Heat Convection • Convection                                              

Latin:  com (together) + vehere (to carry); the bulk movement of thermal energy in fluids

• Convection is the flow of heat through a bulk, macroscopic movement of matter from a hot region to a cool region, as opposed to the microscopic transfer of heat b

etween atoms involved with conduction. • Suppose we consider heating up a local region of air.

As this air heats, the molecules spread out, causing this region to become less dense than the surrounding, unheated air. For reasons discussed in the previous section, being less dense than the surrounding cooler air, the hot air will subsequently rise due to buoyant forces - this movement of hot air into a cooler region is then s

aid to transfer heat by convection.

• Heating a pot of water on a stove is a good example of the transfer of heat by convection. When the stove is first turned on heat is transferred first by conduction between the element through the bottom of the pot to the water. However, eventually the water starts bubbling - these bubbles are actually local regions of hot water rising to the surface, thereby transferring heat from the hot water at the bottom to the cooler water at the top by convection. At the same time, the cooler, more dense water at the top will sink to the bottom, where it is subsequently heated. These convection currents are illustrated in the follow

ing figure.

Heated air rises, cools, then falls.  Air near heater is replaced by cooler air, and the

cycle repeats.

Convection

• Consider now two regions separated by a barrier, one at a higher pressure relative to the other, and subsequently remove the barrier, as in the following figure. These convection currents are illustrated in

the following figure.

Natural/Free Convection

Occur due to density differences caused by temperature gradients within the system and may cause either laminar or turbulent flow of fluid.

Natural/Free Convection

Warm land is cooled during the day, while cooler land is warmed at night.

Very hot, low-density air is buoyed upward, carrying thermal energy with it.

Forced Convection

Forced convection involves use of some mechanical means, such as a pump or a fan, to

induce the movement of the fluid.

Forced Convection

                       

Hot piston cylinders in automobile engine are cooled by water forcedaround them.

                        

 Hot room air is forced outside, while cooler air replaces it.

The velocity of fluid reduces to zero at the

surface of the plate due to the viscous action. Thus, heat transfer in the boundary layer,

where velocity is zero, must occur due to

conduction. Away from the wall, heat transfer to

fluid is due to convection. In practice, it is difficult to determine

the thickness of the boundary layer. The rate

of heat transfer is expressed by Newton’s

law of cooling, which accounts for the overall

effect of convection.q = hA(Tp – Ta)

Heat convection

• Heat transfer to a heated flat plate exposed to a fluid.

Tp

Ta

Newton’s law of cooling

q = -hAdT

q = hA(Tp – Ta)

When Tp > Ta

h = convective or surface heat transfer coefficient

Some approximate values of h

Fluid h (W/m2 K)

Air

free convection

forced convection

Water

free convection

forced convection

Boiling water

Condensing water vapor

5-25

10-200

20-100

50-10,000

3,000-100,000

5,000-100,000

High value of h reflects a high rate of heat transfer. Forced convection offers a high value of h than free convection

Example

The rate of heat flux from a metal plate is 1000 W/m2. The surface temperature of

the plate is 120°C, and ambient temperature is 20°C. Estimate the

convective heat transfer coefficient.

Radiation

• The third and last form of heat transfer we shall consider is that of radiation, which in this context means light (visible or not). This is the means by which heat is transferred, for example, from the sun to the earth through mostly empty space - such a transfer cannot occur via convection nor conduction, which require the movement of material from one place to another or the collisions of

molecules within the material.

Thermal radiationThere are many types of electromagnetic radiation; thermal

radiation is only one. Thermal radiation lies in the range from about 0.1-100 m, while visible-light portion is about

0.35-0.75 m.Thermal radiation

Radiation

• Often the energy of heat can go into making light, such as that coming from a hot campfire. This light, being a wave, carries energy, and so can move from one place to another without requiring an intervening medium. When this light reaches you, part of the energy of the wave gets converted back into heat, which is why you feel warm sitting beside a campfire. Some of the light can be in the form of visible light that we can see, but a great deal of the light emitted is infrared light, whose longer wavelength is detectable only with special infrared detectors. The hotter the object is, the less infrared light is emitted, and the more visible light. For example, human beings, at a temperature of about 37oCelsius, emit almost exclusively infrared light, which is why we don't see each other glowing in the dark. On other hand, the hot filament of a light bulb emits considerably

more visible light.

Radiation

• Heat transfer by electromagnetic waves

• Does not need a material medium

• Black body: perfect absorber perfect emitter (at all wavelengths)

Radiation• Occur between two surfaces by the

emission and later absorption of electromagnetic radiation

• Energy radiated (or emitted) from a surface is proportional to the absolute

temperature raised to the fourth power and surface characteristics.

