Bangladesh University of Engineering and Technology

ME 267: Mechanical Engineering FundamentalsCredit hours: 3.00

Sourav SahaLecturer

Department of Mechanical Engineering,

BUET

1

Email address: ssaha09@me.buet.ac.bd, souravsahame17@gmail.comPersonal websiteMy Google Scholar Page

Lecture 2: Fundamentals

Bangladesh University of Engineering and Technology

2

Why study heat transfer when there is thermodynamics?

Thermodynamics tells us about the quantity of heat transfer from one

equilibrium state to another but it doesn’t give any indication about how

long this transfer process will take. Thermodynamics (equilibrium

thermodynamics) is more concerned with the equilibrium states while

heat transfer actually tells us about the rate of energy transfer. However,

science of heat transfer is based on thermodynamics.

Bangladesh University of Engineering and Technology

3

Some definitions

Internal Energy, U, is defined as the sum of all microscopic forms of energy in a

system. This includes energy due to various levels of microscopic activities.

Specific heat, C, is defined as the heat energy required to increase the temperature of a

unit mass of substance by one degree. Common unit is kJ/kgK.

The sensible heat transfer through any incompressible substance can be modeled as,

U Q m C T

Here ∆Q is the heat transfer. In rate form we may denote this as Q̇

Bangladesh University of Engineering and Technology

4

Definition of Heat Transfer

Energy can be transferred from and to a given mass by two mechanisms: heat

transfer and work transfer. When the transfer of energy from one system to

another or from one substance to another is solely due to the temperature

difference the energy interaction is called heat transfer.

The rate of heat transfer per unit area normal to the direction of heat transfer is

called the heat flux, q. Unit is J/m2

Qq

A

Bangladesh University of Engineering and Technology

5

Heat Transfer Mechanisms

There are three modes of heat transfer from hot region to cold region:

A) Conduction

B) Convection

C) Radiation.

Bangladesh University of Engineering and Technology

6

Conduction

Conduction is the transfer of thermal energy from the more energetic particles of asubstance to the adjacent less energetic ones as a result of interactions betweenparticles. Conduction can take place in solid, liquids, gases and even in plasmas.

When the dimension ∆x tends to zero,

Thermal conductivity

This simple law is known asthe Fouriers’s Law of heatconduction.

Bangladesh University of Engineering and Technology

7

Conduction

Thermal Conductivity, k, is defined as the rate of heat transfer through a

unit thickness of the material per unit area per unit temperature difference.

This is the measure of a material’s ability to transfer heat. Unit of thermal

conductivity is W/mK.

Crystalline solids have a high value of k.

Thermal conductivity of gases and insulating materials ismuch less than that of metals. Why?

Bangladesh University of Engineering and Technology

8

Mechanism of Conduction

From the definition of conduction we know this method is nothing but the transfer of energy

from energetic molecules to non-energetic ones through vibration. This is the basic mechanism.

So the phase of substance which facilitates this transfer process must possess higher thermal conductivity.

Bangladesh University of Engineering and Technology

9

Mechanism of Conduction

In gaseous substances, molecules move randomly and collide with each other in the process.

These molecules are far from each other and hence the only way to transfer energy is collide and

change momentum much like two tennis balls do when they collide with each other. This makes

the thermal transport weaker in gases.

However, from kinetic theory of gas we know,

21 3

2 2B

m v k T

So we see velocity is proportional to the square root ofthermodynamic (absolute) temperature T. Guess what elseis proportional to square root of T??

Thermal conductivity of gases!

In a similar manner we can see that k of gases is inversely proportional to the square root of their molar mass, M.

Bangladesh University of Engineering and Technology

10

Mechanism of Conduction

In liquids, the molecules are more closely spaced compare to gases. But the distance between

those is still larger than that of solids. So, thermal conductivity lies somewhere between gases

and solids.

Unlike gases, thermal conductivity of liquids decreases with increase in temperature (waterbeing an exception).

This behavior of liquids can be explained by Bridgman’s equation

2

3

2 .8 .B s

Nk k v

V

Here, V is the molar volume which is proportional to thetemperature and key factor governing the thermal conductivityof fluids.

Thermal conductivity of fluids is also inversely proportional to the molar mass. This isinformation can be derived from the Bridgman’s equation too.

