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## 311 Heat Transfer

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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.tr

Ege 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)

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

Heat: thermal energy in transit due to temperature difference

Science that deals with the determination of the rates of such energy transfer is Heat transfer

Why is heat transfer important?

Thermodynamics deals with;

- The amountof energyrequiredtochange a systemfromoneequilibriumstatetoanother
- endstates of the process (equilibriumstates)

Thermodynamics can’t tell how long the process will take

Heat Tranfer deals with;

- 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.

Ex)

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

Thermodynamics tells us the loss in energy

(mass)x(specific heat)x(temp change)

(1kg) x (-450J7kgK) x (900K) = 405kJ

Heat Transfer

How long we need to wait for the temperature to drop to 100oC?

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

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

Sizing

Heat transfer process can be studied either

Experimentally

(testing and taking measurements)

Analytically

(by analysis and calculation)

or

Accuracy of the assumptions and idealizations made in the analysis

Measurements, and limits of experimental errors

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

Internal Energy (U)

Nuclearcomponent

Bonds within the nucleus of atom

Chemicalcomponent

Sensiblecomponent

Latentcomponent

Chemical bonds between atoms

Released or absorbed during chemical or nuclear reaction

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

Internal energy is higher in gas phase than in solid/liquid phase

In the analysis of systems that involve fluid flow, we deal with u and Pv,

h= u+ Pv

Flow energy (flow work)

enthalpy

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

(Ability to store thermal energy)

Cp : Specific heat at constant pressure

For an ideal gas: Cp = Cv + R

Cv : Specific heat at constant volume

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

Differential changes in the internal energy, u, and enthalpy, h , of an ideal gas ;

du = CvdT

dh = CpdT

Finite changes in the internal energy, u, and enthalpy, h , of an ideal gas ;

∆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

Change in internal energy for solids and liquids,

Cp=Cv=C

∆U = mCave∆T

Cp and Cv values are constant for incompressible substances

Heat: form of energy that can be transferred from one system to another as a result of temperature difference

Transfer of a thermal energy heat transfer

Amount of heat transfer during a process

Q :

Amount of heat transfer per unit time

Heat transfer rate

q :

Follow the board

Conduction

Convection

Radiation

Heat can be transferred in three different modes:

Conduction:

Transfer of energy from more energetic particles to less energetic particles due to interaction between particles

Gas and liquids; due to collision and diffusion of molecules

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

-Related to atomic or molecular motion in matter

-No bulk motion

-Energy tranfer from high energy molecules to low energy molecules

The mechanism of heat conduction in different phases of substance

Follow the board

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

Introduction to Conduction

At point A: Temperature 50oC

heat flux 80 W/m2

Heat conduction is toward inside (heat gain)?

Heat conduction is toward the outside (heat loss)?

In order to specify the location of that point we need to choose a suitable coordinate system depending on the geometry

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

A

B

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

no change with time

variation with time or time dependence

Steady:

Transient(unsteady):

Temperature or heat flux remains unchanged with time

Cooling of an apple in a refrigerator?

Temperature at any fixed point within the apple will change during cooling

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

Heatdiffusionequation

Heatdiffusionequation

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