Heat and Mass Transfer - Lec 1 Updated PDF

MC 358 – Heat Transfer Lecturer Dr. Clement A. Komolafe [email protected] Office No: SR 009 Class: Monday (12:30 – 2:30 pm) & Thursday (12:30-2:30 pm )  COURSE SYNOPSIS  Conduction: steady and unsteady st...

MC 358 – Heat Transfer Lecturer Dr. Clement A. Komolafe [email protected] Office No: SR 009 Class: Monday (12:30 – 2:30 pm) & Thursday (12:30-2:30 pm )  COURSE SYNOPSIS  Conduction: steady and unsteady state.  Convection: laminar and turbulent flow over plate and in tubes.  Radiation: ideal and non-ideal bodies, gases.  Applications to thermal design of heat exchangers, heat pipes and solar energy collectors. 2  MC 358 - Heat Transfer Lecture 01 Dr. Clement A. Komolafe Recommended textbooks:  Heat and Mass Transfer: Fundamentals and Applications by Cengel Y.A. And Ghajar A.J 6th Edition.  Bergman, T. L., Lavine, A. S., Incropera, F. P. and DeWitt, D. P. (2017), Fundamentals of Heat and Mass Transfer, 8th Edition  Learning Objectives The objectives are to  Examine the basics of conduction, convection, and radiation heat transfer  Solve problems in the above heat transfer mechanisms using the corresponding relations 4  Lecture content Heat Transfer  Introduction  Modes of heat transfer  Physical mechanism of conduction, convection and radiation 5 Conceptual Understanding If the same volume of water Narrow is heated in this containers, which is likely to boil first? WHY? Shallow On a chilly night, in Omuaran, who feels the effect of the cold weather more? 6 Heat Transfer: Introduction  Heat transfer is energy in transition due to temperature difference. Fig 1. Heat flows in the direction of decreasing temperature Heat transfer study concerns the  mode of heat transfer,  rate of energy (heat) transfer under certain specified conditions, thus, cooling or heating time can be evaluated.  Temperature variation in a medium Fig 2. Focus is usually on how long it takes for the hot coffee in a flask to cool to a certain temperature.  Thermodynamics deals with equilibrium states while heat transfer is a non-equilibrium phenomenon. 7 Heat Transfer: Introduction Areas of Practical Engineering Applications Fig 3. Design of heat exchangers Fig 4. Heat treatment of metals e.g. radiators, condensers Fig 5. Human comfort In practice, heat transfer problems are essentially divided in two categories: (1) rating and (2) sizing Fig 6. Refrigeration and air- conditioning units 8 Areas of Application Contd. 9 Areas of Application Contd. 10 Areas of Application Contd. 11 Areas of Application Contd. 12 Areas of Application Contd. 13 Areas of Application Contd. 14 Areas of Application Contd. 15 Areas of Application Contd. 16  Areas of Application Contd. Fig. 12. Inner wall temperature distribution on the absorber plate 17 Modes of Heat Transfer  The transfer of energy on account of temperature difference may occur in any of these three modes: i. Conduction ii. Convection iii. Radiation  In most practical situations the three modes are involved in heat transfer. For example, raising water temp. in the boiler shell.  The three modes of heat transfer are similar in the sense that a i. temperature difference must exist, and ii. heat exchange occurs in the direction of lower temperature  However, each mode has a distinctive controlling law 18 Heat Transfer by Conduction  Conduction heat transfer occurs in a stationary medium, either a solid or a fluid.  The energy exchange is due to atomic or molecular activity in the presence of a temp. difference in the medium.  In solids, heat transfer is often a combination of: i. Lattice vibrations, and ii. Free movement of electrons  For liquids and gases, conduction is primarily by collisions and diffusion of molecules in a state of random motion.  The difference in the intermolecular spacing in gases and liquids is responsible for the difference in conduction heat transfer between the media. 19 Heat Transfer by Conduction  The rate of conduction heat transfer is given as Fourier’s law (Eq.1) (1) 𝑄 = heat transfer rate by conduction (W), A = area (m2), 𝑑𝑇 𝑑𝑥 = temperature gradient ℃ 𝑚 , and k = thermal conductivity 𝑊 𝑚.℃.  Fourier’s law is based on the following assumptions i. Steady-state conditions exist ii. Heat flow is one-dimensional iii. No internal heat generation Fig 7. Heat conduction iv. The temperature gradient is constant and through a large plane wall of thickness ∆𝑇 and area A. the temperature profile is linear. v. The material is homogeneous and isotropic (i.e. thermal conductivity is constant. 20 Thermal Conductivity, k  Materials are classified as thermal conductors or insulators depending on their thermal conductivity.  Thermal conductivity depends on the following factors i. Material structure ii. Moisture content iii. Material density iv. Pressure and temperature (operating conditions)  Generally, thermal conductivities for pure metals are the highest, but it decrease with the inclusion of impurities, e.g. alloys.  