperature with subscripts 1 and 2 being initial and final values.

Phase changes in water are important in many types of food processing including steam generation for process heating (section 10.2), evaporation by boiling (Chapter 14, section 14.1), loss of water during dehydration, baking and frying (Chapters 16, 18, 19) and in freezing (Chapter 22). 'Latent' heat is the heat used to change phase (e.g. latent heat of fusion to form ice, or latent heat of vaporisation to change water to vapour) where the temperature remains constant while the phase change takes place. A phase diagram (Fig. 23.2 in Chapter 23) shows how temperature and pressure control the state of water (solid, liquid or vapour).

Vapour pressure is a measure of the rate at which water molecules escape as a gas from the liquid. Boiling occurs when the vapour pressure of the water is equal to the external pressure on the water surface (boiling point =   100   °C at atmospheric pressure at sea level). At reduced pressures below atmospheric, water boils at lower temperatures as shown in Chapter 14 (Fig. 14.1).

The changes in phase can be represented on a pressure–enthalpy diagram (Fig. 10.1) where the bell-shaped curve shows the pressure, temperature and enthalpy relationships of water in its different states. Left of the curve is liquid water, becoming subcooled the further to the left, and right of the curve is vapour, becoming superheated the further to the right. Inside the curve is a mixture of liquid and vapour. At atmospheric pressure, the addition of sensible heat to liquid water increases its heat content (enthalpy) until it reaches the saturated liquid curve (A–B in Fig 10.1). The water at A is at 80   °C and has an enthalpy of 335   kJ   kg^{−   1} and when heated to 100   °C the enthalpy increases to 418 kJkg^{−   1}. Further addition of heat as latent heat causes a phase change. Moving further across the line (B–C) indicates more water changing to vapour, until at point C all the water is in vapour form. This is then saturated steam that has an enthalpy of 2675   kJ   kg^{−   1} (i.e. the latent heat of vaporisation of water is 2257 (2675 – 418) kJ kg^{−   1} at atmospheric pressure while the temperature remains constant at 100   °C). Within the curve along B–C, the changing proportions of water and vapour are described by the 'steam quality'. For example at point E, the steam quality is 0.9, meaning that 90% is vapour and 10% is water. The specific volume of steam with a quality <   100% can be found using Equation10.9. Further heating (C–D) produces superheated steam. At point D it is at 250   °C and has an enthalpy of 2800   kJ   kg^{−   1}.

Fig. 10.1. Pressure–enthalpy diagram for water: H_c  =   enthalpy of condensate; H_v  =   enthalpy of saturated vapour; H_s  =   enthalpy of superheated steam (from Straub and Scheibner 1984, with kind permission of Springer Science and Business Media).

10.9 ${\mathit{V}}_{\mathrm{s}}=\left(1-{\mathit{x}}_{\mathrm{s}}\right){\mathit{V}}_1+{\mathit{x}}_{\mathrm{s}}{\mathit{V}}_{\mathrm{v}}$

where V _s (m³  kg^{−   1})   =   specific volume of steam, x _s (%)   =   steam quality, V ₁ (m³  kg^{−   1})   =   specific volume of liquid and V _v (m³  kg^{−   1})   =   specific volume of vapour. The data summarised in Fig. 10.1 is also available as steam tables (Keenan et al. 1969), and selected values are shown in Table 10.4 ('steam' is another term for hot water vapour).

