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*Heat Energy:*

Heat (Q) is the form of energy which is transferred from one part of the system to another or to another system by virtue of difference in temperature. Temperature gradient estimates direction of heat flow.

*Methods of Heat Transfer:*

The transfer of heat from one part of the system to another or to another system by virtue of temperature difference can only be by one or more of the three procedures that is conduction, convection, and radiation. Each of such mechanisms or procedures is given below.

*Conduction:*

This is the procedure of heat transfer whereby heat energy is transferred directly through the material without any bulk movement of material.

**Conductors and Insulators:**

Materials can be separated in two groups based on their skill to conduct thermal energy that is; thermal conductor and thermal insulator.

**Conductors:**

Materials which conduct heat well are known as thermal conductors. Examples of thermal conductors are metals (most metals are conductors) such as aluminum, silver, copper, and gold. The behavior of conductors in terms of thermal conductivity can be described with two mechanisms that is; collision mechanism and free electrons in metals.

Molecular collision: Atoms and molecules in the hot part of material vibrate or move with greater velocity (that is higher kinetic energy) than those at colder part. By means of collisions, the more energetic molecules pass on the portion of their energy to their less energetic neighbors. As more energetic molecules collide with less energetic neighbors they transfer some of the energy to neighbors. Collision mechanism doesn't depend on bulk movement of material.

**Free electrons in metals: **

Good conductors of thermal energy, such as metals, have pool of electrons which are more or less free to wander through volume of metal. These free electrons are able to transport energy round whole volume of conductors. Free electrons are also liable for excellent electrical conductivity in metals.

**Insulators:**

Materials which conduct heat poorly are known as thermal insulators. Examples of thermal insulators are wood, glass, and most plastics. These materials poorly conduct heat energy as two mechanisms for conduction are not possible with the materials (that is molecules of these materials are not free to move and or material do not contain free electrons).

**Conduction of Heat through the Material:**

Consider bar of material of area A and thickness L, heat Q transfer through material by conduction is

Q = kAΔTt/L

Where ΔT is temperature difference between ends of bar and k is thermal conductivity of material. Unit of k is J/(s.m.C^{0})

**Thermal Resistance to Conduction (R-Value)**:

There is a term similar to electrical resistance R utilized for thermal resistance to conduction known as R-value. To differentiate this from R that we are familiar with, Rt is utilized here for thermal resistance to conduction.

Thermal resistance R_{t} of slab of thickness L is stated as

R_{t} = L/k

High value of R_{t} indicates bad thermal conduction or good thermal insulation.

**Conduction of Heat through a Composite Material:**

Consider two materials of thickness L_{1} and L_{2} with different thermal conductivities k_{1} and k_{2} respectively. The outer surfaces of slab are in thermal contact with hot reservoir at temperature T_{H} and cold reservoir at temperature T_{C}. Suppose that heat transfer through slabs is a steady rate procedure i.e. temperature everywhere in slab and rate of energy transfer don't change with time. Then, conduction rate through two slabs should be equal. The conduction rate P_{cond} is:

P_{cond} = Q/t = kAΔT/L

Let T_{x }be temperature of interface between two materials, so

P_{cond} = k_{2}A(Th - TX)/L_{2} = k_{1}A(T_{x} - T_{C})/L_{1}

Solving for T_{X} in equation provides

T_{x }= (k_{1}L_{2}T_{C} + k_{2}L_{1}T_{H})/(k_{1}L_{2} + k_{2}L_{1})

Solving equation we get:

P_{cond} = A(T_{H} - T_{X})/[(L_{1}/k_{1}) - (L_{2}/k_{2})]

If apply this to any number n of materials, equation becomes:

P_{cond} = A(T_{H} - T_{X})/Σ_{2}^{n}(L_{i}/k_{i}) for i = 2:n

*Convection:*

Convection is procedure in which heat energy is transferred from place to place by bulk movement of the fluid. The good example of this procedure is convection current in liquid. This bulk movement of the fluid can be described in terms of buoyant force. When the portion of the liquid, like water, is warmed volume of liquid or fluid expands, and density decreases (Ρ = mv). From Archimedes' principle, surrounding cooler and denser fluid applies the buoyant force on warmer fluid and therefore pushes warmer fluid upward. As warmer fluid is pushed upward, surrounding cooler fluid moved downward to replace warmer fluid. Cooler fluid, in turn, is warmer and pushes upward. This cycle is constantly repeated and this is known as convection current. This phenomenon is known as natural convection.

