Review for Final Exa m

1. Review for Final Exam 15th December (Saturday) 1:30-4:30 PM LMS 151

2. Part 1: Closed book and notes (30 minutes) Based on general theoretical concepts Part 2: Open book and notes (120 minutes) Based on numerical problems

3. Heat Exchangers:Design Considerations Chapter 11

4. Counterflow Parallel Flow Heat Exchanger Types Heat exchangers are ubiquitous in energy conversion and utilization. They involve heat exchange between two fluids separated by a solid and encompass a wide range of flow configurations. • Concentric-Tube Heat Exchangers • Simplest configuration. • Superior performance associated with counter flow.

5. Finned-Both Fluids Unmixed Unfinned-One Fluid Mixed the Other Unmixed • Cross-flow Heat Exchangers • For cross-flow over the tubes, fluid motion, and hence mixing, in the transverse direction (y) is prevented for the finned tubes, but occurs for the unfinned condition. • Heat exchanger performance is influenced by mixing.

6. Shell-and-Tube Heat Exchangers One Shell Pass and One Tube Pass • Baffles are used to establish a cross-flow and to induce turbulent mixing of the shell-side fluid, both of which enhance convection. • The number of tube and shell passes may be varied, e.g.: One Shell Pass, Two Tube Passes Two Shell Passes, Four Tube Passes

7. Compact Heat Exchangers • Widely used to achieve large heat rates per unit volume, particularly when one or both fluids is a gas. • Characterized by large heat transfer surface areas per unit volume, small flow passages, and laminar flow. (a) Fin-tube (flat tubes, continuous plate fins) (b) Fin-tube (circular tubes, continuous plate fins) (c) Fin-tube (circular tubes, circular fins) (d) Plate-fin (single pass) (e) Plate-fin (multipass)

8. Overall Heat Transfer Coefficient • An essential requirement for heat exchanger design or performance calculations. • Contributing factors include convection and conduction associated with the • two fluids and the intermediate solid, as well as the potential use of fins on both • sides and the effects of time-dependent surface fouling. • With subscripts c andhused to designate the coldand hotfluids, respectively, • the most general expression for the overall coefficient is:

9. Assuming an adiabatic tip, the fin efficiency is

10. Evaluation of depends on the heat exchanger type. A Methodology for Heat Exchanger Design Calculations - The Log Mean Temperature Difference (LMTD) Method - • A form of Newton’s law of cooling may be applied to heat exchangers by • using a log-mean value of the temperature difference between the two fluids: • Counter-Flow Heat Exchanger:

11. Parallel-Flow Heat Exchanger: • Note that Tc,ocannot exceed Th,ofor a PF HX, but can do so for a CF HX. • For equivalent values of UA and inlet temperatures, • Shell-and-Tube and Cross-Flow Heat Exchangers:

12. Overall Energy Balance • Application to the hot (h) and cold (c) fluids: • Assume negligible heat transfer between the exchanger and its surroundings • and negligible potential and kinetic energy changes for each fluid. • Assuming no l/v phase change and constant specific heats,

13. Case (a): Ch>>Cc or h is a condensing vapor • Negligible or no change in • Case (b): Cc>>Ch or c is an evaporating liquid • Negligible or no change in Special Operating Conditions • Case (c): Ch=Cc.

14. F correction factor depends on the geometry of theheat exchanger and the inlet and outlettemperatures of the hot and coldfluid streams. F for common cross-flow and shell-and-tube heatexchanger configurations is given in the figure versus two temperatureratios P and R defined as 1 and 2 inlet and outlet T and t shell- andtube-side temperatures F = 1 for a condenser or boiler Use of a Correction Factor

17. Effectiveness NTU method • Computational Features/Limitations of the LMTD Method: • The LMTD method may be applied to design problems for which the fluid flow rates and inlet temperatures, as well as a desired outlet temperature, are prescribed. For a specified HX type, the required size (surface area), as well as the other outlet temperature, are readily determined. • If the LMTD method is used in performance calculations for which both outlet temperatures must be determined from knowledge of the inlet temperatures, the solution procedure is iterative. • For both design and performance calculations, the effectiveness-NTU method may be used without iteration.

18. Heat exchanger effectiveness, : Definitions • Maximum possible heat rate: • Will the fluid characterized by Cmin or Cmax experience the largest possible temperature change in transit through the HX? • Why is Cminand not Cmaxused in the definition of qmax?

