LECTURE SLIDE 02

IUBAT- International University of Business Agriculture and Technology

Founded 1991 by Md. Alimullah Miyan

COLLEGE OF ENGINEERING AND TECHNOLOGY(CEAT)

Course Title: Heat and Mass Transfer

Course Code : MEC 313

Course Instructor: Engr. Md. Irteza Hossain

Engr. Md. Irteza Hossain, Faculty,

Mechanical Engineering

Heat Transfer

• The transmission of energy from one region to

another as a result of temperature gradient is

called heat transfer.

• There are three ways heat transfer works:

conduction, convection, and radiation.

• Heat flow depends on the temperature

difference.



Thermal Equilibrium

• Two bodies are in

thermal equilibrium

with each other when

they have the same

temperature.

• In nature, heat always

flows from hot to cold

until thermal

equilibrium is reached.



Heat Conduction

• Conduction is the transfer of heat through

materials by the direct contact of matter.

• Dense metals like copper and aluminum

are very good thermal conductors.



Heat Conduction

• A thermal insulator is a material that

conducts heat poorly.

• Heat flows very slowly through the plastic

so that the temperature of your hand does

not rise very much.



Heat Conduction

• Styrofoam gets its

insulating ability by

trapping spaces of air

in bubbles.

• Solids usually are

better heat conductors

than liquids, and

liquids are better

conductors than

gases. Engr. Md. Irteza Hossain, Faculty,


Heat Conduction

• The ability to conduct heat often

depends more on the structure

of a material than on the

material itself.

– Solid glass is a thermal

conductor when it is formed

into a beaker or cup.

– When glass is spun into fine

fibers, the trapped air makes

a thermal insulator.



HEAT TRANSFER BY CONDUCTION

FOURIER’S LAW OF HEAT CONDUCTION:

The rate of flow of heat through a simple

homogeneous solid is directly proportional to the

area of the section at right angles to the direction of

flow, and to change of temperature with respect to

the length of the path of heat

MATHEMETIACLLY :

q ∞ A.

q = - k. A

Baron Jean Baptiste Joseph Fourier (1768 – 1830)



Variables for conduction



HEAT TRANSFER BY CONDUCTION

Assumption :

Conduction of heat under steady state

Unidirectional

Temperature gradient is constant

No internal heat generation

The material is isotropic ( ie k is constant in

all direction)



Some essential features of Fourier’s Law

• It is applicable to all matter ( Solid, Liquid,

Gas)

• Based on experimental evidence can not

derived from first principle

• Vector expression

• Define thermal conductivity K of the medium

through which the heat is conducted.



Thermal Conductivity

• The thermal conductivity of a material

describes how well the material conducts

heat.



Thermal conductivity of Materials

• Fourier Law : q = - k .A.

• k= (q/A).

if we substitute

A= 1 m2 , = 1 oK, = 1m

> k= q

.



Thermal conductivity of Materials

Thermal Conductivity (K) :

The rate of Heat conducted through a body of

unit area and unit thickness when the temp

difference between the faces causing the heat

flow is unit temperature difference.

• Thermal Conductivity (K) :

( W/m oC)



Some Important features of

Thermal Conductivity • The thermal conductivity of a material is due to flow free electrons in

case of metal

• Thermal conductivity in case of pure metals is the highest(k= 10 to

400 W/m oC)

> Decreasing with increasing of purity

> Alloys k= 12 to 120 W/m0c

> Liquid k=0.2 to 0.5 W/m0c

> Gas k= 0.006 to 0.05 W/m0c

• Thermal conductivity of a metal varies considerably when it is heat

treated or mechanically processed

• Thermal conductivity of most metals decreases with increase in

temperature ( except AL and Uranium)

> due to decrease of density with increase of temperature



Some Important features of

Thermal Conductivity • Thermal conductivity ( a property of material)

depends essentially upon the following factors:

> Material structure

> Moisture content

> Density of the material

> Pressure and temperature ( operating

condition)



Thermal conductivity



Thermal Conductivity



Thermal Resistance (Rth)

• Heat transfer process is compared by analogy with

flow of electricity in an electrical resistance Ohm’ s Law : Flow of Electric current in the electric resistance is directly

proportional to the potential difference ( dV)

Fourier’s law of heat conduction: Heat flow rate (q) is directly propotional to

the temperature difference ( )

Current ( I ) :

By Analogy :

Heat flow rate (q) :



Thermal Resistance (Rth)

• Thermal Conduction Resistance :

( Rth) Cond=

Unit of ( Rth) Cond= oC/W

• The reciprocal of thermal resistance is called

thermal conductance

• Rules of combining electrical resistance in series

and parallel is equally apply for thermal resistance



CONDUCTION THROUGH PLANE WALLS IN SERIES



CONDUCTION THROUGH PLANE WALLS IN SERIES

CC

C

B

B

A

A

K

L

BK

L

AK

L

ttq

...

41

CthAth RRR

ttq

Bth

41



The heat flow rate for a composite wall

having n slabs/layers

n

n

kA

L

ttq

1

)1(1



CONDUCTION THROUGH PLANE WALLS IN PARALLEL



COMPLEX COMPOSITE WALL

ISOMETRIC VIEW THERMAL CIRCUIT



COMPLEX COMPOSITE WALL

• In order to solve more complex problems

involving both series and parallel thermal

resistances, the electrical analogy may be

used

eqiuvalentth

overall

R

tq

)(



PROBLEM & SOLUTION

SESSION Example (1.1): Rajput:

Calculate the rate of heat transfer per unit area through a copper

plate having 45 mm thick, whose one face is maintained at 350 oC

and other face is at 50 oC . Take the thermal conductivity of copper

as 370 W/moC

Example ( 1.2): Rajput

A Plane wall is 150 mm thick and its wall area is 4.5 m2. If its

conductivity is 9.35 W/moC and surface temperatures are steady at

150oC and 45 oC

Calculate : (i) Heat flow rate across the plane wall

(ii) Temperature gradient

(iii) Thermal resistance

\



PROBLEM & SOLUTION SESSION

Example 2.4 ( Rajput)A reactor’s wall 320 mm thick, is made up of an inner

layer of fire brick ( k= 0.84 w/m2 oC).The reactor

operates at a temperature of 1325oC and the ambient

temperature is 25 oC.

Determine:

1. The thickness of fire brick and insulation which

gives

minimum heat loss

2. Calculate the heat loss presuming that the insulating

material has a maximum temperature of 1200 oC

Example 2.16 ( Rajput)

Find the flow rate through the composite wall as shown

in the figure. Assume one dimensional flow:

kA = 150 w/m0c, kB= 30 w/m0c, kC = 65 w/m0c,

kD = 50 w/m0c,



PROBLEM AND SOLUTION



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LECTURE SLIDE 02

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