Physical Mechanism Of Natural Convection

Many familiar heat transfer applications involve natural convection as the primary mechanism of heat transfer. Some examples are cooling of electronic equipment such as power transistors, TVs, and VCRs; heat transfer from electric baseboard heaters or steam radiators; heat transfer from the refrigeration coils and power transmission lines; and heat transfer from the bodies of animals and human beings. Natural convection in gases is usually accompanied by radiation of comparable magnitude except for low-emissivity surfaces.
We know that a hot boiled egg (or a hot backed potato) on a plate eventually cools to the surrounding air temperature. The egg is cooled by transferring heat by convection to the air and by radiation to the surrounding surfaces. Disregarding heat transfer by radiation, the physical mechanism of cooling a hot egg for any hot object in a cooler environment can be explained as follows.
As soon as the hot egg is exposed to cooler air, the temperature of the outer surface of the egg shell will rise as a result of heat conduction from the shell to the air. Consequently, the egg will soon be surrounded by a thin layer of outer layers of air. The cooling process in this case would be rather slow since the egg would always be blanketed by warm air, and it would have no direct contact with the cooler air farther away. We may not notice any air motion in the vicinity of the egg, but careful measurements indicate otherwise.
The temperature of the air adjacent to the egg is higher, and thus its density is lower, since at constant pressure the density of a gas is inversely proportional to its temperature. Thus, we have a situation in which some low-density or “light” gas is surrounded by a high-density or “heavy” gas, and in a vinegar and oil salad dressing rising to the top. This phenomenon is characterized incorrectly by the phrase “heat rises”, which is understood to mean heated air rises. The space vacated by the warmer air in the vicinity of the egg is replaced by the cooler air nearby, and the presence of cooler air in the vicinity of the egg speeds up the cooling process. The rise of warmer air and the flow of cooler air into its place continues until the egg is cooled to the temperature of the surrounding air. The motion that results from the continual replacement of the heated air in the vicinity of the egg by the cooler air nearby is called a natural convection current, and the heat transfer that is enhanced as a result of this natural convection current is called natural convection heat transfer. Note that in the absence of natural convection currents, heat transfer from the egg to the air surrounding it would be by conduction only, and the rate of heat transfer from the egg would be much lower.

CONDUCTION

Conduction is the mode of heat transfer in which energy exchange takes place from the region of high temperature to that of low temperature by the kinetic motion or direct impact of molecules, as in the case of fluid at rest, and by the drift of electrons, as in the case of metals. In a solid which is a good electric conductor, a large number of free electrons move about in the lattice; hence materials that are good electric conductors are generally good heat conductors (i.e., copper, silver, etc.).
The empirical law of heat conduction based on experimental observations originates from Biot but is generally named after the French mathematical physicist Joseph Fourier who used it in his analytic theory of heat. This law states that the rate of heat flow by conduction in a given direction is proportional to the area normal to the direction of heat flow and to the gradient of temperature in that direction. For heat flow in the x direction, for example, the Fourier law is given as
Qx = -kA (dT/dx) Watt (1)
or
qx = Qx/A = -k(dT/dx) W/m2 (2)

where Qx is the rate of heat flow through area A in the positive x direction and qx is called the heat flux in the positive x direction. The proportionality constant k is called the thermal conductivity of the material and is a positive quantity. If temperature decreases in the positive x direction, then dT/dx is negative; hence qx (or Qx) becomes a positive quantity because of the presence of the negative sign in Eqs. (1) and (2). Therefore, the minus sign is included in Eqs. (1) ans (2) to ensure that qx (or Qx) is a positive quantity when the heat flow is in the positive x direction. Conversely, when he right-hand side of Eqs. (1) and (2) is negative, the heat flow is in the negative x direction.
The thermal conductivity k in Eqs. (1) and (2) must have the dimensions W/(m.C) or J/(m.s.C) if the equations are dimensionally correct. There is a wide difference in the range of thermal conductinities of various engineering materials. Beetwen gaes and highly conducting metals, such as copper or silver, k varies by a factor of about 10000. The highest value is for highly conducting pure metals, and the lowest value is for gases and vapors, excluding the evacuated insulating systems. The nonmetallic solids and liquids have thermal conductivities that lie between them. Metallic single crystals are exceptions, which may have vary high thermal conductivities; for example, with copper crystals, value of 8000 W/(m.C) and even higher are possible.
Thermal conductivity also varies with temperature. This variation, for some materials over certain temperature ranges, is small enough to be neglected; but for many cases the variation of k with temperature is signifficant. Especially at very low temperatures k varies rapidly with temperature; for example, the thermal conductivities of copper, aluminum, or silver reach values 50 to 100 times those that occur at room temperature.

Film Condensation Theory

When the temperature of a vapor is reduced below its saturation temperature, the vapor condensed. In engineering applications, the vapor is condensed by bringing it into contact with a cold surface. The steam condensers for power plants are typical examples of the application of condensing of steam. If the liquid wets the surface, the condensation occurs in the form of a smooth film, which flows down the surface under the action of the gravity. The presence of a liquid film over the surface constitutes a thermal resistance to heat flow. Therefore, numerous experimental and theoritical investigations have been conducted to determine the heat transfer coefficient for film condensation over surface. The first fundamental analysis leading to the determination of the heat transfer coefficient during filmwise condensation of pure vapors (i.e., without the presence of non-condensable gas) on a flat plate and a circular tube was given by Nusselt in 1916. Over the years, improvements have been made on Nusselt's theory of film condensation. But with the exception of the condensation of liquid metals, Nusselt's original theory has been succesful and still is widely used.