Modes of Heat Transfer

OBJECTIVES:

-- To study different modes of heat transfer.

-- To determine rate of heat transfer in food and non-food materials

Why study heat transfer?

-- to examine how foods are heated and cooled

-- to calculate the rate of heating and cooling

-- to design new heat transfer equipment

-- to assess the performance of existing heat exchange equipment

CONDUCTION

-- Energy transfer at a molecular level

-- No physical movement of the material

-- Heating/Cooling of the solid material

The rate of heat flux (rate of heat transfer per unit area) in a solid object is proportional to the temperature gradient, this can be stated mathematically as,

We may remove the proportionality by using a constant 'k', to obtain, Fourier’s Law

where

q_x = rate of heat transfer in the x direction by conduction, W

k = thermal conductivity, W/mC

A = area (normal to x-direction) through which heat flows, m²

T = temperature, C

x = length, variable, m

SIGN CONVENTION

Temperature
		Distance

Thermal Conductivity, k unit: W/mC

Metals: k = 50-400 W/mC

Water: k = 0.597 W/mC

Air : k = 0.0251 W/mC

Insulating materials: k = 0.035 - 0.173 W/mC

For foods

k = 0.25 m_c + 0.155 m_p + 0.16 m_f + 0.135 m_a + 0.58 m_m

Where m is mass fraction and subscripts c: carbohydrate, p: protein, f: fat, a: ash, m: moisture.

CONVECTION

Fluid flow over a solid body -- heat transfer between a solid and a fluid.

Newton’s Law of Cooling:

q = h A (T_p-T_a)

where: h is convective heat transfer coefficient (W/m²C), A is area (m²), T_p is plate surface temperature (°C), T_a is surrounding fluid temperature (°C).

Forced Convection - artificially induced fluid flow

Free (Natural) Convection -- caused due to density differences

Fluid condition h (W/m²C)

Air, free convection 5-25

Air, forced convection 10-200

Water, free convection 20-100

Water, forced convection 50-10,000

Boiling water 3,000-100,000

Condensing water vapor 5,000-100,000

RADIATION

Heat transfer between two surfaces by emission and later absorption of electromagnetic radiation

n requires no physical medium

n Stefen-Boltzmann Equation:

q = A s e (T₂⁴ – T₁⁴)

where s = Stefen-Boltzmann's constant, 5.669x10^-8 W/m²K⁴

e = emissivity, (varies from 0 to 1) dimensionless

A = area, m²

T₁ = temperature of surface 1, Absolute

T₂ = temperature of surface 2, Absolute