Modes of Heat Transfer

Intro to Heat Transfer in Fluids – Lesson 3

• DECEMBER 2019

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Basic Modes of Heat Transfer

• In this lesson, we will introduce different modes of heat transfer.

• The three main modes of heat transfer: ‐ Conduction is heat transfer that occurs when a temperature difference

exists across a stationary medium.

‐ Convection is the heat transfer between a surface and a moving fluid when there is a temperature difference between the two.

‐ Radiation (thermal radiation) is the emission of energy in the form of electromagnetic waves. In the absence of an intervening medium, there is net heat transfer by radiation between two surfaces at different temperatures.

Hot transistor surface

Convection Heat Transfer

Radiation Heat Transfer

Stainless Steel Rod

Conduction Heat Transfer

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• Conduction is thermal energy transmission through solid or fluid by the action of translational, rotational and vibrational motion of atoms and molecules.

• Molecular collisions transfer energy from more energetic molecules to less energetic ones.

▪ Higher temperature = Increased atomic/molecular motion

• Conduction occurs in all fluid and solid media.

• Due to the Second Law of thermodynamics, heat must always be conducted from higher to lower temperatures.

• Conduction problems often involve fluid flows at the boundaries of the solid, which serve as a mechanism for heating or cooling the solid.

Conduction

Heat Conduction in this direction

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Physics of Heat Conduction

• Conduction is the transfer of energy from more energetic to the less energetic particles of a substance via interactions between the particles at molecular levels due to a temperature difference.

• The physical mechanism of conduction can be illustrated by an example of a quiescent gas (no macroscopic motion) between two parallel plates maintained at different temperatures which results in a temperature gradient across the gas.

• Temperature at any point can be associated with the energy of random translational, internal rotational and vibrational motions of gas molecules

𝑇𝐴 > 𝑇𝐵

𝑇𝐵

Heat Transfer

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Physics of Heat Conduction

• Molecular collisions transfer energy from more energetic molecules to less energetic ones.

• Higher molecular energies are associated with higher temperatures, and the energy transfer always occurs in the direction of decreasing temperature in the presence of a temperature gradient.

• The mechanism of conduction is the same for liquids as the molecules are closely spaced and the molecular interactions are stronger and more frequent than gases.

• In the case of solids, conduction is associated with atomic activity in the form of lattice vibrations. In the case of an electrical conductor, the translational motion of free electrons also contributes to energy transfer.

Heating of the fire iron Hot steel bloom Hot electric stove

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Physics of Heat Conduction (cont.)

• The heat transfer process can be quantified in terms of appropriate rate equations which are used to compute the amount of energy being transferred per unit time.

• In the case of heat conduction, the rate equation is Fourier’s law. For a one-dimensional plane wall this is expressed as

Here,‐ 𝑞_𝑥^′′(𝑊/𝑚^2) is the heat transfer rate per unit area in the x-direction. ‐ 𝑘 is the thermal conductivity (𝑊/𝑚𝐾) and is a characteristic of the wall material. ‐ The negative sign signifies the fact that the heat transfer is in the opposite direction of the

temperature gradient

• For steady-state conditions, when the temperature gradient is linear, the

heat flux is given by:

Note that this expression provides the heat flux and the heat transfer rate can be computed by multiplying this by the area, 𝐴, of the surface.

𝑞𝑥′′ = −𝑘

𝑑𝑇

𝑑𝑥

𝑞𝑥′′ = −𝑘

𝑇2 − 𝑇1𝐿

= 𝑘𝑇1 − 𝑇2

𝐿= 𝑘

Δ𝑇

𝐿

𝑇(𝑥)

𝑇2

𝑇1

𝐿

𝑇

𝑥

𝑞𝑥′′

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Thermal Conductivity• Fourier’s law introduces a key heat transfer material property: thermal conductivity, 𝑘.

