Chapter 1 Introduction to Heat Transfer Islamic Azad University Karaj Branch Dr. M. Khosravy 1 Introduction Thermodynamics: Energy can be transferred between a system and its surroundgs. A system teracts with its surroundgs by exchangg work and heat Deals with equilibrium states Does not give formation ab: Rates at which energy is transferred Mechanisms through with energy is transferred In this chapter we will learn! What is heat transfer! How is heat transferred! Relevance and importance Dr. M. Khosravy
Defitions Heat transfer is thermal energy transfer that is duced by a temperature difference (or gradient) Modes of heat transfer Conduction heat transfer: Occurs when a temperature gradient exists through a solid or a stationary fluid (liquid or gas). Convection heat transfer: Occurs with a movg fluid, or between a solid surface and a movg fluid, when they are at different temperatures Thermal radiation: Heat transfer between two surfaces (that are not contact), often the absence of an terveng medium. Dr. M. Khosravy 3 Example: Design of a contaer A closed contaer filled with hot coffee is a room whose air and walls are at a fixed temperature. Identify all heat transfer processes that contribute to coolg of the coffee. Comment on features that would contribute to a superior contaer design. Dr. M. Khosravy 4
1. Conduction Transfer of energy from the more energetic to less energetic particles of a substance by collisions between atoms and/or molecules.! Atomic and molecular activity random molecular motion (diffusion) T 1 T 1 >T x o q x x T T Dr. M. Khosravy 5 1. Conduction Consider a brick wall, of thickness L=0.3 m which a cold wter day is exposed to a constant side temperature, T 1 =0 C and a constant side temperature, T =-0 C.! Under steady-state conditions the temperature varies learly as a function of x. Wall Area, A! The rate of conductive heat T 1 =0 C q x transfer the x-direction depends on T T = -0 C x L=0.3 m T1! T L q x Dr. M. Khosravy 6
1. Conduction The proportionality constant is a transport property, known as thermal conductivity k (units W/m.K) T1 T! T q x = k = k L L For the brick wall, k=0.7 W/m.K (assumed constant), therefore q x = 96 W/m? How would this value change if stead of the brick wall we had a piece of polyurethane sulatg foam of the same dimensions? (k=0.06 W/m.K)! q x is the heat flux (units W/m or (J/s)/m ), which is the heat transfer rate the x-direction per unit area perpendicular to the direction of transfer.! The heat rate, q x (units W=J/s) through a plane wall of area A is the product of the flux and the area: q x = q x. A Dr. M. Khosravy 7 1. Conduction In the general case the rate of heat transfer the x-direction is expressed terms of the Fourier law: q x =!k dt dx T 1 (high) q x Mus sign because heat flows from high to low T! For a lear profile dt dx ( T = ( x! T1 )! x ) < 1 0 x 1 x x T (low) Dr. M. Khosravy 8
. Convection Energy transfer by random molecular motion (as conduction) plus bulk (macroscopic) motion of the fluid. Convection: transport by random motion of molecules and by bulk motion of fluid. Advection: transport due solely to bulk fluid motion.! Forced convection: Caused by external means! Natural (free) convection: flow duced by buoyancy forces, arisg from density differences arisg from temperature variations the fluid The above cases volve sensible heat (ternal energy) of the fluid! Latent heat exchange is associated with phase changes boilg and condensation. Dr. M. Khosravy 9. Convection Air at 0 C blows over a hot plate, which is mataed at a temperature T s =300 C and has dimensions 0x40 cm. Air q T!! = 0 C T! S = 300 C The convective heat flux is proportional to q x # T T S! Dr. M. Khosravy 10
