Thermodynamics, Heat Transfer, And Fluid Flow. V.2. Heat Transfer (776131), страница 3
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0Page ixHT-02Heat TransferIntentionally Left BlankHT-02Page xRev. 0Heat TransferHEAT TRANSFER TERMINOLOGYHEAT TRANSFER TERMINOLOGYTo understand and communicate in the thermal science field, certain terms andexpressions must be learned in heat transfer.EO 1.1DESCRIBE the difference between heat and temperature.EO 1.2DESCRIBE the difference between heat and work.EO 1.3DESCRIBE the Second Law of Thermodynamics andhow it relates to heat transfer.EO 1.4DESCRIBE the three modes of heat transfer.EO 1.5DEFINE the following terms as they relate to heattransfer:a.Heat fluxb.Thermal conductivityc.Log mean temperature differenced.Convective heat transfer coefficiente.Overall heat transfer coefficientf.Bulk temperatureHeat and TemperatureIn describing heat transfer problems, students often make the mistake of interchangeably usingthe terms heat and temperature.
Actually, there is a distinct difference between the two.Temperature is a measure of the amount of energy possessed by the molecules of a substance.It is a relative measure of how hot or cold a substance is and can be used to predict the directionof heat transfer.
The symbol for temperature is T. The common scales for measuringtemperature are the Fahrenheit, Rankine, Celsius, and Kelvin temperature scales.Heat is energy in transit. The transfer of energy as heat occurs at the molecular level as a resultof a temperature difference. Heat is capable of being transmitted through solids and fluids byconduction, through fluids by convection, and through empty space by radiation.
The symbolfor heat is Q. Common units for measuring heat are the British Thermal Unit (Btu) in theEnglish system of units and the calorie in the SI system (International System of Units).Rev. 0Page 1HT-02HEAT TRANSFER TERMINOLOGYHeat TransferHeat and WorkDistinction should also be made between the energy terms heat and work. Both represent energyin transition.
Work is the transfer of energy resulting from a force acting through a distance.Heat is energy transferred as the result of a temperature difference. Neither heat nor work arethermodynamic properties of a system. Heat can be transferred into or out of a system and workcan be done on or by a system, but a system cannot contain or store either heat or work.
Heatinto a system and work out of a system are considered positive quantities.When a temperature difference exists across a boundary, the Second Law of Thermodynamicsindicates the natural flow of energy is from the hotter body to the colder body. The Second Lawof Thermodynamics denies the possibility of ever completely converting into work all the heatsupplied to a system operating in a cycle. The Second Law of Thermodynamics, described byMax Planck in 1903, states that:It is impossible to construct an engine that will work in a complete cycle andproduce no other effect except the raising of a weight and the cooling of areservoir.The second law says that if you draw heat from a reservoir to raise a weight, lowering the weightwill not generate enough heat to return the reservoir to its original temperature, and eventuallythe cycle will stop.
If two blocks of metal at different temperatures are thermally insulated fromtheir surroundings and are brought into contact with each other the heat will flow from the hotterto the colder. Eventually the two blocks will reach the same temperature, and heat transfer willcease.
Energy has not been lost, but instead some energy has been transferred from one blockto another.Modes of Transferring HeatHeat is always transferred when a temperature difference exists between two bodies. There arethree basic modes of heat transfer:Conduction involves the transfer of heat by the interactions of atoms or molecules of amaterial through which the heat is being transferred.Convection involves the transfer of heat by the mixing and motion of macroscopicportions of a fluid.Radiation, or radiant heat transfer, involves the transfer of heat by electromagneticradiation that arises due to the temperature of a body.The three modes of heat transfer will be discussed in greater detail in the subsequent chaptersof this module.HT-02Page 2Rev.
0Heat TransferHEAT TRANSFER TERMINOLOGYHeat FluxThe rate at which heat is transferred is represented by the symbol Q̇ . Common units for heattransfer rate is Btu/hr. Sometimes it is important to determine the heat transfer rate per unit area,or heat flux, which has the symbol Q̇ . Units for heat flux are Btu/hr-ft2. The heat flux can bedetermined by dividing the heat transfer rate by the area through which the heat is beingtransferred.Q̇AQ̇(2-1)where:Q̇= heat flux (Btu/hr-ft2)Q̇= heat transfer rate (Btu/hr)A= area (ft2)Thermal ConductivityThe heat transfer characteristics of a solid material are measured by a property called the thermalconductivity (k) measured in Btu/hr-ft-oF.
It is a measure of a substance’s ability to transfer heatthrough a solid by conduction. The thermal conductivity of most liquids and solids varies withtemperature. For vapors, it depends upon pressure.Log Mean Temperature DifferenceIn heat exchanger applications, the inlet and outlet temperatures are commonly specified basedon the fluid in the tubes. The temperature change that takes place across the heat exchanger fromthe entrance to the exit is not linear. A precise temperature change between two fluids acrossthe heat exchanger is best represented by the log mean temperature difference (LMTD or ∆Tlm),defined in Equation 2-2.∆T1m(∆T2∆T1)(2-2)ln(∆T2 / ∆T1)where:∆T2 =∆T1 =Rev. 0thethethethelarger temperature difference between the two fluid streams at eitherentrance or the exit to the heat exchangersmaller temperature difference between the two fluid streams at eitherentrance or the exit to the heat exchangerPage 3HT-02HEAT TRANSFER TERMINOLOGYHeat TransferConvective Heat Transfer CoefficientThe convective heat transfer coefficient (h), defines, in part, the heat transfer due to convection.The convective heat transfer coefficient is sometimes referred to as a film coefficient andrepresents the thermal resistance of a relatively stagnant layer of fluid between a heat transfersurface and the fluid medium.
