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Heat Transfer

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Most of the systems need to exchange thermal energy with their surroundings in order to control their temperature. It is the way of transferring energy from one place/object to another. Our human body also transfers thermal energy to its surroundings by evaporation or perspiration.

The driving force behind the heat transfer are temperature difference and pressure difference. There are different methods by which the heat transfer, In this section we will learn more about different heat transfer methods. 

Methods of Heat Transfer

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Heat is the movement of thermal energy from a region of higher to a region of lower temperature. The movement of thermal energy takes place by three main processes:
  1. Conduction
  2. Convection
  3. Radiation
Conduction usually occurs in solids, convection occurs in liquids and gases. No medium is required for radiation.

Heat Transfer By Conduction

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Transfer of heat within a solid or between solid objects can only be by conduction. It is due the motion of electrons. The hot molecules vibrate faster against the cool, slow molecules causing them to heat up. Heat transfer is always from hotter to cooler objects. If one end of any object or material is heated, the heat will pass through the other end. Gases and fluids are less conductive than solids because the inter atomic distance is more in liquid and gas compared to solid.
Conduction occurs at the atomic level as thermal energy is transferred between adjacent particles making up a substance.

For example, when placing a metal spoon in port of boiling water, the energetic water molecules transfer their energy to the atoms and electrons in the end of the metal spoon immersed in the water. The atoms and electrons of the spoon become more energetic and in turn transfer their energy up the handle of the spoon, which is turn become hotter. Metals are good conductors because their valence electrons hold metal crystals together loosely with metallic bonds.

The amount of heat energy conducted through a material depends on the material, the temperature difference, the distance from the heat source, and the cross-section area. Consider the example of metal rod that is heated at the one end. The amount of conductive thermal energy that is transported through a metal of cross section area $A$, having length $L$ in the given amount of time $t$, $k$ is the coefficient of thermal conductivity, $\Delta T$ = $T_{2} – T_{1}$, is the temperature difference between two ends is given by the equation

$Q$ = $\frac{kA\Delta T}{L}$t

The equation tells that the energy conducted through the rod is directly proportional to the difference in temperature, cross section are , time and $k$. The value of $k$ depends on the type if the materials.

Heat Transfer By Convection

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The convection is the process in which heat is transferred from one place to the other by the actual movement of heated substance. Convection requires medium.
It is the transfer of heat by the movement of fluids. Air or water which is being heated directly becomes less dense and rises up. The cooler part of the fluid settles down to replace it. This cooler fluid then heats up and forms convection current. Convection is the main form of heat transfer in liquids and gases. When a liquid is heated the particle of the liquid which gets heated moves upwards, delivers heat to the other particles by bodily movement and gets cooled. It comes down and get get heated again.

Heat Transfer By Radiation

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The process by which heat is transferred directly from one body to another, without requiring a medium is called radiation
Thermal radiation is the transfer of heat through empty space by electromagnetic waves. All objects above zero degree temperature radiate energy. Radiation does not require any medium, as it is transferred by electromagnetic waves and can take place even in vacuum. The heat energy from the Sun travels through the space vacuum by radiation before warming the earth. The velocity of the radiation is equal to the speed of light.

Stefan Boltzmann Law

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Stefan Boltzmann Law is also known as Stefan's Law It states that the radiant energy emitted per unit area per second of a lack body is directly proportional to the forth power of temperature.

$E_{R}\propto T^{4}$

or

$E_{R}= \sigma T^{4}$
The energy radiated per second or radiant power

$P_{R}$ = $A \epsilon \sigma T^{4}$
Where,

$?$= Power radiated in watts by the substance
$A$ = surface area of the substance in meters
$\sigma$ = Stefan-Boltzmann constant, $5.67 \times 10^{-8}$ $Wm^{-2}K^{-4}$
$\epsilon$ = emissivity constant, $0 \leq \epsilon \leq 1$
$T$ = Surface temperature in K

Heat Transfer Example Problems

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The following are the problems of heat transfer.

Solved Examples

Question 1: A man has total surface area of $1.5$ m2. Find the total rate of radiation of energy from the body. 
($T = 310$ K)

Solution:
 
Given,
$A$ =  $1.5$ m2
$T = 310$ K
$\sigma$ = $5.67 \times 10^{-8}$ $Wm^{-2}K^{-4}$
$\epsilon$ = 1
 
We know that,

$P_{R}$ = $A \epsilon \sigma T^{4}$ 

= $5.67 \times 10^{-8} \times 1.5 \times (310)^{4}$

= $782 J$

 

Question 2: Find the emissivity of a body having surface area $5 cm^{2}$ and at temperature $727^{0}C$ radiating $300 J$ energy per minute.
Solution:
 
Given,
$P= 300/60$
$A$ =  $5 \times 10^{-4}$ m2
$T = 1000$ K
$\sigma$ = $5.67 \times 10^{-8}$ $Wm^{-2}K^{-4}$
$\epsilon$ = ?
 
We know that,

$P_{R}$ = $A \epsilon \sigma T^{4}$ 

$\epsilon$ = $\frac{P}{A \sigma T^{4}}$

= $\frac{300/60}{5 \times10^{-4} \times 5.67 \times 10^{-8}\times (1000)^{4}}$

= $0.18$