4 - 2 introduction to heat transfer and heat conduction eq

7/18/2019 4 - 2 Introduction to Heat Transfer and Heat Conduction Eq

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HEAT TRANSFER

OPERATIONS

Introduction to Heat Transfer

Conduction, Convection, Radiation

Dr. Muhammad Rizwan

Assistant Professor

COMSATS



THERMAL CONDUCTIVITY

Thermal conductivity of a material is a measure of the

ability of the material to conduct heat.

By using fourier’s law it can be defined as “the rate of

heat transfer through a unit thickness of the material

per unit area per unit temperature difference”

A simple experimental setup to determine the

thermal conductivity of a material



THERMAL CONDUCTIVITY

Experimental Set up to determine thermal conductivity:

eat a material of known thickness and area from one side by an electric

resistance heater of known output

!ake sure that the outer surfaces of the heater are well insulated" in this way

all the heat generated will be transferred through the material.

At steady state" measure the two surface temperatures of the material.

Figure: A simple experimental setup to determine

the thermal conductivity of a material



THERMAL DIFFUSIVITY:

The product" ρCp,is called the heat capacity of a material

Both tell about the heat storage capability of material

Thermal diffusivity is the property of material which represents how fast

heat diffuses through a material.

#t can be defined as$

The larger the thermal diffusivity" the faster the movement of

heat into the medium



CONVECTION HEAT TRANSFER: When heat energy is transferred from higher temperature region

to lower temp region through the displacement of particles of the

medium it is called convection.

Also" the heat transfer between a solid surface and the ad%acent li&uid or gas

that is in motion called convection.

The faster the fluid motion" the greater the convection heat transfer.

'epending on the displacement mechanism" it is divided into two types$

(ree convection

(orced convection



CONVECTION HEAT TRANSFER: (orced )onvection$ *ome external energy is applied to force the fluid element

to change its position.

(ree )onvection$ The fluid element changes its position due to density

difference which ultimately arises due to the temperature difference.

+ate of convection heat transfer is observed to be proportional to the

temperature difference" and is conveniently expressed by Newtens’s Law of

Cooling.

,here"

h is the convection heat transfer coefficient in ,-m../)

A s is the surface area through which convection heat transfer takes place

T s is the surface temperature

T ∞ is the fluid temp sufficiently far from the surface



CONVECTION HEAT TRANSFER: The value of h depends on all the

variables influencing convection such as

the surface geometry" the nature of fluid

motion" the properties of the fluid" and the

bulk fluid velocity.



RADIATION: Heat transfer caused by electromagnetic waves emitted by a body

due to its temperature.

#t does not re&uire any medium to transfer the heat.

All bodies at a temperature above absolute 0ero emit thermal radiation.

The maximum rate of radiation that can be emitted from a surface at an

absolute temperature Ts 1in 2 or +3 is given by the *tefan4Bolt0man law$

,here"

σ = 5.670373(21)×10−8 W m−2 K−4is the *tefan4Bolt0man constant



HEAT CONDUCTION EQUATION: Heat transfer has magnitude as well as direction.

eat conduction in a medium is three dimensional and time dependent" T =

T(x, y, z, t).

Temperature distribution is important to determine throughout the medium

in order to calculate the local heat transfer rate" thermal expansion and

thermal stresses at some critical location at a specified time.

'epending on the geometry involved" choose suitable coordinates such as

rectangular" cylindrical or spherical coordinates.



HEAT CONDUCTION EQUATION:

The term steady implies no change with

time at any point within the medium.

,hereas the 5nsteady or transient means the

variation with time in the rate of heat transfer.

'uring steady state" although both &uantities

may vary from one location to another.

#t is assumed that the process is steady to solve

heat transfer problems" since steady processes

are easier to analy0e.

Steady Vs Transient Heat Transfer




Heat transfer problems are classified as

one dimensional, two dimensional or

three dimensional.

6ractically" temperature varies along all three

direction within the medium during heat

transfer process.

eat transfer through the glass of a window

can be considered to be one4dimensional.

eat transfer through a hot water pipe occurs

predominantly in the radial direction from the

hot water to the ambient" and heat transfer

along the pipe and along the circumference of

a cross section is typically negligible.

Multidimensional Heat transfer:




A medium through which heat is conducted may involve the

conversion of electrical, nuclear, or chemical energyinto heat

energy.

#n heat conduction analysis" such conversion processes are characteri0ed as

heat generation.

(or example" the temperature of a wire rises rapidly when electric current

passes through it.

eat generation is a volumetric phenomenon.

The total rate of heat generated in a medium of volume" V " can be determined

from$

7gen 8 egen.V

Heat Generation:



GENERAL HEAT CONDUCTION EQ: Useful to determine the temperature distribution when the

conduction is imposed on a medium

As a result conduction heat flux can be measured at any point in

the medium using Fourier’s Law

Temperature distribution is also useful to ascertain structural

integrity by calculating thermal stresses, expansions and

deflections

Also important to optimize the insulation thickness

Temperature distribution pattern varies with different

configuration (rectangular, cylinder, sphere etc)



GENERAL HEAT CONDUCTION EQ FOR

RECTANGULAR COORDINATED SYSTEM:

Based upon basic energy balance equations

4 - 2 introduction to heat transfer and heat conduction eq

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