Fig. 1. Case of water

Bangladesh University of Engineering and Technology

11

Mechanism of Conduction

Conductivity of the solid substances is the highest. Thermal conduction in solids can be

attributed to two mechanisms:

1) Lattice Vibration.

2) Transport of free electron.

Lattice vibrational waves carry the energy from one part of the substance to another in

solid. Metals typically have a relatively high concentration of free conduction

electrons, and these can transfer heat as they move through the lattice. Phonon-based

conduction also occurs, but the effect is swamped by that of electronic conduction.

Bangladesh University of Engineering and Technology

12

Mechanism of Conduction

Thermal conductivity of solids is obtained by adding the lattice vibration and electronic transport

components. This is why metals (which have plenty of electrons) are good conductors of heat.

Lattice vibrational component of the thermal conductivity depends on how ordered the lattice is.

This is why diamond has the highest known thermal conductivity. There are some crystalline

solids like diamond and semiconductors like silicon which have high thermal conductivity but

relatively poor electrical conductivity. These materials are very popular in electronics industry.

Some recent materials are reported to have very high thermal conductivity. For example,experiments found graphene has thermal conductivity in the order of 2500 W/mK. Single wallCarbon nanotubes also have thermal conductivities around 2000 W/mK. [Thermal properties ofgraphene and nanostructured carbon materials, Alexander A. Balandin,Nature Materials 10,569–581 (2011)]. Coupled with their excellent mechanical attributes these are the materials forfuture. Some other 2D materials like silicene, stanene, germanene, etc are showing greatpotentials.

Bangladesh University of Engineering and Technology

13

Mechanism of Conduction

One would think that alloys, composed of two metals, must have higher thermal conductivities

than both of the parent metals. But actually opposite happens. Alloys are reported to have very

low thermal conductivities. This happens due to disruption of vibrational transport thorough the

lattice of alloys.

Bangladesh University of Engineering and Technology

14

Mechanism of Conduction

Thermal conductivity of solid is also dependent on temperature. Moreover, in anisotropic

materials this property varies spatially.

Temperature dependence of solids

causes considerable complexities in

calculation. This is why throughout this

course we shall assume this to be

constant. For the same reason, all

materials will be assumed isotropic.

Thermal diffusivity is a property frequently used in transient heat conduction and defined as,

.k

c

Bangladesh University of Engineering and Technology

15

Convection

Convection is the mode of heat transfer between a solid surface and adjacent liquid or

gas in motion. It involves combined effect of conduction and liquid motion.

Convection = conduction + advection

Presence of bulk fluid motion is compulsory for convection. Without it, the heat

transfer is just conduction.

Bangladesh University of Engineering and Technology

16

Convection

Convection can be classified in many ways. For the time being, on the basis of

governing mechanism, we shall classify it into natural and forced convection.

Natural convection: When the driving force of fluid motion is the buoyant force arising due totemperature gradient in the fluid the convection mechanism is natural convection.

Forced convection: When bulk fluid motion is created by external means like pump, fan orblower the convection is known as forced convection.

Bangladesh University of Engineering and Technology

17

Convection: Newton’s Law of cooling

THIS GUY AGAIN!!!!!

Sir Isaac Newton took a break fromdiscovering calculus and saving the world tofind a simple and elegant way (as always) tofind heat transfer due to convection

Here,

h is the convective heat transfer coefficient.

As is the surface area over which convection is

taking place.

Ts is the temperature of the heated surface.

and Tα is the convective fluid’s temperature.

The study of convection is centered around finding the value of h for differentcases involving complex geometries, different fluids, different velocities, etc.

( )s s

Q h A T T

&

Bangladesh University of Engineering and Technology

18

Radiation

Radiation is the energy emitted by the matter in the form of electromagnetic waves as aresult of the changes in electronic configurations of the atoms or molecules. Anythingwith a finite temperatures emits some thermal radiation. This mode of heat transferdoesn’t require any medium to transfer heat.

Heat transfer due to radiation is expressed by,

4 4( ) .

s s su r rQ A T T &

Here σ is the Stefan-Boltzman constant = 5.670 × 10-8 W/m2K4.

ε is the emissivity of the surface.

As is the surface area.

Ts is the temperature of the surface.

Tsurr is the surrounding temperature.

Bangladesh University of Engineering and Technology

19

That’s it for today. Some problems on the topic will be covered in next lecture.

EID MUBARAK! Enjoy your vacation.