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Modes of Heat Transfer

- P M V Subbarao
- Professor
- Mechanical Engineering Department

Accounting of Natural Happenings ..

Radiation from a Thermodynamic System

Spectral integration of Planks distribution law

estimates the total energy emitted by a real

system as

- where esys is the emissivity of the system,
- Asys-surface is the surface area,
- Tsys is the temperature, and
- s is the Stefan-Boltzmann constant, equal to

5.6710-8 W/m2K4. - Emissivity is a material property, ranging from 0

to 1, which measures how much energy a surface

can emit with respect to an ideal emitter (e 1)

at the same temperature

Radiative Heat Transfer between System and

Surroundings

Consider the heat transfer between system surface

with surroundings, as shown in Figure. What is

the rate of heat transfer into system surface ?

To find this, we will first look at the emission

from surroundings to system.

Surrounding Surface emits radiation as described

in

This radiation is emitted in all directions, and

only a fraction of it will actually strike system

surface.

This fraction is called the shape factor, F.

The amount of radiation striking system surface

is therefore

The only portion of the incident radiation

contributing to heating the system surface is

the absorbed portion, given by the absorptivity

aB

Above equation is the amount of radiation gained

by System from Surroundings. To find the net

heat transfer rate for system, we must now

subtract the amount of radiation emitted by

system

The net radiative heat transfer (gain/loss) rate

at system surface is

Similarly, the net radiative heat transfer

(loss/gain) rate at surroundings surface is

What is the relation between Qsys and Qsur ?

An Universe consisting of System Surroundings

only

According to Reciprocity theorem

If both system and surroundings are ideal bodies

If system completely engulfs the surroundings.

Nature of Convection Heat Transfer

- Convection involves the transfer of heat by the

motion and mixing of "macroscopic" portions of a

fluid. - This mixing is called as the flow of a fluid past

a solid boundary leading to Heat Convection. - The term natural convection is used if this

motion is generated within. - The term forced convection is used if this motion

and mixing is caused by an outside force, such as

a pump/fan. - Heat transfer by convection is more difficult to

analyze than heat transfer by conduction because

no single property such as thermal conductivity,

can be identified to describe the convection

mechanism.

Natural Convection

- Natural convection (or free convection) refers to

a case where the fluid movement is created by the

warm fluid itself. - The density of fluid decrease as it is heated

thus, hot fluids are lighter than cool fluids. - Warm fluid surrounding a hot object rises, and is

replaced by cooler fluid. - The result is a circulation of air above the warm

surface

Forced Convection

- Forced convection uses external means of

producing fluid movement. - Forced convection is what makes a windy, winter

day feel much colder than a calm day with same

temperature. - The heat loss from your body is increased due to

the constant replenishment of cold air by the

wind. - Natural wind and fans are the two most common

sources of forced convection.

Newtons Law of Cooling

Newton, when asked once about how he gained his

insight into the problems of nature, replied By

constantly thinking unto them. Historians of

science agree that Newtons paper incorporated

two important generalizations on law of cooling.

The first was that the rate of cooling of a hot

body at any moment is proportional to the

difference between the temperature of the body

and of the surrounding fluid. This generalization

has the most far-reaching effect and became the

genesis of the convective heat transfer. The

second was that when a body melts or evaporates,

its temperature remains constant.

A plausible 'wind tunnel' for Newton's

coolingexperiments.

Rate of Convection Heat Transfer

- Convection involves the transfer of heat between

a system at a given temperature (Ts) and fluid at

a bulk temperature (Tb). - The exact definition of the bulk temperature (Tb)

varies depending on the details of the situation. - For flow adjacent to a hot or cold surface, Tb

is the temperature of the fluid "far" from the

surface. - For boiling or condensation, Tb is the saturation

temperature of the fluid. For flow in a pipe, Tb

is the average temperature measured at a

particular cross-section of the pipe. - Newtons law of cooling suggests a basic

relationship for heat transfer by convection

h is called as Convection Heat Transfer

Coefficient, W/m2K

Possible Actions During a change of state?

- Work transfer
- Heat transfer
- Mass transfer
- How to Account for these actions?

Net Work During a Cycle process

The net work done by the system in the process

a1b2a is

Change in any property during a cycle is zero! Is

Conservation of Energy valid here?

Net Heat Transfer During a Cycle

The absolute value of heat transfer during one

cycle is

Change in any other property during a cycle is

zero. Is Conservation of Energy valid here?

Conservation of Energy

- Energy can neither be created nor be destroyed.
- In a Cycle, Net work Transfer Net Heat

Transfer. - This is notes as the First Law of Thermodynamics.

Combined Heat Work Transfer Sign Conventions

The First Law of Thermodynamics

If a control mass undergoes a cyclic process, the

cyclic integral of the heat is proportional to

the cyclic integral of work.

Cyclic Integral of Heat ? Cyclic Integral of Work

- This is a law of nature.
- Can be described only for control mass.
- Basis is only experimental evidence.
- The first law can never be disproved.

Engineering View of First Law

- Any machine which violates first law is called as

Perpetual Motion Machine of first kind. - A PMM-1 is a control mass which works

continuously in a cycle and - generates only work or
- consumes only work or
- accepts only heat or
- rejects only heat.
- It is impossible to construct A Perpetual Motion

Machine of first kind (PMM 1).

Analysis of Cycles using First Law