Heat can transfer by one or more of the three basic mechanisms viz, conduction, convection and radiation.
The Heat Transfer Mechanism of Conduction
In conduction, heat transfer occurs by transmission of momentum of individual molecules without the involvement of actual mixing. So, it is limited to solids and ‘static’ fluids that are bound in some way to prevent their free motion. In solids, heat is mainly transferred by virtue of electron movement. This is the reason why metals are good conductors (as they contain a free electron) and non-metals are not. In fluids, heat transfer by actual molecular collisions is of greater effect. Therefore, in case of gases, conductivity increases remarkably due to the increase in the movement of molecules at higher temperatures, whereas most of the liquids except water show poor conductivity at higher temperatures.
The basic law of heat transfer by conduction can be written as:
$$ Rate=\frac{Driving\;force}{Resistance} $$
Here, driving force is the temperature gradient across the solid, heat flows from the region of higher energy to the region of lower energy and resistance can be defined in terms of Fourier’s law, which states that the rate of heat flow through a uniform material is proportional to the cross-sectional area and the temperature drop, and inversely proportional to the length of the path of the flow.
$$ \frac{∂Q}{∂t}=\frac{KA∂t}{∂L} $$
where, ∂Q/∂t is the rate of heat transfer, A is the area of cross section of heat flow path, ∂t/∂L is the temperature gradient per unit path length, and K is the coefficient of thermal conductivity of the medium. It is the heat passing in unit time from one face of a cube of unit side to the opposite face, at a unit temperature difference. The numerical value of k depends upon the material of which the body is made and upon its temperature. The thermal conductivities vary through a wide range, being highest for metals and lower for non-metals, liquids and gases.
The Heat Transfer Mechanism of Convection
In convection, heat flow results from mixing or turbulence within the fluids wherein the molecules are free to move around. Natural convection occurs when there is heat transfer due to difference in density within the fluids. Hotter regions have lower density owing to greater expansion, hence currents are set up as the warm less dense fluid rises and mixes with colder fluid. If quick heat transfer is desired, then the fluids are forced to move by means of mixer blades or by making the use of baffles. Heat transfer by this means is termed as forced convection.
The Heat Transfer Mechanism of Radiation
The third basic method of heat transfer is through space by electromagnetic waves, which is known as radiation. To understand the principles of radiation, let us consider a hot body that acts as an emitter. Emission of energy occurs when an electron from the higher energy level moves to a lower energy level. Energy being released has all the properties of electromagnetic waves. These waves have photons which strike the electron or nucleus, whichever is susceptible to the energy level of the photon of the receiver. Such a collision results in increase in the energy of the receiver. The waves falling on the receiver are either reflected, transmitted or absorbed. In solids, due to denser surface most of the radiations are absorbed, whereas in liquids, a higher proportion is transmitted and still higher penetration is there in gases. The absorbed radiations are transformed into heat. The extent to which the radiations are absorbed depends upon the properties of the receiver and wavelength of the radiation. A black body is the one which converts all the incident radiation into heat and emits all thermal energy as radiation. It can be stated that:
$$ α+τ+r=1 $$
where, α is the absorptivity, which can be defined as the fraction of the incident radiation that is absorbed, r is the reflectivity, fraction of incident radiation that is reflected and τ is the transmissivity, that is the fraction of incident radiation that is transmitted. For most of the solids transmissivity is zero and therefore, the above equation becomes:
$$ α+r=1 $$
The heat transfer through radiation is based on two important laws viz Kirchhoff’s law and Stefan-Boltzmann law.
Kirchhoff’s law gives the relationship between emissive power of the surface and its absorptivity. The law can be understood with the help of an example of a small body being placed inside a large evacuated enclosure with a wall temperature T. Heat exchange occurs until equilibrium is attained. According to the law, if G is the rate at which energy falls from the hot wall of the evacuated enclosure on the body, α, is its absorptivity and E is the emissive power of the body then at equilibrium, the energy balance can be given by:
$$ Gα=E $$
$$ G=\frac{E}{α} $$
where, G is the function of the temperature and geometrical arrangement of the surface. If the body is small as compared to the enclosure and its effect upon the irradiation is also negligible then G will remain constant. And hence, the Kirchhoff’s law states that the ratio of emissive power to the absoptivity is same for all the bodies in thermal equilibrium and is given by the equation:
$$ \frac{E_1}{α_1}=\frac{E_2}{α_2} $$
As black body is perfect radiator, it is used for comparison of emissive powers. The ratio of emissive power of a surface (E) to the emissive power of a perfectly black body (Eb) at the same temperature is known as emissivity (ε) of the surface. This can be expressed as:
$$ ε=\frac{E}{E_b} $$
Therefore, at thermal equilibrium the emissivity of a body is equal to its absorptivity. Although emissive power of a surface varies with the wavelength, for certain material it is constant fraction of the emissive power of a perfectly black body (Eb), i.e. E/Eb is constant. Such materials which have constant emissivity are known as grey bodies. Thus for grey bodies to apply Kirchhoff’s law, it is not necessary that the two bodies should be at the same thermal equilibrium.
Stefan-Boltzmann law states that emissive power of a black body is proportional to the fourth power of the absolute temperature, which can be expressed as:
$$ E_b=σT^4 $$
where, σ is Stefan-Boltzmann constant, its numerical value being 5.67 × 10−8 W/m2 × K4.
Reference:
- Khar, R.,Vyas, S., Ahmad, F., & Jain, G. (2016). Lachman/Lieberman’s The Theory and Practice of Industrial Industrial Pharmacy. New Delhi, ND: CBS Publishers & Distributors Pvt Ltd.