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MIT 4 42J - Heat Transfer

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Heat Transfer Leon R. Glicksman © 1991, 1997, 2004, 2005, 2010 1)Introduction Heat transfer deals with the rate of heat transfer between different bodies. While thermodynamics deals with the magnitude of heat exchanged in a process, heat transfer is necessary to determine the time required for a process or alternatively the size of a surface necessary to achieve a certain total rate of heat transfer. Heat transfer analysis permits a calculation of the heat loss from a building surface to the surroundings for a given building size, window area and wall design, e.g. the level of insulation in the wall cavity. The comfort conditions for occupants in a room is determined by a balance of heat transfer from the person to the air surrounding him or her as well as the heat transfer to the walls of the interior. The size and cost of a heat exchanger is also determined by considering the heat transfer between the fluid streams in the exchanger. In other fields, heat transfer plays a key role as well. The design of integrated microprocessors which contain very closely spaced elements, each with a finite amount of heat generation, is limited by the requirement for adequate cooling so that the operating temperature of the electronic components is not exceeded. Reentry of the space shuttle in the earth's atmosphere must be carefully programmed so that temperature extremes due to air friction are confined to the insulating tiles on the shuttle's surface. Modes of Heat Transfer Following thermodynamics, heat transfer is that energy transfer which takes place between two bodies by virtue of a temperature difference between the bodies. From the second law considerations it can be demonstrated that there is always a net positive energy transfer from the body at a high temperature to a second body at a lower temperature. Following the definition of heat, there are only two physical mechanisms for heat transfer: (1) electromagnetic waves produced by virtue of the temperature of a body, referred to as thermal radiation heat transfer and (2) atomic or molecular motion in a medium between the bodies exchanging energy, referred to as conduction heat transfer.Sometimes conduction heat transfer takes place during the change of phase and is referred to as boiling or condensation heat transfer. Conduction heat transfer can also take place in the presence of fluid motion, which is called convection heat transfer. The rate of heat transfer between two bodies is proportional to the temperature difference between the bodies and in some cases the temperature level of the bodies as well. In many instances the heat transfer process is analogous to the rate of transfer which appears in other fields. The analogy between heat transfer and DC electrical current flow will be used to illustrate some of the simpler heat transfer processes. Similarly, it can be shown that the rate of transfer of mass in an evaporation process follows a process very similar to that for heat transfer. 2)Conduction Heat Transfer In a homogenous body which experiences a temperature gradient the rate of heat transfer due to microscopic motions is conduction heat transfer. In a gas the gas molecules in the higher temperature portion of the gas will have a higher kinetic energy. As the molecules of the gas randomly move through the gas volume there is a net energy transfer from the high temperature portion to the low temperature zones. In a solid, the energy transfer from high to low temperature may be due to the migration of electrons or the vibration of the molecular bonds. Viewed as a macroscopic phenomena, the rate of heat transfer by conduction represented by the symbol q or Q is found to be directly proportional to the product of the local temperature gradient and the cross-sectional area available for heat transfer, ~q A gradT (2.1) Fig 2.1 One dimensional conductionIn the case of one-dimensional heat transfer normal to a plane slab, figure 1, the conduction heat transfer can be given by Fourier's Equation, dTq kAdx (2.2) The constant k is known as the thermal conductivity. q has the dimensions of BTU/hr or Watts and k has the dimensions of BTU/hrft F or W/m K. The thermal conductivity defined by equation 2.2 is a thermophysical property of the material. If the composition and thermodynamic state is known then the thermal conductivity can be found. Table 2.1 lists the thermal conductivity of common solids, liquids and gases at normal temperatures. Note that these values span many orders of magnitude with electrically conductors having the highest thermal conductivity and high molecular weight gases generally having the lowest thermal conductivity. Consider a slab with a steady conduction heat transfer across it in the x direction, fig. 2, with the temperature equal to T1 and T2 at the surfaces corresponding to x equal to 0 and L, respectively. Then q is a constant and equation 2 can be integrated to give, 12TTq kAL (2.3) For this case the temperature varies linearly across the width of the slab. One can consider an analogy between the solution for steady conduction and for steady D.C. electric current flow, Ohm's Law, Fig. 2,2 Conduction Through a Plane Wall21VVIR (2.4) Table 2.1 Thermal Conductivity of Common Materials k(BTU/hr ft F) (W/mK) Solids Copper 219 378 Aluminum 119 206 Steel 25 43 Brick,common 0.2 - 0.1 0.17 - 0.34 Concrete 0.5 - 0.8 0.87 - 1.38 Glass 0.5 0.87 Glass fiber insulation .03 0.05 Ice 1.3 2.2 Plastic 0.1 0.17 Wood 0.1 - 0.2 0.17 - 0.34 Liquids Ammonia 0.3 0.5 Refrigerant-12 0.04 0.07 Light Oil 0.08 0.14 Water 0.34 0.59 Mercury 5 8.7 Gases Air,dry 0.015 0.026 Carbon Dioxide 0.009 0.016 Helium 0.09 0.16 Hydrogen 0.11 0.19 Water Vapor (Steam) 0.015(at 212 F)0.026 (at 100 C) Refrigerant-11 0.005 0.009 1.0 (BTU/hr ft F)= 1.73 (W/m C) ________________________________________________________________The rate of heat transfer q is analogous to the current flow I, the potential difference V is analogous to T and the balance of equation


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