. Convection The proportionality constant is the convection heat transfer coefficient, h (W/m.K) q x = h( T T S! ) Newton s law of Coolg For air h=5 W/m.K, therefore the heat flux is q x = 7,000 W/m? How would this value change if stead of blowg air we had still air (h=5 W/m.K) or flowg water (h=50 W/m.K) The heat rate, is q x = q x. A = q x. (0. x 0.4) = 560 W. The heat transfer coefficient depends on surface geometry, nature of the fluid motion, as well as fluid properties. For typical ranges of values, see Table 1.1 textbook. In this solution we assumed that heat flux is positive when heat is transferred from the surface to the fluid Dr. M. Khosravy 11 3. Radiation Thermal radiation is energy emitted by matter Energy is transported by electromagnetic waves (or photons). Can occur from solid surfaces, liquids and gases. Dos not require presence of a medium Surroundgs at T sur q cident = G Surface at T s q emitted = E! Emissive power E is the rate at which energy is released per unit area (W/ m ) (radiation emitted from the surface)! Irradiation G is the rate of cident radiation per unit area (W/m ) of the surface (radiation absorbed by the surface), origatg from its surroundgs Dr. M. Khosravy 1
3. Radiation For an ideal radiator, or blackbody: q = E =! T emitted b 4 s Stefan-Boltzmann law where T s is the absolute temperature of the surface (K) and is the Stefan- Boltzmann constant, ( = 5.67x10-8 W/m.K 4 ) For a real (non-ideal) surface: 4 emitted E = T s q =! is the emissivity 0!! 1 The irradiation G, origatg from the surroundgs is: 4 cident = G = T sur q! is the absorptivity For a grey surface, = 0! a! 1 Dr. M. Khosravy 13 3. Radiation Assumg =, the net radiation heat transfer from the surface, per unit area is rad 4 s q = #( T! T The net radiation heat exchange can be also expressed the form: 4 sur ) q = h A T! rad r ( s Tsur) where s h =!( T + T )( T + T r s sur sur ) Dr. M. Khosravy 14
Summary: Heat Transfer Processes Identify the heat transfer processes that determe the temperature of an asphalt pavement on a summer day Dr. M. Khosravy 15 Summary: Heat Transfer Processes Identify the heat transfer processes that occur on your forearm, when you are wearg a short-sleeved shirt, while you are sittg a room. Suppose you mata the thermostat of your home at 15 C through the wter months. You are able to tolerate this if the side air temperature exceedes 10 C, but feel cold if the temperature becomes lower. Are you imagg thgs? Dr. M. Khosravy 16
Example 1 Satellites and spacecrafts are exposed to extremely high radiant energy from the sun. Propose a method to dissipate the heat, so that the surface temperature of a spacecraft orbit can be mataed to 300 K. Given =0.4, =0.7, q solar = 1000 W, T s =300K, T space =0 K, = 5.67x10-8 W/m.K 4 Dr. M. Khosravy 17 Example (1. Textbook) An unsulated steam pipe passes through a room which the air and the walls are at 5 C. The side diameter of the pipe is 70 mm, and its surface temperature and emissivity are 00 C and 0.8 respectively. What are the surface emissive power (E), and irradiation (G)? If the coefficient associated with free convection heat transfer from the surface to the air is h=15 W/m.K, what is the rate of heat loss from the surface per unit length of pipe, q? Dr. M. Khosravy 18
Remder: The General Balance Equation Accumulation = Creation Destruction + Flow Flow Rate Equation Rate of Rate of Rate of Rate of Rate of Accumulation = Creation Destruction + Flow Flow Applicable to any extensive property: mass, energy, entropy, momentum, electric charge Dr. M. Khosravy 19 Remder: System and Control Volume A system is defed as an arbitrary volume of a substance across whose boundaries no mass is exchanged. The system may experience change its momentum or energy but there is no transfer of mass between the system and its surroundgs. The system is closed. A control volume is an arbitrary volume across whose boundaries mass, momentum and energy are transferred. The control volume may be stationary or motion. Mass can be exchanged across its boundaries. Useful fluid mechanics, heat and mass transfer Dr. M. Khosravy 0
