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311 Heat Transfer Ege University Fall 2012

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Instructor: Dr. Lutfiye Altay, e-mail: lutfiye.altay@ege.edu.tr, office: 301lutfiye.altay@ege.edu.tr Schedule: : Lectures: Wednesday: 8:30 -10:15 (room:204), Thursday, 8:30 -10:15 (room:204) Textbook: Fundamentals of Heat and Mass Transfer, F.P. Incropera, D.P. DeWitt, T. L. Bergmann and A. S. Lavine, 6 th ed., Wiley www.pandora.com.tr Ege University library

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Introduction: Conservation of energy, modes of heat transfer (Chp. 1) Conduction: Rate equation, boundary and initial conditions, thermal properties (Chp.2) 1-D Steady State Conduction: Plane wall, cylinder and sphere, composite walls, equivalent circuits, conduction with heat generation, extended surfaces (Chp. 3) 2-D Steady-State Conduction: Graphical and numerical approaches (Chp.4) Transient Conduction: Lumped capacitance and spatial effects (Chp. 5) Convection Fundamentals: Velocity, thermal and concentration boundary layers, dimensionless numbers (Chp. 6) External Flows: Flat plate, cylinder, sphere (Chp. 7) Syllabus

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What is heat transfer ?Why is it important? Energy can exist in various forms such as thermal, mechanical, kinetic, potential, electrical, magnetic, chemical and nuclear. In thermodynamics you learned that energy can be transferred by work and heat Hot coffee will cool down by the transfer of energy from warm medium to the cold one This energy transfer is always from higher temperature to lower temperature and the energy transfer stops when two mediums reach the same temperature Heat: form of energy that can be transferred from one system to another as a result of temperature difference

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Thermodynamics deals with; The amount of energy required to change a system from one equilibrium state to another end states of the process (equilibrium states) Heat: thermal energy in transit due to temperature difference Again, Heat Tranfer deals with; Thermodynamics cant tell how long the process will take Science that deals with the determination of the rates of such energy transfer is Heat transfer Why is heat transfer important? the rates of energy transfer (times of cooling or heating) the variation of the temperature

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You can determine the amount of heat transferred from a thermos bottle while coffee cools from 90 o C to 60 o C by a thermodynamic analysis alone. But, if you are interested in how long it will take for coffee to cool down to 60 o C, a thermodynamic analysis can not answer this question. When 1 kg of iron quenched from 1000 o C to 100 o C in an oil bathEx) Thermodynamics tells us the loss in energy (mass)x(specific heat)x(temp change) (1kg) x (-450J7kgK) x (900K) = 405kJ How long we need to wait for the temperature to drop to 100 o C? Heat Transfer

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Heating and air conditioning systems,refrigerator, freezer, water heater, iron, computer, TV, car radiators, solar collectors, power plants, spacecrafts, heat exchangers, boilers,furnaces, optimum insulation thicknesses in the walls and roofs,on steam pipes and many more systems are designed on the basis of a heat transfer analysis.

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Heat transfer problems encountered in practise can be divided into two groups Sizing Rating Determination of the heat transfer rate for an existing system at a specified temperature difference Determination of the size of a system in order to transfer heat at a specified rate for a specified temperature difference Heat transfer process can be studied either Experimentally (testing and taking measurements) Analytically (by analysis and calculation) or Measurements, and limits of experimental errors Accuracy of the assumptions and idealizations made in the analysis Good results are reached by reducing the choices to a few by analysis and then verifying the findings experimentally Ex) Heating system of a building? Size should be determined before building is built on the basis of dimensions and specifications given

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Internal Energy (U): related to molecular structure of a system and degree of the molecular activity, microscopic energy. Sum of all microscobic forms of energy is called internal energy Sensible component Latent component Internal Energy (U) Total Energy E Translational, vibrational and/or rotational motion of the atoms/molecules (kinetic energy of the molecules) Intermoleculer forces (that binds molecules to each others) influencing phase change between solid,liquid and vapor states Strongest in solids weakest in gases. If sufficient energy is added binding bonds gets weaker : phase change Velocity and degree of activity of molecules are proportional to temperature. Higher T molecules will have higher kinetic energy,thus system will have higher internal energy Chemical component Nuclear component Chemical bonds between atoms Bonds within the nucleus of atom Internal energy is higher in gas phase than in solid/liquid phase Released or absorbed during chemical or nuclear reaction

