The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 49
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This results in larger radiation and conduction errors. In liquids,radiation error is not a problem, but velocity error and conduction error may both be significant.Conduction error becomes a problem in liquid-temperature measurements when thermowells are used.The depth of immersion of the well is frequently too short to eliminate conduction error.Steady-State Errors in Solid and Surface-Temperature MeasurementsWhen probes are used to measure solid temperature by inserting them into a hole in the specimen, theyare subject to conduction errors proportional to their size and conductivity.
A general rule of thumb isto keep the insertion depth at least 20 times the diameter (or wall thickness) of the probe. This assumesa close-fitting hole, backfilled with a material with higher thermal conductivity than air. For more-exactadvice regarding a specific installation, a careful thermal circuit analysis of the installation should bedeveloped, and its results used to guide the selection of diametrical clearance, backfill materials, andpenetration depth.A thermocouple attached to a hot surface surrounded by cooler fluid will exchange heat with the fluidby convection and with the surrounding solids by radiation. Heat lost from the thermocouple must bemade up from the surface by conduction, which will result in a cold spot at the point of attachment.Figure 4.6.14 shows the system disturbance error caused by a surface-attached thermocouple, as afraction of the maximum possible error for the installation.
If the surface is irradiated (e.g., by heatinglamps), the irradiation will raise the surface temperature, but will also affect the system disturbanceerror. The effect on the system disturbance error caused by turning on the irradiation is similar to thatof raising the temperature of the surrounding fluid to a new value, T¥°,where Tind = indicated temperature from an otherwise error-free thermocouple, °CTs = undisturbed substrate temperature, °C© 1999 by CRC Press LLC4-200Section 4FIGURE 4.6.14 System disturbance errors caused by an attached thermocouple (worst case).T¥ohDkwks=====effective fluid temperature, °Cheat transfer coefficient, TC to fluid, W/m, °Coutside diameter of TC, meffective thermal conductivity of TC, W/m, °Cthermal conductivity of substrate, W/m, °CThe effective gas temperature is defined in terms of the incident irradiation and the heat transfer coefficientasT¥* = T¥ +where T¥aGAR/Ach=====aGAR *ThAC ¥(4.6.14)actual gas temperature, °Cabsorptivity of the TC for thermal radiationincident thermal radiation flux, W/m2ratio of irradiated surface to convective surfaceheat transfer coefficient between the TC and the gas, W/m°CSteady-State Errors in Heat Flux Gauges for Convective Heat TransferIf the gauge is not flush with the surface, it may disturb the flow, and if it is not at the same temperatureas the surface, it will disturb the heat transfer.
Thus, the gauge may properly report the heat flux whichis present when the gauge is present, but that may be significantly different from the heat flux whichwould have been there if the gauge had not been there.For planar gauges, both effects are usually small. The thermal resistance of such a gauge is generallysmall, and they are thin enough to avoid disturbing most flows. Circular foil gauges pose a more seriousproblem, since they are often cooled significantly below the temperature of the surrounding surface.Dropping the wall temperature at the gauge location can significantly increase the local heat load in twoways: one due to the fact that, for a given value of h, a cold spot receives a higher heat load from thegas stream.
The second effect arises because the value of the heat transfer coefficient itself depends onthe local wall temperature distribution: a local cold spot under a hot gas flow will experience a higherheat transfer coefficient than would have existed had the surface been of uniform temperature.© 1999 by CRC Press LLC4-201Heat and Mass TransferEvaluating the Heat Transfer CoefficientThe heat transfer coefficient is a defined quantity, given byh=where hq˙ conv¢¢ToTref====q˙ conv¢¢(To - Tref )(4.6.15)heat transfer coefficient, W/m2, °Cconvective heat flux, W/m2temperature of the considered surface, °Ctemperature used as reference for this definition, °CDifferent reference temperatures are conventionally used for different situations:• T¥: The free-stream temperature.