Table 10.4. Properties of saturated steam

Temperature (°C)	Vapour pressure (kPa)	Latent heat (kJ   kg−   1)	Enthalpy (kJ   kg−   1)		Specific volume (m3  kg−   1)
			Liquid	Saturated vapour	Liquid	Saturated vapour
30	4.246	2431	125.79	2556.3	0.001 004	32.89
40	7.384	2407	167.57	2574.3	0.001 008	19.52
50	12.349	2383	209.33	2592.1	0.001 012	12.03
60	19.940	2359	251.13	2609.6	0.001 017	7.67
70	31.19	2334	292.98	2626.8	0.001 023	5.04
80	47.39	2309	334.91	2643.7	0.001 029	3.41
90	70.14	2283	376.92	2660.1	0.001 036	2.36
100	101.35	2257	419.04	2676.1	0.001 043	1.67
110	143.27	2230	461.30	2691.5	0.001 052	1.21
120	198.53	2203	503.71	2706.3	0.001 060	0.89
130	270.1	2174	546.31	2720.5	0.001 070	0.67
140	316.3	2145	589.13	2733.9	0.001 080	0.51
150	475.8	2114	632.20	2746.5	0.001 091	0.39
160	617.8	2083	675.55	2758.1	0.001 102	0.31
170	791.7	2046	719.21	2768.7	0.001 114	0.24
180	1002.1	2015	763.22	2778.2	0.001 127	0.19
190	1254.4	1972	807.62	2786.4	0.001 141	0.15
200	1553.8	1941	852.45	2793.2	0.001 156	0.13
250	3973.0	1716	1085.36	2801.5	0.001 251	0.05
300	8581.0	1405	1344.0	2749.0	0.001 044	0.02

Adapted from Singh and Heldman (2001b) original data from Keenan, J.H., Keyes, F.G., Hill, P.G. and Moore, J.G., (1969), Steam tables metric units, Wiley, New York, copyright John Wiley &amp; Sons

When a phase change from water to vapour occurs, there is a substantial increase in the volume of vapour. In some unit operations, such as dehydration, this is not important, but in freeze drying (Chapter 23, section 23.1) and evaporation (Chapter 14, section 14.1) the removal of large volumes of vapour requires special equipment designs.

In steam production using boilers, the vapour produced by the phase change is contained within the fixed volume of the boiler vessel and there is therefore an increase in vapour (or steam) pressure. Higher pressures result in higher-temperature steam (moving further right of the curve in the superheated vapour section of Fig. 10.1). The required pressure and temperature of process steam are controlled by the rate of heating in the boiler (see also section 10.2).

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Heat Transfer in Food Processing

R. Paul Singh , Dennis R. Heldman , in Introduction to Food Engineering (Fifth Edition), 2014

Heat transfer is ubiquitous in food processing. Heat exchangers are commonly used for the purposes of heating and cooling foods. In designing heating or cooling systems, thermal properties of foods and food contact materials are required. The key thermal properties include specific heat, thermal conductivity, and thermal diffusivity. Heat exchange between a heating or cooling medium and food occurs by conduction, convection and/or radiation. Mathematical expressions are useful in determining the rate of heat transfer and for designing process equipment. Heat transfer calculations are conducted for steady state and unsteady state conditions. Most common shapes of heat exchangers used in food processing are either tubular or plate. Fouling is a common occurrence in thermal operations and its impact on heat transfer can be determined with appropriate expressions. Dimensionless relationships involving Biot number, Prandtl number, and Fourier number are used in determining unsteady state heat transfer. Understanding mechanisms that are involved in heating foods in a microwave field is necessary to develop novel foods for microwave applications.

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MEAT | Preservation

D.A. Ledward , in Encyclopedia of Food Sciences and Nutrition (Second Edition), 2003

Product Cooling

Refrigerated meats are generally classified as chilled or frozen. However, there may be several steps involved in reducing a hot product to chill or frozen storage temperature, with several additional links before final consumption. The design and operation of equipment to perform these functions require an understanding of the thermal properties of foods and an appreciation of their complexity and that of prevailing legislation.

Immediately after heat treatment or cooking, it will be necessary to commence cooling under controlled conditions. Filtered ambient air or mains water are suitable media for cooling the product temperature to about 35°C. Naturally, the latter would only be used where there is a hermetically sealed skin packaging. These represent cheaper energy sources than mechanical refrigeration or expendable refrigerants, which are required for achieving the statutory temperatures, which lie below 10°C.