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h= u+ Pv enthalpy Flow energy (flow work) In the analysis of systems that involve fluid flow, we deal with u and Pv, Internal energy u represents the microskobic energy of a nonflowing fluid. enthalpy, h, represents the microscobic energy of flowing fluid. Ideal gasPv = RT or P = ρRT At low pressures and high temperatures density of a gas decreases, gas behave like an ideal gas Air, nitrogen,oxygen,hydrogen, helium, argon, neon, krypton,carbon dioxide can be treated as ideal Dense gases such as water vapor, refrigerator vapor should not always be treated as ideal gases

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Specific heat: energy required to raise the temperature of a unit mass of a substance by one degree C p : Specific heat at constant pressure C v : Specific heat at constant volume For an ideal gas: C p = C v + R Specific heats in general depends on temperature and pressure, however for ideal gases they depend on temperature only (At low pressures all real gases aproach ideal gases) Specific heat of air changes with temperature (Ability to store thermal energy)

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Differential changes in the internal energy, u, and enthalpy, h, of an ideal gas ; Finite changes in the internal energy, u, and enthalpy, h, of an ideal gas ; du = C v dTdh = C p dT u = C v,ave T h = C p,ave T or, U = mC v,ave T H = mC p,ave T m=mass of the system Incompressible substance= whose specific volume (or density) does not change with temperature and pressure C p and C v values are constant for incompressible substances U = mC ave T C p =C v =C Change in internal energy for solids and liquids,

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Transfer of a thermal energy heat transfer Amount of heat transfer during a process Q : Heat: form of energy that can be transferred from one system to another as a result of temperature difference Heat transfer rateAmount of heat transfer per unit time q : Follow the board

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How is heat transferred? Conduction Convection Radiation Heat can be transferred in three different modes: The mechanism of heat conduction in different phases of substance Conduction: Transfer of energy from more energetic particles to less energetic particles due to interaction between particles -Related to atomic or molecular motion in matter -No bulk motion -Energy tranfer from high energy molecules to low energy molecules Gas and liquids; due to collision and diffusion of molecules Solids; vibrations of the molecules and energy transport by free electrons Follow the board

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Introduction to Conduction Heat conduction is toward inside (heat gain)? Heat conduction is toward the outside (heat loss)? At point A: Temperature 50 o C heat flux 80 W/m 2 Heat transfer has direction as well as magnitude and therefore it is a vector quantity A positive quantity indicates heat transfer in the positive direction and negative quantity indicates heat transfer in the negative direction

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Driving force for any kind of heat transfer is the temperature difference. Larger the temperature difference larger the rate of heat transfer In many engineering problems we need to calculate temperature distribution (variation of T) throughout the medium so that we can calculate local heat transfer at any point In order to specify the location of that point we need to choose a suitable coordinate system depending on the geometry A B C

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Rectangular coordinates (x, y, z) Cylindrical coordinates (r, Φ, z) Spherical coordinates (r, Φ, θ) Then temperature at a point (x, y, z) at time t in rectangular coordinates can be expressed as T (x,y,z,t) temperature changes with respect to x, y,z directions as well as time T (x) temperature changes in the x direction only, no variation with time

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Heat transfer problems no change with time variation with time or time dependence Steady: Transient(unsteady): Cooling of an apple in a refrigerator? Temperature or heat flux remains unchanged with time Temperature at any fixed point within the apple will change during cooling

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Heat Transfer Problems One dimensional, two dimensional, three dimensional Two dimensional heat transfer in a long rectangular bar Heat transfer through the window of a house can be taken as one dimensional

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Rectangular Coordinates Heat diffusion equation x y z

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Cylindrical Coordinates Heat diffusion equation

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Spherical Coordinates Heat diffusion equation

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How to solve an engineering problem

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