Used for isolated objects of uniform temperature in a uniformfree stream, where an average value of h is desired which describes the overall heat transferbetween the object and the flow. Also used in boundary layer heat transfer analyses where localvalues of h are needed to deal with locally varying conditions.• Tm: The mixed mean fluid temperature. Used for internal flows where the intent of the calculationis to describe the changes in mixed mean fluid temperature (e.g., heat exchangers).• Tadiabatic: The adiabatic surface temperature. Used for isolated objects or small regions of uniformtemperature in either internal or external flows, where the overall thermal boundary conditionsare neither uniform heat flux nor uniform temperature.For a given data set, the value of the heat transfer coefficient will depend on the reference temperaturechosen, and h should be subscripted to inform later users which reference was used: e.g., h¥, hm, or hadiabatic.Direct MethodsThe two most commonly used methods for measuring the heat transfer coefficient are both derived fromthe same energy balance equation:hA(To - Tref ) = e˙in + q˙ cond,in + q˙ rad,in - Mcwhere h =A=Tref =To =ėin =q̇cond,in =q̇rad,in =Mc dT/dt =dTdt(4.6.16)the heat transfer coefficient, W/m, °Cthe area available for convective transport, m2the reference temperature used in defining h, °Cthe average surface temperature over the area A, °Cexternally provided input, Wnet energy conducted in, Wnet energy radiated in, Wrate of increase of thermal energy stored within the system, WSteady State.
In the steady-state method, the transient term is zero (or nearly so), and h is determinedby measuring the input power and the operating temperature, and correcting for losses. Equation (4.6.16)can be applied to differentially small elements or to whole specimens. The considered region must bereasonably uniform in temperature, so the energy storage term and the convective heat transfer term usethe same value.For tests of isolated objects, or embedded calorimeter sections, steady-state tests usually use highconductivity specimens (e.g., copper or aluminum) with embedded electric heaters. The resulting valueof h is the average over the area of the specimen.
The Biot number, hL/k, for the specimen should below (on the order of 0.01 or less) if only one temperature sensor is used in the specimen, so the surfacetemperature can be determined from the embedded sensor.© 1999 by CRC Press LLC4-202Section 4If a single heated element is used within an array of unheated elements, the resulting heat transfercoefficient is implicitly defined as hadiabatic and should be identified as such.
Heat transfer coefficientsmeasured with single-active-element tests cannot be used with the mixed mean fluid temperature.When the variation of h over a surface is required, one common steady-state technique is to stretcha thin foil (stainless steel, or carbon impregnated paper, or gold deposited on polycarbonate) over aninsulating substrate, and electrically heat the foil surface. Liquid crystals or infrared techniques can beused to map the surface temperature, from which the heat transfer coefficient distribution can bedetermined. The “heated foil with liquid crystal” approach was used by Cooper et al.
in 1975 to measureheat transfer coefficients, and has since been used by many others. Hippensteele et al. (1985) have madeextensive use of the foil technique in studies of gas turbine heat transfer. An example of their work onthe end wall of a turbine cascade is shown in Figure 4.6.15.FIGURE 4.6.15 Heat transfer coefficient distribution on the end wall of a turbine cascade. (From Hippensteele,S.A. et al., NASA Technical Memorandum 86900, March, 1985.
With permission.)Hollingsworth et al. (1989) used a stainless steel foil heater for a study in air for an electronics coolingapplication, illustrated in Figure 4.6.16.FIGURE 4.6.16 Visualization of the heat transfer coefficient distribution on a heated plate around three unheatedcubes.© 1999 by CRC Press LLC4-203Heat and Mass TransferAnother steady-state technique which reveals the distribution of h on the surface was introduced byden Ouden and Hoogendoorn (1974) and is currently in use by Meinders (1996).
It uses a uniform andconstant-temperature substrate (originally, a tank of warm water, now a copper block) covered with alayer of known thermal resistance (originally, a plate of glass, now a thin layer of epoxy). The surfacewas painted with liquid crystals (now visualized using infrared imaging) and the surface-temperaturedistribution determined.
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