Heat Transfer: Physical Origins and Rate Equations PDF

Heat Transfer: Physical Origins and Rate Equations Chapter One MEEN343 SP2024 – Md. Didarul Islam 1  Objectives At the end of this chapter you will be able to: Explain briefly different modes of heat transfer and their difference Explain the importance o...

Heat Transfer: Physical Origins and Rate Equations Chapter One MEEN343 SP2024 – Md. Didarul Islam 1  Objectives At the end of this chapter you will be able to: Explain briefly different modes of heat transfer and their difference Explain the importance of heat transfer Explain briefly by examples how heat transfer knowledge may be used with the first law of thermodynamics to solve technology problems. 2  Heat Transfer: Physical Origins and Rate Equations Chapter One Sections 1.1 and 1.2 3 Heat Transfer and Thermal Energy What is heat transfer? Heat transfer is thermal energy in transit due to a temperature difference. What is thermal energy? Thermal energy is associated with the translation, rotation, vibration and electronic states of the atoms and molecules that comprise matter. It represents the cumulative effect of microscopic activities and is directly linked to the temperature of matter. 4 Heat Transfer and Thermal Energy (cont.) DO NOT confuse or interchange the meanings of Thermal Energy, Temperature and Heat Transfer Quantity Meaning Symbol Units Thermal Energy+ Energy associated with microscopic behavior of matter U or u J or J/kg Temperature A means of indirectly assessing the amount of thermal energy stored in T K or °C matter Heat Transfer Thermal energy transport due to temperature gradients Heat Amount of thermal energy transferred Q J over a time interval  t  0 Heat Rate Thermal energy transfer per unit time q W Heat Flux Thermal energy transfer per unit time q W/m 2 and surface area + U Thermal energy of system 5 u Thermal energy per unit mass of system Modes of Heat Transfer Modes of Heat Transfer Conduction: Heat transfer in a solid or a stationary fluid (gas or liquid) due to the random motion of its constituent atoms, molecules and /or electrons. Convection: Heat transfer due to the combined influence of bulk and random motion for fluid flow over a surface. Radiation: Energy that is emitted by matter due to changes in the electron configurations of its atoms or molecules and is transported as electromagnetic waves (or photons). Conduction and convection require the presence of temperature variations in a material medium. Although radiation originates from matter, its transport does not require a material medium and occurs most efficiently in a vacuum. 6  Heat Transfer Rates Heat Transfer Rates: Conduction Conduction: General (vector) form of Fourier’s Law: q  k T Heat flux Thermal conductivity Temperature gradient W/m 2 W/m K °C/m or K/m Application to one-dimensional, steady conduction across a plane wall of constant thermal conductivity: dT T T qx  k  k 2 1 dx L T1  T2 qx k (1.2) L Heat rate (W): qx qx A 7 Example: The wall of an industrial furnace is constructed from 0.15 m thick fireclay brick having a thermal conductivity of 1.7 W/m.K. Measurements made during steady-state operation reveal temperatures of 1400 and 1150 K at the inner and outer surfaces. What is the rate of heat loss through the wall that is 0.5 m x 1.2 m on a side? 8 9 Heat Transfer Rates: Convection Heat Transfer Rates Convection Relation of convection to flow over a surface and development of velocity and thermal boundary layers: Newton’s law of cooling: q h Ts  T  (1.3a) h : Convection heat transfer coeffi cient (W/m 2 K) 10 Radiation Car Damage due to Radiation in London 11 Heat Transfer Rates: Radiation Heat Transfer Rates Radiation Heat transfer at a gas/surface interface involves radiation emission from the surface and may also involve the absorption of radiation incident from the surroundings (irradiation, G), as well as convection if Ts T . 4 Energy outflow due to emission: Gabs  G E  T s E  Eb  Ts4 (1.5) E : Emissive power W/m 2   : Surface emissivity 0  1 Eb : Emissive power of a blackbody (the perfect emitter)  : Stefan-Boltzmann constant 5.67 10-8 W/m 2 K 4  Energy absorption due to irradiation: Gabs  G (1.6) Gabs :Absorbed incident radiation (W/m 2 )  : Surface absorptivity 0  1 G : Irradiation W/m 2  12 Heat Transfer Rates: Radiation (cont.) Heat Transfer Rates Irradiation: Special case of surface exposed to large surroundings of uniform temperature, Tsur G Gsur  Tsur4 If   , (gray surface) the net radiation heat fl ux from the surface due to exchange with the surroundings is:   Eb Ts    G  Ts4  Tsur4  qrad (1.7) 13 Heat Transfer Rates: Radiation (cont.) Heat Transfer Rates Alternatively,  hr Ts  Tsur  qrad (1.8) hr : Radiation heat transfer coefficient W/m 2 K  hr  Ts  Tsur Ts2  Tsur2  (1.9) For combined convection and radiation, q qconv  h Ts  T   hr Ts  Tsur    qrad (1.10) Read Example 1.2 p 10 in your book 14 Example: An uninsulated steam pipe passes through a room in which the air and walls are at 25oC. The outside diameter of the pipe is 70 mm and its surface temperature and emissivity are 200oC and 0.8. What are the surface emissive power and irradiation? If the coefficient associated with free convection heat transfer from the surface to the air is 15 W/m2.K, what is the rate of heat loss from the