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Neural network method of modeling heat penetration during retorting

C. Chen , in In-Pack Processed Foods, 2008

Publisher Summary

Conventional thermal processing can be divided into two types: retort processing and aseptic processing. The retort processing method is one of the most mature processing technologies. In retort thermal processing, the heat is transferred by conduction and/or convection from the heating medium to the food, depending on the type of foods being processed. The temperature inside the food during heating will be determined by a variety of processing conditions, including the type of heating medium and its temperature, initial product temperature, thermal properties of food being heated, and rheological properties for liquid foods. Theoretically, it is possible to apply a mathematical modeling method combined with modern computation techniques for the simulation of thermal processing of solid or particulate liquid foods, provided all the processing conditions can be discovered and all the thermo-physical properties of the food obtained by independent experiments. However, the biggest challenge that food modeling researchers are facing is that, unlike other engineering materials, food materials have variable thermal and/or physical properties, most of which are temperature and processing time dependent. This means that it is very difficult to discover the properties and their changes with processing temperature and time under conditions simulating the real processes. In recent years, Artificial Neural Networks (ANNs) have opened alternative pathways for modeling of complex and nonlinear processes. The advantages of ANNs over conventional mathematical methods in modeling performance have been recognized and confirmed by many research reports. This chapter focuses on an introduction to the basic principles of neural networks, the development of neural network models, and their application advances in food thermal processing areas.

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Electrical properties

M.J. Lewis , in Physical Properties of Foods and Food Processing Systems, 1996

12.4 ELECTRICAL ENERGY

When a current flows through a potential difference, a quantity of energy is dissipated in the form of heat. This is used to define the unit of potential difference as follows. One volt (1   V) is the difference of electric potential between two points of a conducting wire carrying a constant current of 1 A, when the power dissipated between these points is equal to 1   W (Js^{−   1}). Instruments used for measuring potential difference are known as voltmeters.

The total amount of electrical energy E evolved when a current I flows over a potential difference V for a time t is given by

$\mathit{E}\left(\mathrm{J}\right)=\mathit{V}\left(\mathrm{V}\right)\times \mathit{I}\left(\mathrm{A}\right)\times \mathit{t}\left(\mathrm{s}\right)$

The electrical power rating P is given by VI (W). In this way, electrical energy is converted to thermal energy. Electrical methods are used for estimating thermal properties of foods (see sections 8.5 and 9.7).

Thus an electric bulb rated at 60   W running off a power source of 240   V would carry a current of 60/240   =   0.25   A. Energy would be dissipated at the rate of 60   J   s^{−   1}.

The amount of electrical energy used by the consumer is measured in terms of kilowatt hours or units. The number of units used is equal to the product of the power rating in kilowatts and the time in hours:

$\mathrm{number}\mathrm{of}\mathrm{units}\mathrm{used}\left(\mathrm{kWh}\right)=\mathrm{power}\mathrm{rating}\left(\mathrm{kW}\right)\times \mathrm{time}\left(\mathrm{h}\right)$

Thus a lamp rated at 60   W alight for 20   h would use (60/1000)   ×   20   =   1.2 units. Currently the cost of electricity to the UK domestic consumer is 5.2p per unit.

The pricing system for industrial users is not so straightforward, being based on the maximum demand as well as the total number of units. Electricity costs can be reduced by trying to spread the load throughout the day, thereby ensuring that there are no excessive peaks in electrical demand.

It is perhaps interesting to note that one unit of electricity is equivalent to l000 Js^{−   1}  ×   3600   s, i.e. 3.6   ×   10⁶  J (3.6   MJ) of energy. The latent heat of vaporization of water at atmospheric pressure is 2.257   MJ   kg^{−   1}; so the evaporation of 1   kg of water vapour by direct electrical methods would require 0.63 units of electricity and would cost 3.28p (assuming no heat losses and ignoring sensible heat changes). In contrast, heating 1   kg of milk from 5   °C to 72   °C would require 1   ×   67   ×   4000   =   0.268   MJ and would cost 0.387p.

Other expressions for electrical power can be derived from Ohm's law:

$\mathit{P}={\mathit{I}}^2\mathit{R}\mathrm{or}\frac{{\mathit{V}}^2}{\mathit{R}}$

Electrical power is measured using a wattmeter, the most common types being those to measure AC power consumption for household supply.