The phenomenon explained above is known as natural convection. Forced convection takes place if fluid is made to move in the similar way as natural convection by action of the pump or a fan. Consider the fluid in contact with the flat or curved wall which temperature is higher than that of main body of the fluid, rate of heat transfer because of both conduction through film and convection in fluid is

Q/t = hAΔT

Where h is convection coefficient and it comprises combined effect of conduction through film and the convection in fluid, A is area of the wall, and ΔT is temperature difference between surface of wall and main body of fluid. Finding the value of h that is suitable for the particular arrangement is problematic as h depends on following factors:

- whether wall is flat or curved
- whether wall is horizontal or vertical
- whether fluid in contact with wall is gas or liquid
- specific heat, density, viscosity, and thermal conductivity of fluid
- whether velocity of the fluid is small enough to give rise to laminar flow or large enough to cause turbulent flow
- Whether evaporation, condensation, or formation of scale happens.

*Radiation:*

This is a procedure in which energy is transferred by means of electromagnetic waves. The good example of this is solar radiation from sun traveling in all directions in space. Part of this radiation is reaching earth on daily basis and in actual sense; bulk of energy on earth is from sun. All bodies, hot or cold, constantly radiate energy in form of electromagnetic waves. But amount of this radiation is proportional to temperature of the body and nature of its surface.

**Absorption and Emission of Radiant Energy:**

Surface of the object is very significant in determination of amount of radiant energy a body or object can absorb or emit. The experiment set-up to justify this comprises of two identical blocks, one coated in black and other coated with silver. If the thermometer is inserted on each of blocks and they are exposed to direct sunlight. It will be see that temperature of the block coated in black will increase faster than that of one coated with silver. Reason for this is that block coated in black absorbed larger percentage of solar radiation falling on it and therefore rapid increase in temperature because of large heat energy input.

Perfect Blackbody: This is the body which absorbs all electromagnetic waves falling on it.

Usually, all objects can emit and also absorb electromagnetic waves. So when the object is in thermal equilibrium with its surroundings, it means that amount of radiant energy object absorbs balances with amount the object emits. Though, if absorption is greater than emission, object will experience a net gain of radiant energy and therefore temperature will increase If emission is greater than absorption, object will experience the net loss of radiant energy and temperature will fall. The good absorber is also good emitter while the poor absorber is also a poor emitter. Therefore, perfect black body is a perfect absorber and also perfect emitter of radiant energy.

**Stefan-Boltzmann Law of Radiation:**

All matter continuously radiates energy in form of electromagnetic waves.

Q/t = σεAT^{4}

Where σ is Stefan-Boltzmann constant, ε is emissivity and it has value between 0 and 1. For the perfect reflector, ε =0 and for black body ε =1.

This equation is called as Stefan-Boltzmann law of radiation, and law defined that radiant energy, emitted in time t by object that has Kelvin temperature of T, surface area A, and emissivity ε, is given by

Q = σεT^{4}At

Emissivity e of the Object: This is a ratio of radiant energy emitted by the object to one it would have emitted if it were to be the perfect black body. Suppose that radiation a body would emit if it were to be a perfect body is represented by Rad_{pbb}, then

ε = radiation emitted/Radpbb

*Newton's Law of Cooling:*

Energy is lost to surroundings by conduction, convection, and radiation. Rate at which object loses energy to surrounding is determined by temperature difference between object (T_{o} ) and surrounding (T_{s}).

By conduction energy loss rate = kA(T_{s} - T_{0})/l

By convection, energy loss rate depends on whether air is forced to flow (e.g. by fan) or moves by natural convection. Energy loss rate = hA(T_{s} -T_{o} )

By radiation, energy loss rate = σA(T_{0}^{4} - T_{S}^{4})

Total effect of these three processes is to give the rate of energy loss per second that is proportional to temperature difference between object and its surroundings. This is called as Newton's law of cooling.

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