By implication then heat conduction occurs readily in metals, less in alloys, and much less in non-metals.  Thermal conductivities for liquids and gases, respectively are next to solids. 21 Thermal Conductivity, k TC of various materials at 0 °C MATERIAL TC 𝑾 𝒎. ℃ METALS: Silver (pure) 410 Copper (pure) 385 Nickel (pure) 93  From Fourier's Law of Heat Chrome-nickel steel 16.3 Conduction, TC, 𝑘 is expressed (18% Cr, 8% Ni) as NOMETALLIC SOLIDS: Diamond 2300 Glass 0.78 𝑄 𝑑𝑇 𝑊 𝑘=. (3) Hard rubber 0.15 𝐴 𝑑𝑥 𝑚.𝐾 LIQUIDS: Mercury 8.21 Water 0.556 Lubricating oil, SAE 50 0.147 GASES Hydrogen 0.175 Air 0.024 Water vapour (saturated) 0.0206 22 Heat Transfer by Convection  Convection heat transfer occurs as a result of bulk fluid motion over a surface at a different temperature.  Convection heat transfer is categorised according to the nature of fluid flow as (1) natural (free) or (2) forced convection  Natural (free) convection heat transfer is induced by buoyancy effects arising from density variation caused by temperature difference in the fluid medium.  Forced convection occurs when the fluid motion is initiated by external means such as a fan, pump or wind. 23 Heat Transfer by Convection  The rate of convection heat transfer is defined by Newton’s law of cooling (Eq.2) (2) 𝑄 = heat transfer rate by convection (W), A = area (m2), h = heat transfer coefficient 𝑚𝑊2.℃ , Ts = surface temp., 𝑇∞ = fluid temp.  The convection heat transfer Fig 8. Heat transfer from a hot coefficient, h, depends on the factors surface to air by convection i. Fluid properties e.g. density, viscousity, specific heat, thermal conductivity. ii. Nature of fluid flow e.g. forced or natural flow iii. Surface geometry 24 Heat Transfer by Radiation  Thermal radiation is energy emitted by matter at finite temperature  All bodies at temperature above absolute zero (-273.15 ºC or 0 K) radiates heat  Radiation energy is transported by electromagnetic waves (or photons)  Unlike convection and conduction heat transfer that requires the presence of a medium, radiation heat transfer occurs efficiently in a vacuum. The rate at which energy is released per unit area (W/m2) is termed the surface emissive power, E. There is an upper limit to the emissive power, which is prescribed by the Stefan–Boltzmann law as 25  Heat Transfer by Radiation where T s is the absolute temperature (K) of the surface and s is the Stefan– Boltzmann constant. Such a surface is called an ideal radiator or blackbody. The heat flux emitted by a real surface is less than that of a blackbody at the same temperature and is given by where ε is a radiative property of the surface termed the emissivity. With values in the range 0≤ ε ≤, this property provides a measure of how efficiently a surface emits energy relative to a blackbody. 26 Heat Transfer by Radiation  The maximum radiation heat transfer from a surface (blackbody [BB]) is defined by Stefan-Boltzmann law (Eq. 3) (3) A = area (m2), 𝜎 = Stefan-Boltzmann constant σ = 5.67 x 10-8 W/m2.K4, Ts = surface temperature (K), 𝜀 = emissivity 0 < 𝜀 < 1 for real surfaces  The net radiation heat transfer between a surface and its surroundings is expressed as (Eq.4 and 5) (4 ) 𝑄𝑟𝑎𝑑 = ℎ𝑟 𝐴 (𝑇𝑠 − 𝑇𝑠𝑟 ) (5 ) ℎ𝑟 ≡ 𝜀𝜎 𝑇𝑠 + 𝑇𝑠𝑟 (𝑇𝑠 2 + 𝑇𝑠𝑟 2 ) Fig 8. Radiation heat transfer between a surface and the surfaces surrounding it 27 Simultaneous Heat Transfer Mechanism The irradiation may be approximated by emission from a blackbody at Tsur, as.  Heat transfer phenomena through a medium or at a surface usually occur by two modes of heat transfer simultaneously.  For example in opaque solids it is purely by conduction, however, in semitransparent solids it is by conduction and radiation.  Again a surface exposed to fluid motion and the surroundings, loses heat by convection and radiation.  Note that heat transfer through a fluid is either by conduction or convection. 28 Classwork 1. Define thermal conductivity and explain its significance in heat transfer. 2. What are the mechanisms of heat transfer? 3. How are they distinguished one from another? 4. What is the physical mechanism of heat conduction in a solid, liquid, and a gas? 5. How does heat conduction differ from natural convection? 6. Write down the expressions for the physical laws that govern each mode of heat transfer, and identify the variables involved in each relation. 7. Does any of the energy of the sun reach the earth by conduction or convection? 29  Classwork Contd. 8. The wall of an industrial furnace is constructed from 0.15-m-thick fireclay brick having a thermal conductivity of 1.7 W/m z K. Measurements made during steady-state operation reveal temperatures of 1400 and 1150 K at the inner and outer surfaces, respectively. What is the rate of heat loss through a wall that is 0.5 m 3 1.2 m on a side? 9. 30 Cut away view of a steam boiler 31