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

Reading: Incropera & DeWitt Chapter 1 Introduction Reading: Incropera & DeWitt Chapter 1 1/22/05 ME 259

Heat Transfer as a Course Has a “reputation” for being one of the most challenging courses in ME 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 However, Heat Transfer is interesting, fun, and readily applicable to the real world 1/22/05 ME 259

Relevance of Heat Transfer Electric Power Generation Alternate Energy Systems Combustion/Propulsion Systems Building Design Heating & Cooling Systems Domestic Appliances Materials/Food Processing Electronics Cooling & Packaging Cryogenics Environmental Processes Space Vehicle Systems 1/22/05 ME 259

Definition of Heat Transfer 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 1/22/05 ME 259

Heat Quantities 1/22/05 ME 259

Relationship Between the Study of Heat Transfer & Thermodynamics 1st Law of Thermodynamics for Closed System: 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”) 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) 1/22/05 ME 259

Heat Transfer Modes Conduction transfer of heat due to random molecular or atomic motion within a material (aka diffusion) most important in solids 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 Radiation transfer of heat due to emission of electromagnetic waves, usually between surfaces separated by a gas or vacuum 1/22/05 ME 259

Heat Transfer Modes - Conduction Rate equation (Fourier & Biot, 1820) is known as Fourier’s law; for 1-D conduction, where qx = heat rate in x-direction (W) q”x = heat flux in x-direction (W/m2) T = temperature (°C or K) A = area normal to heat flow (m2) k = thermal conductivity of material (W/m-K); see Tables A.1-A.7 1/22/05 ME 259

Heat Transfer Modes - Conduction Steady-state heat conduction through a plane wall: T1 T2 k L q (T1>T2) x 1/22/05 ME 259

Heat Transfer Modes - Conduction 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 (T1-T2) ? 1/22/05 ME 259

Heat Transfer Modes - Conduction Insulation “R-value”: where 1 W/m-K = 0.578 Btu/hr-ft-°F 1/22/05 ME 259

Heat Transfer Modes - Convection Rate equation (Newton, 1700) is known as Newton’s law of “cooling”: where q” = heat flux normal to surface q = heat rate from or to surface As Ts = surface temperature T = freestream fluid temperature As = surface area exposed to fluid h = convection heat transfer coefficient (W/m2-K) q Fluid flow, T Ts (>T) As 1/22/05 ME 259

Heat Transfer Modes - Convection 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 1/22/05 ME 259

Heat Transfer Modes - Convection 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 1/22/05 ME 259

Heat Transfer Modes - Radiation 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: For non-black bodies, where E = emissive power (W/m2)  = Stefan-Boltzmann constant = 5.67x10-8 W/m2-K4  = emissivity (0< <1) of surface Ts = surface temperature in absolute units (K) 1/22/05 ME 259

Heat Transfer Modes - Radiation 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) E and the interaction of G with each participating object determines the net heat transfer between objects G G G G 1/22/05 ME 259

Heat Transfer Modes - Radiation Heat transfer between a small object and larger surroundings (As<<Asur): where  = emissivity of small object As = surface area of small object Ts = surface temperature of small object (K) Tsur = temperature of surroundings (K) Tsur q  , As Ts 1/22/05 ME 259

Conservation of Energy – Control Volume Control volume energy balance: from thermodynamics: Incropera & DeWitt text notation: Q mass out mass in W 1/22/05 ME 259

Conservation of Energy – Control Volume Energy rates: where: 1/22/05 ME 259

Conservation of Energy – Control Surface 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: Eout Ein 1/22/05 ME 259

Summary: The Laws Governing Heat Transfer Fundamental Laws Conservation of mass Conservation of momentum Conservation of energy Heat Rate Laws Fourier’s law of heat conduction Newton’s law of convection Stefan-Boltzmann law for radiation Supplementary Laws Second law of thermodynamics Equations of state: ideal gas law tabulated thermodynamic properties caloric equation (definition of specific heat) 1/22/05 ME 259

Objectives of a Heat Transfer Calculation 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 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 1/22/05 ME 259

Classes of Heat Transfer Problems Thermal Barriers insulation radiation shields Heat Transfer Enhancement (heat exchangers) boilers, evaporators, condensers, etc. solar collectors finned surfaces Temperature Control cooling of electronic components heat treating & quenching of metals minimizing thermal stress heating appliances (toaster, oven, etc.) 1/22/05 ME 259