Heat Transfer

Heat Transfer Fundamentals

Thermal Properties

• Main function of systems such as heaters, evaporators, coolers, and freezers:

  • Heat Transfer

Problem Example: Heating Vegetables

• Question: If you heat a plate for 10 minutes, which vegetable will be the hottest? Why?

Thermal Properties of Interest

• Before delving into heat transfer fundamentals, it is essential to understand properties influencing heat transfer, including:

  • Specific Heat

  • Thermal Conductivity

  • Thermal Diffusivity

Specific Heat

• Definition: The amount of heat required to raise or lower the temperature of 1 kg of a substance by 1°C.

  • Mathematically, this is represented as:

  • Heat to raise temperature: $Q = m imes c imes riangle T$

  • Where:

    • Q = heat (in kJ)

    • m = mass (in kg)

    • c = specific heat capacity (in kJ/(kg·°C))

    • $riangle T$ = change in temperature (°C)

• Storage capacity of a material is described by specific heat.

• Examples of specific heat for various materials:

  • Specific heat of water: $4.2 ext{ kJ/(kg.K)}$

  • Specific heat of ice: $2.09 ext{ kJ/(kg.K)}$

  • Specific heat of aluminum: $0.890 ext{ kJ/(kg.K)}$

Thermal Conductivity

• Definition: Amount of heat transferred per unit time through a unit thickness of a material if a unit temperature gradient exists across that thickness.

  • Expressed mathematically as:

  • $Q = k imes A imes rac{(T<em>1 - T</em>2)}{ riangle x}$

    • Where:

    • Q = heat conducted (in watts)

    • k = thermal conductivity (in W/(m·°C))

    • A = area (in m²)

    • $T_1$ = temperature on one side of the material

    • $T_2$ = temperature on the opposite side

    • $riangle x$ = thickness (in meters)

• Examples of thermal conductivity for select materials:

  • Pure water at 25°C: $0.606 ext{ W/(m.°C)}$

  • Ice: $2.22 ext{ W/(m.°C)}$

  • Aluminum at 0°C: $235 ext{ W/(m.°C)}$

Thermal Conductivity of Food

• Empirical relationships for predicting thermal conductivity in food:

  • For Fruits and Vegetables:

  • $k = 0.14810 + 0.493X_w$

  • For Meats and Fish:

  • $k = 0.08 + 0.52X_w$

  • Where $X_w$ is the water content expressed as a mass fraction.

Example - Heating Vegetables

• If heating this plate for 10 minutes:

  • Product temperature ranking:

  • Tomato > Carrots > Broccoli

  • Water content ranking:

  • Tomato > Carrots > Broccoli

  • Thermal conductivity ranking:

  • Broccoli > Tomato > Carrots

  • Specific heat ranking:

  • Tomato > Carrots > Broccoli

Example - Thermal Conductivity Calculation

• Estimate the thermal conductivity of hamburger beef with 68.3% water content:

  • Using the empirical formula for meats:

  • $k = 0.081 + (0.52 imes 0.683)$

  • Result: $k = 0.435 ext{ W/(m°C)}$

Thermal Diffusivity

• Definition: Measure of a material's ability to conduct thermal energy relative to its ability to store thermal energy.

• For product mixtures, thermal diffusivity $\beta$ is expressed as:

  • $\beta = rac{k}{<br>ho imes C_P}$

  • Where:

    • $\beta$ = thermal diffusivity

    • k = thermal conductivity

    • $<br>ho$ = density

    • $C_P$ = specific heat

Predictive Equations for Food Components

• Thermal Conductivity Equations:

  • Fiber, Ash, Water, Ice, Protein, Fat, Carbohydrate equations with respective coefficients and errors are provided.

• Each component's thermal properties are expressed as a function of temperature, illustrating how they change with temperature.

Components for Select Foods

• Composition of common foods:

  • E.g., Apples, Fresh:

  • Water: 84.4%, Protein: 0.2%, Fat: 0.6%, Carbohydrate: 14.5%, Ash: 0.3%

  • E.g., Beef, Hamburger, Raw:

  • Water: 68.3%, Protein: 20.7%, Fat: 10.0%, Carbohydrate: 0.0%, Ash: 1.0%

  • Further compositions of various foods are documented with percentages of water, protein, fat, carbohydrate, and ash.

Example - Excel Calculation

• Task: Set up an Excel spreadsheet to calculate thermal conductivity, specific heat, and density of food based on its composition.

• Considerations: Apply the composition values from previous sections to perform calculations for specific food items such as hamburger beef, raw potatoes, and turkey.

Modes of Heat Transfer

• **Quantities:

  • Q:** Quantity of heat transferred, measured in joules (J)

  • q: Rate of heat transfer, measured in joules/second (J/s) or watts (W).

Mechanisms of Heat Transfer

1. Conductive Heat Transfer:

   • Takes place at the molecular level through vibration or drift of free electrons.

   • Common in heating or cooling opaque solid food.

2. Convective Heat Transfer:

   • Involves fluid motion (forced or natural) and heat exchange between fluid and solid:

     • Formula:
       $Q = h imes A imes (T<em>s - T</em>{ ext{inf}})$

     • Where:

       • h = convective heat transfer coefficient

       • A = area of the solid

       • $T_s$ = temperature of the solid surface

       • $T_{ ext{inf}}$ = temperature of the fluid

3. Radiative Heat Transfer:

   • Emission and absorption of electromagnetic waves with no physical medium for propagation.

   • All objects above absolute zero emit thermal radiation.

Example - Heat Transfer Calculation

• Example Calculation:

  • A) Stainless Steel Plate:

  • Conditions: One face at 110°C, the other at 90°C, Thickness = 1 cm.

  • Given: Thermal conductivity of stainless steel = 17 W/(m°C).

  • Calculated Rate of Heat Transfer per Unit Area:

    • $Q/A = rac{k(T<em>1 - T</em>2)}{d} = 34,000 ext{ W}$

  • B) Convective Transfer:

  • Fluid-specific calculations and ambient conditions.

Conclusion

• This guide covers the essential aspects of heat transfer, thermal properties, and their implications, particularly in food technology and processing. Students should grasp the intricacies of a material's thermal properties, applications in real-world scenarios, and mathematical formulations vital for precise outcomes in heat transfer calculations.