19. Number of Transfer Units, NTU • A dimensionless parameter whose magnitude influences HX performance:

20. Cr Heat Exchanger Relations • Performance Calculations:

21. For Cr = 0, to all HX types. • Design Calculations: • For all heat exchangers,

22. Radiation: Processes and Properties-Basic Principles and Definitions- Chapter 12 12.1 through 12.8

23. Attention is focused on thermal radiation, whose origins are associated • with emission from matter at an absolute temperature • Consider a solid of temperature • in an evacuated enclosure whose walls • are at a fixed temperature • What changes occur if • What changes occur if General Considerations • Emission is due to oscillations and transitions of the many electrons that comprise • matter, which are, in turn, sustained by the thermal energy of the matter. • Emission corresponds to heat transfer from the matter and hence to a reduction • in its thermal energy. • Radiation may also be intercepted and absorbed by matter, resulting in its increase • in thermal energy.

24. For an opaque solid or liquid, emission originates from atoms and molecules within 1 of the surface. • Emission from a gas or a semitransparent solid or liquid is a volumetric • phenomenon. Emission from an opaque solid or liquid is treated as a surface phenomenon. • The dual nature of radiation: • In some cases, the physical manifestations of radiation may be explained by viewing it as particles (aka photons or quanta). • In other cases, radiation behaves as an electromagnetic wave.

25. In all cases, radiation can be characterized by a wavelength and frequency which are related through the speed at which radiation propagates in the medium of interest: For propagation in a vacuum,

26. Thermal radiation is confined to the infrared, visible and ultraviolet regions of the • spectrum . The Electromagnetic Spectrum • The amount of radiation emitted by an opaque • surface varies with wavelength, and we may • speak of the spectral distribution over all • wavelengths or of monochromatic/spectral • components associated with particular wavelengths.

27. Radiation Heat Fluxes and Material Properties • → reflectivity → fraction of irradiation (G) reflected. • a → absorptivity → fraction of irradiation absorbed. • t → transmissivity → fraction of irradiation transmitted through the medium. • r + a + t = 1 for any medium. r + a = 1 for an opaque medium.

28. Direction may be represented in a spherical • coordinate system characterized by the zenith • or polar angle and the azimuthal angle . • The amount of radiation emitted from a surface, • and propagating in a particular direction, • is quantified in terms of a differential • solid angle associated with the direction. unit element of surface on a hypothetical sphere and normal to the direction. Directional Considerations and Radiation Intensity • In general, radiation fluxes can be determined • only from knowledge of the directional and • spectral nature of the radiation. • Radiation emitted by a surface will be in all • directions associated with a hypothetical • hemisphere about the surface and is • characterized by a directional distribution.

29. The solid angle has units of steradians (sr). • Spectral Intensity: A quantity used to specify the radiant heat flux within • a unit solid angle about a prescribed direction and within a unit • wavelength interval about a prescribed wavelength • The solid angle associated with a complete hemisphere is

30. The spectral intensity associated with emission from a surface element • in the solid angle about and the wavelength interval about • is defined as: • The rationale for defining the radiation flux in terms of the projected surface area • stems from the existence of surfaces for which, to a good approximation, • is independent of direction. Such surfaces are termed diffuse, and the radiation is • said to beisotropic. • The projected area is how would appear if observed along . • What is the projected area for ? • What is the projected area for ? • The spectral heat rate and heat flux associated with emission from • are, respectively,

31. Relation of Intensity to Emissive Power, Irradiation, and Radiosity • The spectral emissive power corresponds to spectral emission • over all possible directions. • The total emissive power corresponds to emission over all directions • and wavelengths. • The spectral intensity of radiation incident on • a surface, , is defined in terms of the unit • solid angle about the direction of incidence, • the wavelength interval about , • and the projected area of the receiving • surface, • For a diffuse surface, emission is isotropic and

32. The spectral irradiation is then: and the total irradiation is • How may and G be expressed if the incident radiation is diffuse? • The radiosity of an opaque surface accounts for all of the radiation leaving the • surface in all directions and may include contributions from both reflection and • emission.

33. How may and J be expressed if the surface emits and reflects diffusely? • With designating the spectral intensity associated with radiation • emitted by the surface and the reflection of incident radiation, the spectral • radiosity is: and the total radiosity is • How can the intensities that appear in the preceding equations be quantified?

34. Blackbody Radiation and Its Intensity • The Blackbody • An idealization providing limits on radiation emission and absorption by matter. • For a prescribed temperature and wavelength, no surface can emit more radiation than a blackbody: the ideal emitter. • A blackbody is a diffuse emitter. • A blackbody absorbs all incident radiation: the ideal absorber. • The Isothermal Cavity (Hohlraum). (a) After multiple reflections, virtually all radiation entering the cavity is absorbed. • Emission from the aperture is the maximum possible emission achievable for • the temperature associated with the cavity and is diffuse.

