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# Heat Transfer - Mechanical

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```Thermodynamics tells us that heat flow occurs whenever there is a temperature difference and this heat always flows from higher temperature to lower temperature. But it does not tell us about the rate at which this heat is being transferred. This is where the subject of heat transfer comes into the picture. Heat transfer is the study of the flow of heat in transient and the rate at which the heat flow is occurring.
There are three modes of heat transfer by which heat can flow from one body to another or within the same body with a temperature gradient. The three modes of heat transfer are:
1.  Conduction
2.  Convection
Out of the three, Conduction is the basic mode of heat transfer that occurs within the same body whether solid or a fluid. Convection is the mode that causes heat transfer between a solid and fluid.

Conduction
Conduction is the independent mode of heat transfer occurring in a medium. The mechanism of heat conduction is different in a solid and a fluid. Conduction in solids can be due to free electron transfer and propagation of lattice vibrational waves. In metallic solids, heat is conducted due to the presence of free electron cloud at the periphery of atoms. These electrons are transferred from one molecule to another and in the process transfer heat. In non-metallic solids, heat conduction takes place due to the propagation of lattice vibrational waves.
Heat conduction in liquids is due to the momentum transfer between the colliding molecules. The law governing the heat conduction in a medium was given Fourier and is described mathematically by the equation:
Where  is the rate of heat flux defined as the rate of heat transfer per unit area, k is the property of the material which governs the ability of the material to conduct heat and is known as Thermal Conductivity,   is the temperature gradient within the material which causes the heat flow to occur. In general, the thermal conductivity of metals is higher than those of non-metals, Diamond being an exception. The thermal conductivity of Diamond(2300 W/m.k) is one of the highest known for a solid. The reason for this is the perfect crystalline structure of Diamond. The thermal conductivity of liquids is very low but is higher than that of gases. For example, the thermal conductivity of water is 0.555 W/m.k which is more than an order times higher than that of Air having a thermal conductivity value of 0.026 W/m.k. The thermal conductivity is a material property and depends on temperature.

Convection
Convection occurs between a solid surface and a fluid flowing past the solid surface. Convection is basically Conduction followed by Advection. First, the heat is conduction within the solid surface and comes to the surface. Then, this heat is carried away from the surface by the fluid flowing over the surface. This bulk motion of the fluid is known as Advection. The equation which governs the heat transfer through convection is given by:
Where  is the rate of heat transfer between the solid surface and the fluid, h is the property governing the ability of the luid to carry away the heat known as Heat Transfer Coefficient, ∆T is the temperature difference between the solid surface and the free stream of fluid or vice-versa depending on the direction of heat flow and A is the surface of the solid surface over which the fluid flows.
There are two types of convection depending on the type of fluid flow occurring past the solid surface. First is the Forced convection which occurs when the flow of fluid has been brought by some external agency like a fan or a pump. The more is the velocity of fluid flow, more is the rate of heat transfer. Second is the Free convection which occurs due to the flow of fluid caused due to the force of Buoyancy which in turn is caused due to the difference in density of fluid occurring at two different locations due to the temperature difference. The heat transfer coefficient is not a property of the fluid itself, instead, it depends on a number of factors like dynamic viscosity of the fluid, the velocity of fluid flow, the thermal conductivity of fluid etc.

The two modes of heat transfer discussed above differ from radiation in a way that they both require a material medium to occur. But radiation is the mode of heat transfer which does not require any material medium to occur. Radiation heat is emitted in the form of Electromagnetic waves emitted by the bodies. All the bodies radiate heat at all the temperatures except at absolute zero. The equation governing the radiation from a body at an absolute temperature T is given by:

Where  is a property of the body known as emissivity,  is Stephen-Boltzmann constant, A is the surface area of the body.
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