ME 259 Heat Transfer Lecture Slides IV

1. ME 259Heat TransferLecture Slides IV Dr. Gregory A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University, Chico ME 259

2. Natural (Free) Convection Heat Transfer ME 259

3. Natural Convection Fundamentals • Heat transfer is due to fluid motion by buoyancy forces • Buoyancy arises from a density variation in the fluid, most commonly due to a temperature gradient: • Velocities are generally much smaller than those associated with forced convection, hence • For air, h = 2 – 10 W/m2-K • For H2O, h = 50 – 1000 W/m2-K ME 259

4. Natural Convection Fundamentals, cont. • Radiation and natural convection heat transfer are comparable in most applications • Analysis often leads to an iterative solution technique ( IHT ! ) since qrad = f (T4) and qconv = f (T4/3) or f (T5/4) • Natural convection strongly influences • Heating & cooling of rooms • Cooling of electronics, engines, refrigeration coils, transmission lines • Human and animal comfort • Environmental pollution • Atmospheric motions • Oceanic currents ME 259

5. Natural Convection Fundamentals, cont. • Physical considerations – consider a quiescent fluid between parallel, heated horizontal plates: ME 259

6. Physics of Natural Convection • Consider a wood stove or fireplace: Buoyant force per unit area: ME 259

7. Physics of Natural Convection, cont. • Now consider a vertical heated plate: Buoyant force per unit area: • The quantity (-) is related to a thermodynamic property called the volumetric thermal expansion coefficient ( ): ME 259

8. Physics of Natural Convection, cont. • This buoyant force will cause fluid motion that is resisted by viscous forces: • The ratio is important in determining the magnitude of natural convection - known as the Grashof number (Gr): ME 259

9. Important Dimensionless Parameters in Natural Convection • For a particular geometric shape and orientation, • Dimensional analysis shows that • The Grashof number plays a similar role to the Reynolds number in forced convection • The product Gr •Pr appears frequently in analysis of natural convection, so we also define the Rayleigh number (Ra): ME 259

10. Empirical Correlations for Natural Convection Heat Transfer • Many natural convection geometries have been studied; the correlations are typically written as • Geometries: • vertical plate, vertical cylinder • horizontal plate • horizontal cylinder • sphere • array of horizontal cylinders • inclined plate • parallel plates, or channel • rectangular cavity, or enclosure • annular cavity ME 259

11. Thermal Expansion Coefficient, b • For an ideal gas, r = P/RT, so • For liquids and non-ideal gases, b is found from Appendix tables in text, e.g., A.4 - A.6 ME 259

12. Combined Natural and Forced Convection • Both types of convection are comparable when • the resulting flow field is complicated and difficult to predict; it is strongly influenced by the direction of the buoyancy relative to that of the flow; the effect on NuL can be estimated for three special cases by • where n = 3 for vertical plates & cylinders n = 3.5 for horizontal plates n = 4 for horizontal cylinders & spheres and + refers to assisting and transverse flows - refers to opposing flows ME 259

13. Heat Exchangers ME 259

14. Introduction • Heat exchangersenable efficient heat transfer between two fluids at different temperatures, separated by a solid wall. • Boilers, condensers, regenerators, recuperators, preheaters, intercoolers, economizers, feedwater heaters, “radiators”, are all HXers. • Types of HXers: • Concentric tube – simple, inexpensive, easy to analyze • Shell and tube – high efficiency, expensive, common for large-scale liquid-liquid heat exchange; difficult to analyze; performance based on empirical data • Cross Flow – high-efficency, moderately expensive, common for gas-liquid heat exchange; difficult to analyze; performance based on empirical data. ME 259

15. HXer Energy Balance Equations • Hot-side heat transfer rate • Cold-side heat transfer rate • Heat capacities • For an evaporating or condensing fluid: ME 259

16. Log-Mean Temperature Difference (LMTD) Method of Analysis • For concentric tube hxers, • If hxer is shell-and-tube or cross flow type, ME 259

17. Effectiveness()-NTU Method of Heat Exchanger Analysis • LMTD method requires an iterative procedure if only the inlet temperatures are known; in such cases, the -NTU method is preferred. • Effectiveness () is defined as • qmax corresponds to a CF hxer of infinite length where the fluid with the least heat capacity experiences the maximum possible temperature change, Thi-Tci . • Thus, the actual heat transfer rate is found by ME 259

18. Effectiveness-NTU Method, cont. • For any hxer, it can be shown that • Cmin/Cmax is equal to Ch/Cc or Cc/Ch, depending on the relative magnitudes of the fluid mass flow rates and specific heats; the number of transfer units (NTU) is a dimensionless parameter given by • NTU typically has values between 0 - 5 and indicates the relative size, or heat exchange area, of the hxer. ME 259

19. Effectiveness-NTU Method, cont. • Relations for = f(NTU) and NTU = f() are given in Tables 11.3 and 11.4, respectively, for the three types of hxers. • Figures 11.14 - 11.19 give this same information in graphical form. • In summary, either the LMTD or -NTU methods may be used to solve hxer problems and both will yield identical values. However, the LMTD method is best-suited for design calculations, i.e., where one outlet temperature is known and the required heat exchange area (A) is sought. ME 259