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Heat Transfer

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1. 1. Heat Transfer DM23815 Chapter 1. Introduction Eunseop Yeom esyeom@pusan.ac.kr School of Mechanical Engineering, Pusan National University
2. 2. 2 1.1 What is heat transfer? The form of energy that can be transferred from one system to another as a result of temperature difference.  Thermodynamics  Heat It deals with the amount of energy as a system undergoes a process from one state to another, and gives no indication about how long the process will take. (equilibrium)  Heat transfer It deals with the rate of heat transfer to or from a system, and thus determine the rates of heat transfer and the times of cooling or heating, as well as the variation of the temperature. (non-equilibrium) “Heat transfer is energy in transit due to temperature difference.” E=[J] q=[W]=[J/s], q'=q/L=[W/m], q''=q/A=[W/m2] Time State 1 Temp State 2
3. 3. 3 Examples of heat transfer mechanisms Conduction (Heat diffusion) Convection Radiation
4. 4. 4 1.2.1 Conduction Heat transfer from the more energetic to the adjacent less energetic particles of a substance due to interactions between the particles. Fourier’s law of heat conduction k : thermal conductivity (열 전도율) [W/m·K] Two mechanisms 1. The atoms and molecules having energy will pass those energy with their adjacent atoms or molecules by means of lattice vibrations. 2. Through the translational motion of free electrons, heat energy can be transferred in a conductor like metals having a plenty of free electrons. Conductive heat flux Under steady-state conditions and temperature distribution is linear L T - T dx dT 1 2   L T k L T T k q 2 1 x       x q 
5. 5. 5 1.2.1 Conduction Thermal conductivity (k) is a measure of material’s ability to conduct heat. Material k (W/m·K) Water (liquid) 0.607 Air(gas) 0.026 Human artery 0.476 ± 0.041 Human blood (43%Ht) 0.530 Human plasma 0.572 Human bone 0.373 - 0.496 Human fat 0.23 - 0.27 Human kidney 0.513 - 0.564 Human liver 0.467 - 0.527 Human lung 0.302 - 0.550 Human muscle 0.449 - 0.546 Human skin 0.385 - 3.393  Thermal conductivities Duck, Physical properties of tissues: a comprehensive reference book. (Academic press, 2013). - If k is high, the material is a good conductor. - If k is low, the material is a poor conductor or an insulator. - Thermal conductivity varies with temperature.
6. 6. 6 1.2.1 Convection Heat transfer due to a superposition of energy transport by the random motion of the molecules (diffusion), and by the bulk motion of the fluid (advection). Newton's law of cooling h : Convection heat transfer coefficient [W/m2·K]. (The term convection refers to heat transfer that will occur between a solid surface and the adjacent fluid when they are at different temperatures.) Convective heat flux Ts and T∞ : Temperatures at surface and fluid [K]. conv q 
7. 7. 7 1.2.1 Convection  Forced convection  Natural convection Process h (W/m2·K) Free convection Gases 2 - 25 Liquids 50 - 1,000 Forced convection Gases 25 - 250 Liquids 100 - 20,000 Convection with phase change Boiling and condensation 2,500 - 100,000 Fluid motion is set up by buoyancy effects resulting from density difference caused by temperature difference in the field. Fluid motion is forced by external means, such as a fan, a pump, etc. h depends on conditions in the boundary layer, which are influenced by ① Surface geometry ② The nature of the fluid motion ③ An assortment of fluid thermodynamic properties  Convection with phase change A latent heat exchange is associated with phase change between liquid and vapor states of the liquid. Two special cases are boiling and condensation.  Convection heat transfer coefficient Forced convection Free convection conv q  conv q  Boiling Condensation
8. 8. 8 1.2.3 Radiation This mode of heat transfer didn’t require any medium to occur. Every matter having a temperature above absolute zero will emit energy in the form of electromagnetic waves (or alternatively, photons) and called radiation. Radiation transfer occurs most efficiently in a vacuum. Stefan-Boltzmann’s law 4 s b T E   σ : Stefan-Boltzmann’s constant (5.67×10-8) [W/m2·K4]. T : Absolute temperature of surface [K] (For black body; ideal radiator) 4 s T E   (For real body) ε : Emissivity(방사율). (0 ≤ ε ≤ 1) A measure of how efficiently a surface emits energy relative to a blackbody. It depends strongly on the surface material and finish. rad q 
9. 9. 9 1.2.3 Radiation G Gabs   αG εE q b rad       sur s r rad T T A h q      2 2 sur s sur s r T T T T h     hr : Radiation heat transfer coefficient Radiation may also be incident (입사) on a surface from its surroundings. Irradiation G (조사) is all radiation on a unit area of the surface. A portion or all of irradiation may be absorbed by the surface. α : Absorptivity (흡수율) (0 ≤ α ≤ 1) When the surface is opaque (α < 1), portions of the irradiation are reflected. 4 sur T G   (For black body; ideal absorber) σ : Stefan-Boltzmann’s constant (5.67×10-8) [W/m2·K4]. T : Absolute temperature of surrounding black body [K] abs G E When the surface is assumed to be α = ε.  Net rate of radiation heat transfer from surface   4 surr 4 s rad T T ε q     
10. 10. 10 1.3 Relationship to thermodynamic  First law of thermodynamics The increase in the amount of energy stored in a control volume must equal the amount of energy that enters the control volume, minus the amount of energy that leaves the control volume. g out in st st E E - E dt dE E        Energy transported by the medium into the control volume. → surface phenomena Energy transported by the medium out of the control volume → surface phenomena Energy generated in the control volume → volumetric phenomena (e.g., chemical, electrical, electromagnetic, or nuclear) V q Eg    : heat generation rate per unit volume : volume q  V Energy stored in the control volume → volumetric phenomena in E  out E  g E  st E    CVT t Est      ρ: density volume, V : volume, C : specific heat, t : time, T : temperature For steady-state conditions → 0  st E 
11. 11. 11 1.3 Relationship to thermodynamic rad q  conv q  cond q   The surface energy balance In the special case, the control surface of a medium contains no mass or volume. Accordingly, the generation and storage terms of the conservation equation are no longer relevant. out in E E    0          rad conv cond q q q
12. 12. 12 1.3 Relationship to thermodynamic  Second law of thermodynamics It is impossible for any system to operate in a thermodynamic cycle and deliver a net amount of work to its surroundings while receiving energy by heat transfer from a single thermal reservoir. Kelvin-Plank statement The second law states that if the physical process is irreversible, the combined entropy of the system and the environment must increase. The final entropy must be greater than the initial entropy for an irreversible process: in out in out in in Q Q - 1 Q Q Q Q W η     Efficiency of a heat engine h c c T T - η 1  Carnot efficiency The Carnot efficiency is the maximum possible efficient that any engine can achieve operating between low and high temperature reservoirs. i h, i c, in out in out m T T - q q - Q Q - η 1 1 1    Modified efficiency for realistic heat transfer process tot in h c R q T T -  1 m in q W            tot in h c in R q T T - q 1 Power output of heat engine   h t, /R i h, h in T T q     c t, /R c i c, out T T q  
13. 13. 13 1.4 Units and Dimensions  SI base units  Multiplying prefixes Basic dimensions Length (L), Mass (M), Time (t), and Temperature (T) All physical quantities of heat transfer may be related to these four basic dimensions. Celsius temperature scale remains widespread. Zero on the Celsius scale (0°C) is equivalent to 273.15 K