surface per unit length of pipe? 15 16 Relationship to Thermodynamics Chapter One Section 1.3 17 Alternative Formulations CONSERVATION OF ENERGY (FIRST LAW OF THERMODYNAMICS) First Law is an important tool in heat transfer analysis, often providing the basis for determining the temperature of a system. Alternative Formulations Time Basis: At an instant or Over a time interval Type of System: Control volume Control surface 18 CV at an Instant and over a Time Interval APPLICATION TO A CONTROL VOLUME At an Instant of Time: Note how the system is defined by a control surface (dashed line) at the boundaries. Surface Phenomena Ein E out : , rate of thermal and/or mechanical energy transfer across the control surface due to heat transfer, fluid flow and/or work interactions. Volumetric Phenomena E g : rate of thermal energy generation due to conversion from another energy form (e.g., electrical, nuclear, or chemical); energy conversion process occurs within the system. E st : rate of change of energy storage in the system. Conservation of Energy dE E  E  E  st E (1.12c) in out g dt st Each term has units of J/s or W. Over a Time Interval Ein  Eout  Eg Est (1.12b) Each term has units of J. 19 Closed System Special Cases (Linkages to Thermodynamics) (i) Transient Process for a Closed System of Mass (M) Assuming Heat Transfer to the System (Inflow) and Work Done by the System (Outflow). Over a time interval Q  W Esttot (1.12a) For negligible changes in potential or kinetic energy Q  W U t Internal thermal energy At an instant  dU t q W  dt Do Example 1.3 p 17 in your book. 20 Open System (ii) Steady State for Flow through an Open System without Phase Change or Generation: q (ut, pv, V)out (ut, pv, V)in W At an Instant of 2 2   m  ut  pv  V Time:  gz   q  m  ut  pv  V  gz   W 0 (1.12d)  2  in 2   out  pv  flow work ut  pv  i enthalpy For an ideal gas with constant specific heat: iin  iout c p Tin  Tout  For an incompressible liquid: uin  uout c Tin  Tout   pv in   pv out 0 For systems with significant heat transfer:     V 2 2 in  V 2 2 out 0  gz in   gz out 0 21 Example: The blades of a wind turbine turn a large shaft at relatively low speed. The rotational speed is increased by a gear box with an efficiency of 0.93. The gearbox shaft output drives an electric generator with efficiency 0.95. The cylindrical nacelle has a length of 6 m and diameter 3 m. If the turbine produces 2.5 MW of electrical power and the air and surroundings are at 25 deg. C and 20 deg. C: Determine the minimum operating temperature inside the nacelle The emissivity of the nacelle is =0.83, the convective heat transfer coefficient is h=35 W/m2.K. The surface of the nacelle that is adjacent to the blade hub can be considered adiabatic and solar irradiation may be neglected. 22 23 24 Surface Energy Balance THE SURFACE ENERGY BALANCE A special case for which no volume or mass is encompassed by the control surface. Conservation of Energy (Instant in Time): Ein  Eout 0 (1.13) Applies for steady-state and transient conditions. With no mass and volume, energy storage and generation are not pertinent to the energy balance, even if they occur in the medium bounded by the surface. Consider surface of wall with heat transfer by conduction, convection and radiation.   qconv qcond  0   qrad T1  T2 k L    h T2  T    2 T24  Tsur 4 0 25 Example: Humans are able to control their heat production and heat loss to maintain their temperature constant at 37 C under a wide range of environmental situations. From the perspective of calculating heat transfer between the human body and its surroundings, we focus on a layer of skin and fat with its outer surface exposed to the environment and its inner surface to T = 35 deg C. Consider a person with a skin fat/layer thickness of L= 3mm and effective thermal conductivity k = 0.3 W/m.K. The area of the person is A = 1.8 m2 and is wearing a bathing suit. The emissivity of the skin is = 0.95. 1.When the person is in still air at T = 297 K, what is the skin temperature and rate of heat loss to the environment? Free convection coefficient on the air side is h = 2 W/m2.K 2.When the person is in water T = 297 K, what is the skin temperature and rate of heat loss to the water? Free convection coefficient on the water side is h = 200 W/m2.K 26 27 Methodology METHODOLOGY OF FIRST LAW ANALYSIS On a schematic of the system, represent the control surface by dashed line(s). Choose the appropriate time basis. Identify relevant energy transport, generation and/or storage terms by labeled arrows on the schematic. Write the governing form of the Conservation of Energy requirement. Substitute appropriate expressions for terms of the energy equation. Solve for the unknown quantity. 28 Summary of Heat Transfer Processes Conduction  Diffusion of energy due to qW / m 2   k T k (W/m.K) random molecular motion Convection Diffusion of energy due to random molecular motion + q h Ts  T  h (W/m2.K) energy transfer due to fluid motion (Advection) Radiation q W  hr A Ts  Tsur  or Energy transfer by , hr (W/m2.K) electromagnetic waves qrad W / m 2   Ts4  Tsur4  29  Typical values of heat transfer coefficient Modes h(W/m2.K) Free or natural convection Gases 2-25 Liquids 50-1000 Forced Convection Gases 25-250 Liquids 100-20,000 Convection with phase change 2500-100,000 30