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# Note for Heat & Mass Transfer - HMF By ANNA SUPERKINGS

• Heat & Mass Transfer - HMF
• Note
• ANNA UNIVERISTY - HITECH
• Mechanical Engineering
• 4 Topics
• 6253 Views
Anna Superkings
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Fatima Michael College of Engineering & Technology UNIT I - CONDUCTION INTRODUCTORY CONCEPTS AND BASIC LAWS OF HEAT TRANSFER We recall from our knowledge of thermodynamics that heat is a form of energy transfer that takes place from a region of higher temperature to a region of lower temperature solely due to the temperature difference between the two regions. With the knowledge of thermodynamics we can determine the amount of heat transfer for any system undergoing any process from one equilibrium state to another. Thus the thermodynamics knowledge will tell us only how much heat must be transferred to achieve a specified change of state of the system. But in practice we are more interested in knowing the rate of heat transfer (i.e. heat transfer per unit time) rather than the amount. This knowledge of rate of heat transfer is necessary for a design engineer to design all types of heat transfer equipments like boilers, condensers, furnaces, cooling towers, dryers etc. The subject of heat transfer deals with the determination of the rate of heat transfer to or from a heat exchange equipment and also the temperature at any location in the device at any instant of time. The basic requirement for heat transfer is the presence of a ―temperature difference‖. The temperature difference is the driving force for heat transfer, j ust as the voltage difference for electric current flow and pressure difference for fluid flow. One of the parameters , on which the rate of heat transfer in a certain direction depends, is the magnitude of the temperature gradient in that direction. The larger the gradient higher will be the rate of heat transfer. Heat Transfer Mechanisms :There are three mechanisms by which heat transfer can take place. All the three modes require the existence of temperature difference. The three mechanisms are: (i) conduction, (ii) convection and (iii) radiation Conduction:It is the energy transfer that takes place at molecular levels. Conduction is the transfer of energy from the more energetic molecules of a substance to the adjacent less energetic molecules as a result of interaction between the molecules. In the case of liquids and gases conduction is due to Fatima Michael College of Engineering & Technology2

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Fatima Michael College of Engineering & Technology collisions and diffusion of the molecules during their random motion. In solids, it is due to the vibrations of the molecules in a lattice and motion of free electrons. Fourier’s Law of Heat Conduction:The empirical law of conduction based on experimental results is named after the French Physicist Joseph Fourier. The law states that the rate of heat flow by conduction in any medium in any direction is proportional to the area normal to the direction of heat flow and also proportional to the temperature gradient in that direction. For example the rate of heat transfer in x-direction can be written according to Fourier‘s law as Qx α − A (dT / dx) …………………….(1.1) Or Qx = − k A (dT / dx) W………………….. ..(1.2) In equation (1.2), Qx is the rate of heat transfer in positive x-direction through area A of the medium normal to x-direction, (dT/dx) is the temperature gradient and k is the constant of proportionality and is a material property called ―thermal conductivity‖. Since heat transfer has to take place in the direction of decreasing temperature, (dT/dx) has to be negative in the direction of heat transfer. Therefore negative sign has to be introduced in equation (1.2) to make Qx positive in the direction of decreasing temperature, thereby satisfying the second law of thermodynamics. If equation (1.2) is divided throughout by A we have qx is called the heat flux. qx = (Qx / A) = − k (dT / dx) W/m2 ………..(1.3) In the case of solids heat conduction is due to two effects: the vibration of lattice induced by the vibration of molecules positioned at relatively fixed positions, and energy transported due to the motion of free electrons. The relatively high thermal conductivities of pure metals are primarily due to the electronic component. The lattice component of thermal conductivity strongly depends on the way the molecules are arranged. For example, diamond, which is highly ordered crystalline solid, has the highest thermal conductivity at room temperature. Fatima Michael College of Engineering & Technology3

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Fatima Michael College of Engineering & Technology Unlike metals, which are good electrical and heat conductors, crystalline solids such as diamond and semiconductors such as silicon are good heat conductors but poor electrical conductors. Hence such materials find widespread use in electronic industry. Despite their high price, diamond heat sinks are used in the cooling of sensitive electronic components because of their excellent thermal conductivity. Silicon oils and gaskets are commonly used in the packaging of electronic components because they provide both good thermal contact and good electrical insulation. One would expect that metal alloys will have high thermal conductivities, because pure metals have high thermal conductivities. For example one would expect that the value of the thermal conductivity k of a metal alloy made of two metals with thermal conductivities k1 and k2 would lie between k1 and k2.But this is not the case. In fact k of a metal alloy will be less than that of either metal. 4