1. 1/22/05ME 2591 ME 259 Heat Transfer Lecture Slides I Dr. Gregory A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University, Chico

2. 1/22/05ME 2592 Introduction Reading: Incropera & DeWitt Chapter 1

3. 1/22/05ME 2593 Heat Transfer as a Course u Has a “reputation” for being one of the most challenging courses in ME u Why?? – Physically diverse: thermodynamics, material science, diffusion theory, fluid mechanics, radiation theory – Higher-level math: vector calculus, ODEs, PDEs, numerical methods – Physically elusive: heat is invisible; developing intuition takes time – Appropriate assumptions: required to simplify and solve most problems u However, Heat Transfer is interesting, fun, and readily applicable to the real world

4. 1/22/05ME 2594 Relevance of Heat Transfer u Electric Power Generation u Alternate Energy Systems u Combustion/Propulsion Systems u Building Design u Heating & Cooling Systems u Domestic Appliances u Materials/Food Processing u Electronics Cooling & Packaging u Cryogenics u Environmental Processes u Space Vehicle Systems

5. 1/22/05ME 2595 Definition of Heat Transfer u Flow of energy due solely to a temperature difference –all other forms of energy transfer are categorized as work –from 2nd Law of Thermodynamics, heat flows in direction of decreasing temperature –heat energy can be transported through a solid, liquid, gas, or vacuum

6. 1/22/05ME 2596 Heat Quantities

7. 1/22/05ME 2597 Relationship Between the Study of Heat Transfer & Thermodynamics u 1st Law of Thermodynamics for Closed System: u Thermodynamics - allows calculation of total heat transferred ( Q ) during a process in which system goes from one equilibrium state to another (i.e., the “big picture”) u Heat Transfer - provides important physical laws that allow calculation of instantaneous heat rate, length of time required for process to occur, and temperature distribution within material at any time (i.e., the “details” required for design)

8. 1/22/05ME 2598 Heat Transfer Modes u Conduction –transfer of heat due to random molecular or atomic motion within a material (aka diffusion) –most important in solids u Convection –transfer of heat between a solid surface and fluid due to combined mechanisms of a) diffusion at surface; b) bulk fluid flow within boundary layer u Radiation –transfer of heat due to emission of electromagnetic waves, usually between surfaces separated by a gas or vacuum

9. 1/22/05ME 2599 Heat Transfer Modes - Conduction u Rate equation (Fourier & Biot,  1820) is known as Fourier’s law; for 1-D conduction, u where q x = heat rate in x -direction (W) q” x = heat flux in x -direction (W/m 2 ) T = temperature (°C or K) A = area normal to heat flow (m 2 ) k = thermal conductivity of material (W/m-K); see Tables A.1-A.7

10. 1/22/05ME 25910 Heat Transfer Modes - Conduction u Steady-state heat conduction through a plane wall: L T1T1 T2T2 x q  (T 1 >T 2 ) k

11. 1/22/05ME 25911 Heat Transfer Modes - Conduction u Example: What thickness of plate glass would yield the same heat flux as 3.5  of glass-fiber insulation with the same S-S temperature difference ( T 1 -T 2 ) ?

12. 1/22/05ME 25912 Heat Transfer Modes - Conduction u Insulation “R-value”: u where 1 W/m-K = 0.578 Btu/hr-ft-°F

13. 1/22/05ME 25913 Heat Transfer Modes - Convection u Rate equation (Newton,  1700) is known as Newton’s law of “cooling”: u where q” = heat flux normal to surface q = heat rate from or to surface A s T s = surface temperature T  = freestream fluid temperature A s = surface area exposed to fluid h = convection heat transfer coefficient (W/m 2 -K) Fluid flow, T  AsAs T s (>T  ) qq

14. 1/22/05ME 25914 Heat Transfer Modes - Convection u The convection heat transfer coefficient ( h ) –is not a material property –is a complicated function of the many parameters that influence convection such as fluid velocity, fluid properties, and surface geometry –is often determined by experiment rather than theory –will be given in most HW problems until we reach Chapter 6

15. 1/22/05ME 25915 Heat Transfer Modes - Convection u Types of Convection –Forced convection: flow caused by an external source such as a fan, pump, or atmospheric wind –Free (or natural) convection: flow induced by buoyancy forces such as that from a heated plate –Phase change convection: flow and latent heat exchange associated with boiling or condensation

16. 1/22/05ME 25916 Heat Transfer Modes - Radiation u Rate equation is the Stefan-Boltzmann law which gives the energy flux due to thermal radiation that is emitted from a surface; for a black body: u For non-black bodies, u where E = emissive power (W/m 2 )  = Stefan-Boltzmann constant = 5.67x10 -8 W/m 2 -K 4  = emissivity (0<  <1) of surface T s = surface temperature in absolute units (K)

17. 1/22/05ME 25917 Heat Transfer Modes - Radiation u Radiation incident upon an object may be reflected, transmitted, or absorbed : where G = irradiation (incident radiation)  = reflectivity (fraction of G that is reflected)  = transmissivity (fraction of G that is transmitted  = absorptivity (fraction of G that is absorbed)  = emissivity (fraction of black body emission) u E and the interaction of G with each participating object determines the net heat transfer between objects G GG GG GG

18. 1/22/05ME 25918 Heat Transfer Modes - Radiation u Heat transfer between a small object and larger surroundings ( A s <<A sur ): u where  = emissivity of small object A s = surface area of small object T s = surface temperature of small object (K) T sur = temperature of surroundings (K) q TsTs T sur , A s

19. 1/22/05ME 25919 Conservation of Energy – Control Volume u Control volume energy balance: –from thermodynamics: –Incropera & DeWitt text notation: W Q mass in mass out

20. 1/22/05ME 25920 Conservation of Energy – Control Volume u Energy rates: –where:

21. 1/22/05ME 25921 Conservation of Energy – Control Surface u Surface energy balance: –since a control surface is a special control volume that contains no volume, energy generation and storage terms are zero; this leaves: E in E out

22. 1/22/05ME 25922 Summary: The Laws Governing Heat Transfer u Fundamental Laws –Conservation of mass –Conservation of momentum –Conservation of energy u Heat Rate Laws –Fourier’s law of heat conduction –Newton’s law of convection –Stefan-Boltzmann law for radiation u Supplementary Laws –Second law of thermodynamics –Equations of state: »ideal gas law »tabulated thermodynamic properties »caloric equation (definition of specific heat)

23. 1/22/05ME 25923 Objectives of a Heat Transfer Calculation u ANALYSIS –Calculate T(x,y,z,t) or q for a system undergoing a specified process »e.g., calculate daily heat loss from a house »e.g., calculate operating temperature of a semiconductor chip with heat sink/fan u DESIGN –Determine a configuration and operating conditions that yield a specified T(x,y,z,t) or q »e.g., determine insulation needed to meet a specified daily heat loss from a house »e.g., determine heat sink and/or fan needed to keep operating temperature of a semiconductor chip below a specified value

24. 1/22/05ME 25924 Classes of Heat Transfer Problems u Thermal Barriers –insulation –radiation shields u Heat Transfer Enhancement (heat exchangers) –boilers, evaporators, condensers, etc. –solar collectors –finned surfaces u Temperature Control –cooling of electronic components –heat treating & quenching of metals –minimizing thermal stress –heating appliances (toaster, oven, etc.)