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Methodology

Yrjö H. Roos , Stephan Drusch , in Phase Transitions in Foods (Second Edition), 2016

3.4.1.2 DSC and DTA

DTA and DSC are closely related methods, which are probably the most common techniques in the determination of phase transitions in inorganic, organic, polymeric, and also food materials. DTA measures temperature of a sample and a reference as a function of temperature. A phase transition causes a temperature difference between the sample and the reference, which is recorded. DSC may use the same principle, but the temperature difference between the sample and the reference is used to derive the difference in the energy supplied. DSC may also measure the amount of energy supplied to the sample and the reference. The use of DTA and DSC in food applications was reviewed by Biliaderis (1983) and Lund (1983). DSC and DTA in various modifications, such as modulated DSC and hyperheating DSC, have been used to determine melting properties of sugars, lipids, and various other thermal properties of food components and foods (Roos et al., 2013).

DTA and DSC are used to detect endothermal and exothermal changes that occur during a dynamic measurement as a function of temperature or isothermally as a function of time. The thermograms obtained show the heat flow to the sample and DSC data can be used to calculate enthalpy changes and heat capacities. First-order phase transitions produce peaks and a step change in heat flow occurs at second-order transitions. As shown in Figure 3.10 thermograms showing first-order transitions can be analyzed to obtain transition temperatures. The latent heat of the transition is obtained by peak integration. Thermograms showing second-order transitions can be used to derive transition temperatures and changes in heat capacity as shown for glass transition in Figure 3.11. The transition occurs over a temperature range of 10–30°C. Both the onset and midpoint temperatures of the glass transition temperature range are commonly referred to as T _g . Enthalpy recovery of an amorphous material after annealing around T _g may also be used to indirectly estimate molecular mobility (Baird and Taylor, 2012).

Figure 3.10. A schematic DSC thermogram showing an endothermal, first-order phase transition, for example, melting. The onset of the transition occurs at T _o , which is the transition temperature. In broad melting transitions the peak temperature of the endotherm, T _p , and the endset temperature, T _e , may also be determined. T _o and T _e are obtained from the intercept of tangents drawn at the point at which deviation from the baseline occurs. Peak integration is used to obtain the latent heat of the transition, ΔH _l .

Figure 3.11. Determination of second-order and glass transition temperatures, T _g , and change in heat capacity, ΔC _p , that occurs over the glass transition temperature range from DSC thermograms. The endothermal step change in heat flow during heating of glassy materials occurs due to ΔC _p at the second-order transition temperature.

Applications of DSC in the determination of phase transitions in foods include such changes as crystallization and melting of water, lipids, and other food components; protein denaturation and gelatinization; and retrogradation of starch. The samples are usually placed in pans that can be hermetically sealed. Therefore, the method can be used to observe phase transitions and to determine transition temperatures without changes in water content. A constant water content is extremely important in the determination of phase transitions of food materials. Water has an enormous effect on transition temperatures, and its impact on food behavior cannot be overemphasized.

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High-Pressure Processing of Foods

Yang Tao , ... Alan L. Kelly , in Emerging Technologies for Food Processing (Second Edition), 2014

1.6 Modeling HP Processes

Since the discovery by Pasteur that microorganisms are responsible for food spoilage, scientists have attempted to develop mathematical models to predict the effects of processing and storage on food constituents. Some of these models have been based on thermodynamic principles, while others were strictly empirical. Today, both types of models are in common use by researchers, industry, and regulatory agencies.

1.6.1 Modeling HP Processes

Currently, most of the models developed to predict the inactivation of microorganisms by HP and the influence of HP on food critical quality parameters are statistically based, including several specific empirical models, response surface models, artificial neural networks, and partial least square regression models (Amina et al., 2010; Belletti et al., 2013). Although these models do not express the physical meaning of the HP process, they are able to correlate HP-related processing parameters with the determined responses well and provide robust predictive results. Consequently, the optimum HP treatment conditions for processing can be determined.