Remder: Approaches for Analysis of Flow In analyzg fluid motion we may take two paths: 1. Workg with a fite region (=the control volume), makg a balance of flow versus flow and determg flow effects such as forces, or total energy exchange. This is the control volume method. This approach is also called macroscopic or tegral method of analysis.. Analysg the detailed flow pattern at every pot (x,y,z) the field. This is the differential analysis, sometimes also called microscopic. Dr. M. Khosravy 1 Conservation of Energy Surroundgs, S Control Volume (CV) Boundary, B (Control Surface, CS) Addition through let E! -Accumulation (Storage) -Generation E! st E! g Loss through let E! Energy conservation on a rate basis: Units W=J/s de dt st E! + E! g! E! = = E! st (1.1)! Inflow and flow are surface phenomena! Generation and accumulation are volumetric phenomena Dr. M. Khosravy
The Energy Balance Dr. M. Khosravy 3 The Energy Balance & V # u g z m! + q + W! $ + +! %! Rate of Energy Flow to CV: t & V # u g z m! + q + W! $ + +! %! Rate of Energy Flow of CV: t! Rate of Energy Accumulation: d dt &, $ m * u % + t V )# + + g z '! ( CV u t :ternal energy, V: velocity, z: potential energy, q: heat rate, W: work Dr. M. Khosravy 4
The Energy Balance! Substitutg equation (1.1) and assumg steady-state conditions: &, $ * u $ % + t &, $ * u $ % + t V + V + + g + g ) z ' ( ) z ' ( m! m! + q + q + W! #! -! + W! #!! = 0 q Convention net, = net, q! q W! = W!! W! q is positive when transferred from surroundgs to system. W is positive when transferred from system to surroundgs Dr. M. Khosravy 5 The Energy Balance For steady-state conditions the energy balance reduces to: ' % u & t V $ # ' % & V + + + g z m!! % + ut g z m! + q! W! net, $ # = 0 (1.) The work term is divided two contributions: Flow work, associated to pressure forces (=p, where is the specific volume) and (shaft) work done by the system. The net work is: Injection Work W!! [(P!!! net, = Wshaft +!) m] [( P ) m] Dr. M. Khosravy 6
Steady-Flow Energy Equation ' V m! % u + p( + & + q! W! = 0 Recall: shaft Enthalpy per unit mass: + g $ z # i = ut + p! '! m! % u & V + p( + m! =! VA Mass flow rate (kg/s) c m!! = VAc =! Volumetric flow rate (m 3 /s) + g $ z # + Units of [J/s] and i! i ) = c ( T! T ) ( p Dr. M. Khosravy 7 Simplified steady-flow energy equation For steady state conditions, no changes ketic or potential energy, no thermal energy generation, neglible pressure drop: q = mc! ( T! T ) p Dr. M. Khosravy 8
Example (Problem 1.36 textbook) In an orbitg space station, an electronic package is housed a compartment havg a surface area A s =1 m, which is exposed to space. Under normal operatg conditions, the electronics dissipate 1kW, all of which must be transferred from the exposed surface to space. (a) If the surface emissivity is 1.0 and the surface is not exposed to the sun, what is its steady-state temperature? (b) If the surface is exposed to a solar flux of 750 W/m and its absorptivity to solar radiation is 0.5, what is its steady-state temperature? Dr. M. Khosravy 9 Surface Energy Balance For a control surface: T 1 q cond q rad E!! E! or = 0 q conv q cond! q conv! q rad = 0 T T x T! Dr. M. Khosravy 30
Example (Problem 1.55 textbook) The roof of a car a parkg lot absorbs a solar radiant flux of 800 W/m, while the underside is perfectly sulated. The convection coefficient between the roof and the ambient air is 1 W/m.K. a) Neglectg radiation exchange with the surroundgs, calculate the temperature of the roof under steady-state conditions, if the ambient air temperature is 0 C. b) For the same ambient air temperature, calculate the temperature of the roof it its surface emissivity is 0.8 Dr. M. Khosravy 31 Chapter 1: Summary Modes of Heat Transfer: Conduction Convection Radiation dt q x =!k 4 4 qx = h( TS T! ) q rad = #( Ts! Tsur) dx q x (W/m ) is the heat flux q x (W=J/s) is the heat rate q = h A T! rad r ( s Tsur) Energy Balances written on a rate basis (J/s):! Conservation of Energy for a Control Volume! Surface Energy Balance (does not consider volumetric phenomena) Dr. M. Khosravy 3