35. The cumulative effect of radiation emission from and reflection off • the cavity wall is to provide diffuse irradiation corresponding to • emission from a blackbody for any surface in the cavity. • Does this condition depend on whether the cavity surface is highly reflecting or absorbing?

36. First radiation constant: Second radiation constant: The Spectral (Planck) Distribution of Blackbody Radiation • The spectral distribution of the blackbody emissive power (determined • theoretically and confirmed experimentally) is

37. (and Il,b) varies continuously with and increases with T. • The distribution is characterized by a maximum for which is given by Wien’s displacement law: • The fractional amount of total blackbody emission appearing at lower wavelengths increases with increasing T.

38. the Stefan-Boltzmann law, where • The fraction of total blackbody emission that is in a prescribed wavelength • interval or band is The Stefan-Boltzmann Law and Band Emission • The total emissive powerof a blackbody is obtained by integrating the Planck • distribution over all wavelengths. where, in general, and numerical results are given in Table 12.2.

39. • • • • • • • • • • • •

40. Note ability to readily determine and its relation to the maximum intensity from the 3rd and 4th columns, respectively. • If emission from the sun may be approximated as that from a blackbody at 5800 K, at what wavelength does peak emission occur? • Would you expect radiation emitted by a blackbody at 800 K to be discernible by the naked eye? • As the temperature of a blackbody is increased, what color would be the first to be discerned by the naked eye?

41. Surface Emissivity • Radiation emitted by a surface may be determined by introducing a property • (the emissivity) that contrasts its emission with the ideal behavior of a blackbody • at the same temperature. • The definition of the emissivity depends upon one’s interest in resolving • directional and/or spectral features of the emitted radiation, in contrast • to averages over all directions (hemispherical) and/or wavelengths (total). • The spectral, directional emissivity: • The spectral, hemispherical emissivity (a directional average):

42. The total, hemispherical emissivity (a directional and spectral average): • To a reasonable approximation, the hemispherical emissivity is equal to • the normal emissivity. • Representative values of the total, normal emissivity: • Note: • Low emissivity of polished metals and increasing emissivity for unpolished and oxidized surfaces. • Comparatively large emissivities of nonconductors.

43. Note decreasing with increasing for metals and different behavior for nonmetals. Why does increase with increasing for tungsten and not for aluminum oxide? • Representative spectral variations: • Representative temperature variations:

44. Reflection from the medium • Absorption within the medium • Transmission through the medium • In contrast to the foregoing volumetric effects, the response of an opaque material • to irradiation is governed by surface phenomena and Radiation balance Response to Surface Irradiation: Absorption, Reflection and Transmission • There may be three responses of a semitransparent medium to irradiation: • The wavelength of the incident radiation, as well as the nature of the material, • determine whether the material is semitransparent or opaque. • Are glass and water semitransparent or opaque?

45. Unless an opaque material is at a sufficiently high temperature to emit visible • radiation, its color is determined by the spectral dependence of reflection in • response to visible irradiation. • What may be said about reflection for a whitesurface? A black surface? • Why are leaves green?

46. The absorptivity is approximately independent of the surface temperature, but if the irradiation corresponds to emission from a blackbody, why does depend on the temperature of the blackbody? Absorptivity of an Opaque Material • The spectral, directional absorptivity: Assuming negligible temperature dependence, • The spectral, hemispherical absorptivity: • To what does the foregoing result simplify, if the irradiation is diffuse? If the surface is diffuse? • The total, hemispherical absorptivity: • If the irradiation corresponds to emission from a blackbody, how may the above expression be rewritten?

47. Reflectivity of an Opaque Material • The spectral, directional reflectivity: Assuming negligible temperature • dependence: • The spectral, hemispherical reflectivity: • To what does the foregoing result simplify if the irradiation is diffuse? If the surface is diffuse? • The total, hemispherical reflectivity: • Limiting conditions of diffuse and • specular reflection. Polished and rough surfaces.

48. Note strong dependence of • Is snow a highly reflective substance? White paint?

49. Transmissivity • The spectral, hemispherical transmissivity: Assuming negligible temperature dependence, Note shift from semitransparent to opaque conditions at large and small wavelengths. • The total, hemispherical transmissivity: • For a semitransparent medium,

50. Kirchhoff’s Law • Kirchhoff’s law equates the total, hemispherical emissivity of a surface to its • total, hemispherical absorptivity: However, conditions associated with its derivation are highly restrictive: Irradiation of the surface corresponds to emission from a blackbody at the same temperature as the surface. • But, Kirchhoff’s law may be applied to the spectral, directional properties • without restriction: Why are there no restrictions on use of the foregoing equation? How might we take advantage of the foregoing equation?