Furthermore, it is a challenging task to simulate the temperature variation in processed products under pressure and to predict the local temperature profiles during processing using mathematical tools, which can provide valuable information for designing HP equipment and ensuring the food quality and microbiological safety. There are several difficulties that hinder the construction of heat transfer models during HP treatment, including:

1.

a lack of data for the thermal properties of food materials under pressure;

2.

the pressure and temperature dependency of thermal properties;

3.

the calculation of the adiabatic temperature increase/decrease after the pressure buildup/release;

4.

the convective heat transfer that takes place in the pressurizing fluid between the inner wall of the vessel and the sample (Otero and Sanz, 2003).

The temperature changes of specified materials during pressurization depend on their thermophysical properties. The compression heating behavior of water has been extensively investigated, since all raw foods contain high levels of water and water is commonly employed as the pressure-transmitting fluid during pressurization (Otero and Sanz, 2003). Also Knoerzer et al. (2010a,b) have developed a numerical routine to determine the compression heating properties of various materials as functions of temperature and pressure, including liquid, solid, and semi-solid compressible materials. In addition to the thermophysical properties of the materials, several other variables should be taken into account, including temperature in the HP vessel chamber prior to processing, product temperature, uniformity of temperature throughout the product, ratio of pressurizing fluid to product, and pressurization time.

There is a growing interest in modeling the heat transfer during HP processing of food products by means of computational fluid dynamics (CFD) technology (Ghani and Farid, 2007; Knoerzer and Chapman, 2011). Knoerzer and Chapman (2011) found that the predictive accuracy of CFD models was closely related to the compression heating properties of the compressed materials and the pressure profile characteristic during processing.

1.6.2 Modeling HP Freezing Processes

Because of the advantages of HPSF over classical atmospheric freezing methods, some attempts to model this process have been made (Otero et al., 2002; Otero and Sanz, 2006; Norton et al., 2009). Generally, it is difficult to model processes that involve a phase change at atmospheric pressure in foods because of their heterogeneous biological structure; i.e., water is not totally available for freezing. The current literature available lacks enough thermophysical data for food and its components to be used for modeling high pressure domains. In addition, modeling the freezing process is further complicated when the phase change is induced under pressure or by fast pressure release (Otero and Sanz, 2003).

Any model developed for a classical freezing process at atmospheric pressure should reproduce the process under pressure if appropriate thermophysical properties are considered. Such models might take into account the temperature and pressure dependence of the thermophysical properties of the products, including their latent heat, freezing point, and convective heat transfer coefficient. It is also essential to consider the temperature change that the system undergoes after an adiabatic compression or expansion. Furthermore, a properly developed model must quantify the amount of ice instantaneously produced after the adiabatic expansion.

When modeling HP processes at sub-zero temperatures, pressure/temperature phase transition data and values for latent heat under pressure are usually needed. Another modeling strategy is based on enthalpy formation instead of considering latent heat, since it is difficult to handle the latter under pressure (Norton et al., 2009). Experimental determinations of the aforementioned properties in food models and real food systems are essential to improve models. To develop more accurate tools to allow real thermal control in HP processes, all the thermal exchanges involved in the HP freezing process, including those between the pressure-transmitting medium and the steel mass of the vessel, should be considered (Otero and Sanz, 2003). Thermal expansion, isothermal compressibility, specific volume, and specific isobaric heat capacity are some of the essential thermodynamic properties in modeling phase transition phenomena involved in HPSF and HP thawing around the liquid–ice I melting curve of water (Otero et al., 2002). Other interesting thermophysical parameters, such as thermal conductivity and diffusivity and phase change enthalpies, behave more independently in their derivation and measurements (Otero et al., 2002).

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Quality Measurement of Cooked Meats

C.-J. Du , ... D.-W. Sun , in Computer Vision Technology for Food Quality Evaluation (Second Edition), 2016

