Modes of Heat Transfer

P M V SubbaraoProfessor

Mechanical Engineering Department

Accounting of Natural Happenings …..

Spectral integration of Planks distribution law estimates the total energy emitted by a real system as:

4syssurfacesyssysemitted TAQ

• where εsys is the emissivity of the system,• Asys-surface is the surface area, • Tsys is the temperature, and • σ is the Stefan-Boltzmann constant, equal to 5.67×10-8 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 (ε = 1) at the same temperature

Radiation from a Thermodynamic System

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 ?

4, sursursuremittedsur TAQ

This radiation is emitted in all directions, and only a fraction of it will actually strike system surface.

To find this, we will first look at the emission from surroundings to system.

Surrounding Surface emits radiation as described in

This fraction is called the shape factor, F.

The amount of radiation striking system surface is therefore:

4, sursursursyssurincidentsys TAFQ

The only portion of the incident radiation contributing to heating the system surface is the absorbed portion, given by the absorptivity αB:

4, sursursursyssursysabsorbedsys TAFQ

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:

4, syssyssysemittedsys TAQ

The net radiative heat transfer (gain/loss) rate at system surface is

emittedsysabsorbedsyssys QQQ ,,

44syssyssyssursursursyssursyssys TATAFQ

Similarly, the net radiative heat transfer (loss/gain) rate at surroundings surface is

44sursursursyssyssyssursyssursur TATAFQ

What is the relation between Qsys and Qsur ?

44syssyssyssursursursyssursyssys TATAFQ

An Universe consisting of System & Surroundings only

sursys QQ

According to Reciprocity theorem:

syssursyssursyssur AFAF

44syssyssyssursursyssursyssyssys TATAFQ

44syssyssursursursyssyssyssys TTFAQ

44syssursursyssyssys TTFAQ

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.

Newton’s Law of CoolingNewton, 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 Newton’s 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.

• Newton’s law of cooling suggests a basic relationship for heat transfer by convection:

bs TThAQ

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 :

WW cyclenet

Change in any property during a cycle is zero!

Is Conservation of Energy valid here?

Net Heat Transfer During a Cycle

QQ cyclenet

TThe 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.

T

Combined Heat Work Transfer : Sign Conventions

The First Law of Thermodynamics

• 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.

Cyclic Integral of Heat Cyclic Integral of Work

If a control mass undergoes a cyclic process, the cyclic integral of the heat is proportional to the cyclic integral

of work.

WQ WQ

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