Radiation

Speed of light

Radiated Power from Blackbody

• When the temperature of a blackbody radiator increases, the overall radiated energy increases and the peak of the radiation curve moves to shorter wavelengths. When the maximum is evaluated from the Planck radiation formula, the product of the peak wavelength and the temperature is found to

be a constant.

Increasing temperature results in decreasing wavelength

• The radiated power in a given wavelength interval Δλ at wavelength λ can be approximated b

y

Stefan-Boltzmann Law of Radiation

• By considering the radiation as such a gas, the principles of quantum-statistical thermodynamics can be applied to derive

an expression for energy density of radiation per unit volume and per unit

wavelength. When the energy density is integrated over all wavelengths, the total energy emitted is proportional to absolute

temperature to the fourth power.

Stefan-Boltzmann Law of Radiation

 qemitted = AT4

= emissivity (0-1) = Stefan-Boltzmann constant   = 5.67 x 10-8 J/(s-m2-K4)A = surface area of objectT = Kelvin temperature

The energy radiated by a blackbody radiator per second per unit area is proportional to the fourth power of the absolute temperature a

nd is given by

- The Stefan Boltzmann Law The total power per unit area from a blackbody radiator ca

n be obtained by integrating the Planck radiation formula o ver all wavelengths. The radiated power per unit area as a

function of wavelength is

so the integrated power is

It is helpful to make the substitution

- The Stefan Boltzmann Law

Making the substitution gives

Making use of the standard form integral

- gives the final form of the Stefan Boltzmann law

Example How much energy is radiated by this

 object in ten minutes?

---------------------------------------------------

t = 10 x 60 seconds = 600 s

 Q = radiant energy = q.t

 q =  A T4

 Q = (0.8)(5.67x10-8)(5)(500)4 x (600)     = 8.5 x 106 J

               

      q = AT4

= 0.8

Blackbody radiation

• The materials which obey this law appear black to the eye; they do not reflect any radiation.

• Thus a blackbody is also considered as one which absorbs all radiation incident upon it. Therefore;

Eb = T4

where Eb is called emissive power of a black body.

Absorption and Emission of  Radiation

                                              

 Energy out = Energy in  Emitted energy/Incident energy = Emissivity = .

Incident

energy

Black Bodies

Summer clothing:  white reflects radiant energy better than black.

 Until equilibrium is reached, white  stripes on roads are at a lower  temperature than unpainted asphalt.

 Wrap an ice-cube in black cloth and another in aluminum foil and  place both in the sunshine.  What will happen?

Pipes in Solar Panels are Painted Black

Example:  How much does the human body radiate?

• Body temperature = 37 C = 37 +273 = 310 K, Estimate surface area A = 1.5 m2         = 0.70

q = A T4

        = (0.70)(5.67 x 10-8)(1.5 m2)(310)4

        = 550 watts (5 light bulbs)------------------------------------------------------------------------The sun provides about 1000 watts per square meter at the Earth's surface.  30 % is reflected byhuman skin.  700 watts is absorbed per square meter.  

• Radiation is heat transfer by the emission of electromagnetic waves which carry energy away from the

emitting object. For ordinary temperatures (less than red hot"), the radiation is in the infrared region of the

electromagnetic spectrum. The relationship governing radiation from

hot objects is called the Stefan-Boltzmann law:

If object at temperature T is surrounded by an environment at temperature T0 (heat transfer surface of the object enclosed by a much larger surface or environment), the net heat flow or net radiant exchange is:     qnet = A [T4 - T0

4]

Example:  Standing outdoors on hot August day:

Body temperature: 37 C = 37 +273 = 310 K, Air temperature:     37 C = 310 K

   qnet = A [T4 - T04]  =   A [3104 - 3104]

          = 0

Example:  Standing outdoors on a cold February morning:

Body temperature = 37 C = 37 +273 = 310 K, Air temperature = 0 C = 273 K

A = 1.5 m2     = 0.70

qnet = A [T4 - T04]  

        = (0.70)(5.67 x 10-8)(1.5 m2)(3104 - 2734)        = 219 watts 

Radiation shape factor

• Consider 2 black surfaces, we wish to obtain a general expression for the energy exchange between these

surfaces when they are maintained at different temperatures. The problem becomes essentially one of determinating the amount of energy which leaves one

surface and reaches the other. To solve this problem the radiative shape factors are used.

• Radiation shape factor = view factor = angle factor = configuration factor = Fm-n = fraction of energy leaving

surface m which reaches surface n.• Energy leaving surface 1 and arriving at surface 2 =

Eb1A1F12

• Energy leaving surface 2 and arriving at surface 1 = Eb2A2F21

Since the surfaces are black, all the incident radiation will be absorbed, and net

energy exchange isEb1A1F12 - Eb2A2F21 = q1-2

If both surface are at the same temperature, they can be no heat

exchange or q1-2 = 0. Also Eb1 = Eb2

A1F12 = A2F21

Therefore:q = A1 (T1

4-T24) . FA1A2