8.3.2 Correlations With Water Content, Processing Time, and Texture

Being a defect often observed in cooked meats, internal pore formation is normally unappealing for the consumers and therefore negative for the meat industry (Hullberg et al., 2005). Du and Sun (2006b) reported that the total number of pores (TNP) is significantly negatively related with the water content of pork ham (P  <   0.05). For the raw meat, the variation in the total extracellular space is found to explain 39% of the variation in early postmortem drip loss in pork (Schäfer et al., 2002). During cooking, heat denaturation of myofibrillar proteins and collagen will create more pores, and at the same time increase water loss (Ofstad et al., 1993). As a result, the more pores exist, the more water is lost during processing. Similarly, water content is found highly negatively correlated with porosity (P  <   0.05). The action of cooking causes loss of water, and consequently decreases water content and increases the porosity of cooked meats. Water evaporation plays an important role in energy exchanges during cooling (Girard, 1992). To facilitate the cooling process, it is necessary to remove a certain proportion of sample mass in the form of water vapor (McDonald and Sun, 2001a). In the mean time, as moisture transport is closely related to the formation of pores (Rahman, 2001), the more water loss during cooling, the higher porosity can be achieved.

Both TNP and porosity are negatively correlated with the cooking time. More TNP (r  =   −0.56) and higher porosity (r  =   −0.67) will result in quicker cooking time (Du and Sun, 2006b). The cooking efficiency is affected by the thermal properties of foods, which can be calculated from the compositions of foods and the thermal properties of each composition. The main compositions of cooked meats are water, protein, and fat, while the amount of other compositions, such as salt and ash, are very small. Thermal conductivity of protein and fat is considerably less than that of water (Mittal and Blaisdell, 1984). Typical thermal conductivity of meats increases with increasing water content. Since the pork ham is immersed in a water bath for cooking, the pores are filled up with water during the whole cooking procedure. A higher number of pores and higher porosity mean that more water is contained in the cooked meats, leading to shorter cooking time.

The similar relationships between the cooling time and TNP and porosity were found by Du and Sun (2006b). During the air blast cooling process, the heat is transferred from the core of cooked meats to the surface by conduction and released to a cooling environment mainly by convection. The cooling rate of the air blast cooling is governed by the thermal conductivity of the cooked meats (Wang and Sun, 2002b). For the same reason, higher thermal conductivity of the cooked meats with more TNP and higher porosity would result in shorter cooling time. However, as the cooling procedure progresses, the thermal conductivity of cooked meats decreases with the decrease in liquid water mass due to the moisture loss and the generation of vapor in the pores. Therefore compared with the cooking time, the cooling time has a poorer linear relation with TNP and porosity. As the total processing time (TPT) is the sum of cooking and cooling times, TPT thus has negative relationships with TNP and porosity.

For texture analysis, positive correlations are found between the pore characterizations and WBS, hardness, cohesion, and chewiness, respectively, while springiness and gumminess are negatively related to TNP and porosity (Du and Sun, 2006b). Measured by using the mechanical method, the textural characteristics are profoundly affected by their porous structure of food materials (Huang and Clayton, 1990). It has been demonstrated that both cooking and cooling can lead to the increase of the porosity of cooked meats due to water loss. Greater porosity indicates higher water loss of cooked meats. Water is not only a medium for reaction but also an active agent in the modification of physical properties (Huang and Clayton, 1990). Loss of water might lead to the compression of muscle fibers and increase of the concentration of the interstitial fluid, and thus enhance the adhesive power and strength (McDonald et al., 2000). Therefore the cooked meats with greater TNP and porosity will result in higher shear force values and cause a reduction in tenderness while an increase in hardness, cohesion, and chewiness. The decreasing trends of springiness and gumminess with an increase in TNP and porosity could be explained by stress–strain analysis. Structurally, the porosity and number of cavities might influence the ability of deformation. The meat sample with larger porosity and more pores becomes weaker, and less mechanical stress is needed to cause yielding and fracturing.

The relations between the pore characteristics and the quality attributes of cooked meats are very complex in nature (Rahman and Sablani, 2003). Pore formation is dependent on the quality of raw meat, pretreatment, and processing, which will influence the pore size, geometry or shape, porosity, and size distribution of the meat matrix. The variation in pore characteristics has various effects on the processing time, water content, textural, and other quality attributes of the cooked meats. A well-structured matrix and a fine, uniform structure with numerous small pore or open spaces would probably result in more absorptive capacity and better retention of water compared to coarse structures with large pores (DeFreitas et al., 1997; Hermansson, 1985), thus having a positive effect on the quality of cooked meats.

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