311 Heat Transfer

Ege UniversityFall 2012

Instructor: Dr. Lutfiye Altay, e-mail: lutfiye.altay@ege.edu.tr, office: 301 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, 6th ed., Wiley

www.pandora.com.trEge University library

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

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

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 can’t 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

You can determine the amount of heat transferred from a thermos bottle while coffee cools from 90oC to 60oC by a thermodynamic analysis alone.

But, if you are interested in how long it will take for coffee to cool down to 60oC, a thermodynamic analysis can not answer this question.

When 1 kg of iron quenched from 1000oC to 100oC in an oil bath Ex)

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 100oC? Heat Transfer

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.

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

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

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 gas Pv = 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

Specific heat: energy required to raise the temperature of a unit mass of a substance by one degree

Cp : Specific heat at constant pressure

Cv : Specific heat at constant volumeFor an ideal gas: Cp = Cv + 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)

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 = CvdT dh = CpdT

∆u = Cv,ave∆T ∆h = Cp,ave∆T

or,

∆U = mCv,ave∆T ∆H = mCp,ave∆T m=mass of the system

Incompressible substance= whose specific volume (or density) does not change with temperature and pressure

Cp and Cv values are constant for incompressible substances

∆U = mCave∆T

Cp=Cv=C Change in internal energy for solids and liquids,

Transfer of a thermal energy heat transfer

Amount of heat transfer during a processQ :

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

How is heat transferred?Conduction ConvectionRadiation

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 moleculesSolids; vibrations of the molecules and energy transport by free electrons

Follow the board

Introduction to Conduction

Heat conduction is toward inside (heat gain)?

Heat conduction is toward the outside (heat loss)?

At point A: Temperature 50oC heat flux 80 W/m2

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

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

AB

C

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

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

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

Rectangular Coordinates

Heat diffusion equation

x y z

Cylindrical Coordinates

Heat diffusion equation

Spherical Coordinates

Heat diffusion equation

How to solve an engineering problem