• Thermal conductivity can be measured in a laboratory and varies greatly based on the physical structure of the material. Thermal conductivity of materials varies with temperature, and for solids there is no a uniform trend. Even metals have vastly different conductivity-temperature curves.

Material 𝒌,𝑊/(𝑚 ∙ 𝐾)

Silver 418

Copper 387

Aluminum 112.7

Zinc 73

Iron 66

Lead 34.7

Quartz 19.1

Corundum 10.4

Marble 2.78

Ice (H2O) 2.22

Pyrex Glass 1.05

Material 𝒌,𝑊/(𝑚 ∙ 𝐾)

Mercury 8.21

Water (liquid) 0.552

Sulfur Dioxide 0.211

Methyl Chloride 0.178

Carbon Dioxide 0.105

Freon 0.073

Hydrogen 0.175

Helium 0.141

Air 0.0243

Pentane 0.0128

Chloroform 0.0066

𝑘 evaluated @ 273K (Source: Eckert, E. R. G. and R. M. Drake, Analysis of Heat and Mass Transfer, McGraw-Hill, 1972)

met

als

no

n-m

etal

so

lids

gase

sliq

uid

s

Platinum

Silver

Copper

Aluminum

Brass

IronType 304 stainless steel

0 200 400 600 800 1000-2000

100

200

300

400

T(deg𝐶 )

Ther

mal

Co

nd

uct

ivit

y, 𝜆,(𝑊𝑚

−1𝐾−1)

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• Convection is transfer of heat by the combination of the bulk motion of a fluid and random molecular motion (diffusion).

• Heat is transferred to/from the fluid via conduction at walls.

• Fluid carries thermal energy to other parts of the system.

• Heat transfer only due to the bulk motion of the fluid (no diffusion) is referred to as advection.

Convection

• Convection heat transfer can be classified into:

• Forced convection: Flow is caused by external means, such as by a fan, a pump or atmospheric winds.

• Free (or natural) convection: Flow is induced by buoyancy forces, caused by density differences due to the temperature variations in the fluid.

• Mixed (combined) connection: Forced and natural convection can also exist if both external driving forces and buoyancy forces exist.

Free convection currents set up in a room warmed by a radiator

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• Heat transfer by convection is rooted in the idea that the heat transfer rate is proportional to the temperature difference between a fluid and a heated/cooled body.

• This idea is called Newton’s Law of Cooling. The parameter governing the rate of heat transfer is the heat transfer coefficient, usually denoted ℎ.

• One of the central problems in convection is determining the heat transfer coefficient for a given flow field.

• The heat transfer coefficient depends on the conditions in the boundary layer, and it is affected by the surface geometry, the nature of the fluid flow and various fluid thermodynamic and transport properties.

Convection (cont.)

ℎ = heat transfer coefficient𝑞′′ = Convective heat flux𝑇𝑠= Temperature of the solid surface𝑇∞= Temperature of the fluid

𝑇𝑠

Hot transistor surface𝑞′′

𝑞′′ = ℎ(𝑇𝑠 − 𝑇∞)

Electronics cooling via forced convection

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Radiation Heat Transfer

• Thermal radiation heat transfer is the emission of energy via electromagnetic waves.

• All matter at a nonzero temperature emits thermal radiation.

• This emission is due to changes in the electron configurations of the atoms or molecules, and the energy is transported via electromagnetic waves (or photons).

• Radiation intensity depends on body temperature and surface characteristics.

Body temperature check at an airport using infrared radiation scanners

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Radiation Heat Transfer (cont.)

• Unlike conduction or convection, radiation does not require the presence of a material medium and can occur in a vacuum.

• Radiation is an important mode of heat transfer at high temperatures.

• It is also the only mode of heat transfer in outer space, and this is how the solar energy reaches Earth.

Solar radiation incident on Earth Heat from campfire (or fireplace)Hot operational household oven

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Summary

• In this lesson we introduced the modes of heat transfer:

‐ Conduction

‐ Convection

‐ Radiation