Common units used to measure the convective heat transfercoefficient are Btu/hr - ft2 - oF.Overall Heat Transfer CoefficientIn the case of combined heat transfer, it is common practice to relate the total rate of heattransfer ( Q̇ ), the overall cross-sectional area for heat transfer (Ao), and the overall temperaturedifference (∆To) using the overall heat transfer coefficient (Uo). The overall heat transfercoefficient combines the heat transfer coefficient of the two heat exchanger fluids and the thermalconductivity of the heat exchanger tubes. Uo is specific to the heat exchanger and the fluids thatare used in the heat exchanger.Q̇UoAo∆T0(2-3)where:Q̇=the rate heat of transfer (Btu/hr)Uo=the overall heat transfer coefficient (Btu/hr - ft2 - oF)Ao=the overall cross-sectional area for heat transfer (ft2)∆To=the overall temperature difference (oF)Bulk TemperatureThe fluid temperature (Tb), referred to as the bulk temperature, varies according to the details ofthe situation.
For flow adjacent to a hot or cold surface, Tb is the temperature of the fluid thatis "far" from the surface, for instance, the center of the flow channel. For boiling orcondensation, Tb is equal to the saturation temperature.HT-02Page 4Rev. 0Heat TransferHEAT TRANSFER TERMINOLOGYSummaryThe important information in this chapter is summarized below.Heat Transfer Terminology SummaryHeat is energy transferred as a result of a temperature difference.Temperature is a measure of the amount of molecular energy containedin a substance.Work is a transfer of energy resulting from a force acting through adistance.The Second Law of Thermodynamics implies that heat will not transferfrom a colder to a hotter body without some external source of energy.Conduction involves the transfer of heat by the interactions of atoms ormolecules of a material through which the heat is being transferred.Convection involves the transfer of heat by the mixing and motion ofmacroscopic portions of a fluid.Radiation, or radiant heat transfer, involves the transfer of heat byelectromagnetic radiation that arises due to the temperature of a body.Heat flux is the rate of heat transfer per unit area.Thermal conductivity is a measure of a substance’s ability to transfer heatthrough itself.Log mean temperature difference is the ∆T that most accurately represents the∆T for a heat exchanger.The local heat transfer coefficient represents a measure of the ability to transferheat through a stagnant film layer.The overall heat transfer coefficient is the measure of the ability of a heatexchanger to transfer heat from one fluid to another.The bulk temperature is the temperature of the fluid that best represents themajority of the fluid which is not physically connected to the heat transfer site.Rev.
0Page 5HT-02CONDUCTION HEAT TRANSFERHeat TransferCONDUCTION HEAT TRANSFERConduction heat transfer is the transfer of thermal energy by interactions betweenadjacent atoms and molecules of a solid.EO 1.6Given Fourier’s Law of Conduction, CALCULATE theconduction heat flux in a rectangular coordinate system.EO 1.7Given the formula and the necessary values,CALCULATE the equivalent thermal resistance.EO 1.8Given Fourier’s Law of Conduction, CALCULATE theconduction heat flux in a cylindrical coordinate system.ConductionConduction involves the transfer of heat by the interaction between adjacent molecules of amaterial. Heat transfer by conduction is dependent upon the driving "force" of temperaturedifference and the resistance to heat transfer. The resistance to heat transfer is dependent uponthe nature and dimensions of the heat transfer medium.
All heat transfer problems involve thetemperature difference, the geometry, and the physical properties of the object being studied.In conduction heat transfer problems, the object being studied is usually a solid. Convectionproblems involve a fluid medium. Radiation heat transfer problems involve either solid or fluidsurfaces, separated by a gas, vapor, or vacuum. There are several ways to correlate the geometry,physical properties, and temperature difference of an object with the rate of heat transfer throughthe object. In conduction heat transfer, the most common means of correlation is throughFourier’s Law of Conduction. The law, in its equation form, is used most often in its rectangularor cylindrical form (pipes and cylinders), both of which are presented below.HT-02RectangularQ̇ ∆T k A ∆x (2-4)CylindricalQ̇ ∆T k A ∆r (2-5)Page 6Rev.
0Heat TransferCONDUCTION HEAT TRANSFERwhere:Q̇A∆x∆r∆Tk======rate of heat transfer (Btu/hr)cross-sectional area of heat transfer (ft2)thickness of slab (ft)thickness of cylindrical wall (ft)temperature difference (°F)thermal conductivity of slab (Btu/ft-hr-°F)The use of Equations 2-4 and 2-5 in determining the amount of heat transferred by conductionis demonstrated in the following examples.Conduction-Rectangular CoordinatesExample:1000 Btu/hr is conducted through a section of insulating material shown in Figure 1 thatmeasures 1 ft2 in cross-sectional area.
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