MCL141
THERMAL SCIENCE FOR MANUFACTURING
Krishnakant Agrawal (Assistant PROFESSOR)
Dept. of MECHANICAL ENGINEERING
Lecture 3
Continuum
Disregard the atomic nature of a substance and view it as a continuous,
homogeneous matter with no holes, that is, a continuum
Allows continuous variation of properties without any discontinuity and
makes differential governing equations possible
Size of the system we deal with should be large relative to the space
between the molecules.
Example.
The diameter of the oxygen molecule is about 3x10-10 m and its mass is
5.3x10-26 kg. Also, the mean free path of oxygen at 1 atm pressure and 20°C
is 6.3x10-8 m. That is, an oxygen molecule travels, on average, a distance of
6.3x10-8 m (about 200 times of its diameter) before it collides with another
molecule.
Still, a tiny volume of 1 mm3 at atmospheric conditions (1 atm pressure and
20°C) contains about 3x1016 molecules of oxygen
Before applying differential
equations, continuum
validity must be checked
Types of System
• Closed system – Fixed mass, only energy transfer. Volume can
change against flexible boundary
• Open system – Both mass and energy are allowed to transfer.
Volume can change against flexible boundary
• Isolated system – No interaction with the surroundings
• A control volume approach is better to analyze open systems –
A fixed (volume) imaginary boundary allowing both energy and
mass transfer
Volume is allowed to change of
isolated system if there is no
pressure outside (vacuum)
Types of System
Alternating
between
control
volume and
closed system
Adiabatic system
A process during which there is no heat transfer is called an adiabatic
Process
• The word adiabatic comes from the Greek word adiabatos, which
means not to be passed.
• There are two ways a process can be adiabatic: Either the system
is well insulated, or both the system and the surroundings are at
the same temperature.
•
An adiabatic process should not be confused with an isothermal
process. Even though there is no heat transfer during an adiabatic
process, the energy content and thus the temperature of a system
can still be changed by other means such as work.
• Adiabatic Control Mass or Control Volume : A system through
which no heat interactions with surroundings but it can do other
actions equivalent to work.
System and boundaries
Fixed and Moving control volumes
Hydroelectric dam
Pelton wheel
Fixed and Moving control volumes
Sun and Tan, 2020, Journal of Fluids Engineering
142:051206, DOI: 10.1115/1.4045615
Fluid domain
of Centrifugal
impeller
Water pump
Centrifugal impeller
Control volume for
Computational Fluid
Dynamics analysis
Type of system/volume for manufacturing processes
https://www.mdpi.com/1996-1073/13/9/2266
Forging: Soft material punched into a shape
Arc welding with sputtering of metal
Type of system ?
Heat, Work interactions?
Type of system/volume for manufacturing processes
OR
Heating lamp
Qin
Ceramic
mass out
Ceramic
mass in
Win
Conveyor belt
Ceramic mass in
OR
Ceramic
mass out
Heat, Work interactions?
Type of system ?
Heating lamp
Qin
Win Conveyor pulleys
Types of Mechanical work
Thermodynamic Properties of a system
• Macroscopic properties of system useful for thermodynamic analysis
• State variables: P, V, T, U, H, G, S (capital: Extensive, small letter: intensive = per kg, except P and T)
• P- Pressure, V- Volume, v – specific volume, T- Temperature, U- Internal energy, u – specific
internal energy, H – Enthalpy, h – specific enthalpy, G – Gibbs free energy, S - Entropy
• Intensive properties – Independent of mass of the system : P, T
• Definite values of properties → Fixed State of the system
• State Postulate: The state of a simple compressible system is completely specified by two
independent, intensive properties.
• Simple compressible system: Absence of electrical, magnetic, gravitational, motion, and surface
tension effects
• Any two thermodynamic variables can fix the state for substance in single phase; all variables can
be derived u = f(T,v), h = f(T,P) etc.
Functional relations
• What kind of Functional Relation?
• Assume that variables P, V, T are functionally related.
•
Say F(P, V, T) = Constant.
• Assume that each variable can be explicitly “solved” from this functional relation in terms of two
other variables, which are allowed to vary freely.
• P to obtain an expression of the form P = g(V, T), where V and T are chosen as free variables.
• Any function of p, V, T can be expressed as a function of any pair of free variables of your choice.
•
F(p, V, T) = F(g(V, T), V, T) is expressed as a function of a pair of free variables V and T.
• Ideal gas law for gases with molecules sufficiently apart (low pressure, high temperature)
෨
𝑃𝑉 = 𝑛𝑅𝑇,
𝑚
෨
𝑃𝑉 = 𝑀𝑊 𝑅𝑇,
𝑃𝑉
𝑚
𝑅෨
= 𝑀𝑊 𝑇,
𝑃𝑣 = 𝑅𝑇,
𝑃
𝜌
= 𝑅𝑇
෨
Where 𝑅෨ is universal gas constant (8.314 J/mol-K) and R = 𝑅/MW
is gas constant
• A functional relationship for real gases, liquid and solids are also available
Equilibrium
As many equilibriums as the energy types…
Thermal equilibrium - Temperature is same throughout
the entire system (within tolerance as per analysis
purpose). So, no temperature differential or driving force
for heat flow.
Mechanical equilibrium – Pressure is same throughout
the entire system (except for variation due gravitational
head, which is usually small and can be neglected in most
systems). No driving force for mechanical work.
Phase equilibrium when the mass of each phase reaches
an equilibrium level and stays there.
Chemical equilibrium if its chemical composition does
not change with time, that is, no chemical reactions occur
Similarly Electric, magnetic, nuclear, elastic etc.
Properties can define state of a system only it is in equilibrium
Processes: Change of state
Any change that a system undergoes from one equilibrium state to another
is called a process, and the series of states through which a system passes
during a process is called the path of the process
Change in such a way that the system always remains infinitesimally close
to an equilibrium state, it is called a quasistatic, or quasi-equilibrium,
process
Slow processes (relatively) allows system to adjust such that there is no
change of properties from one part of the system to another can be
classified as quasi-equilibrium processes.
During the process, constant Temperature T, pressure P, volume V (or
specific volume v) → Isothermal process, isobaric process, isochoric (or
isometric) process respectively.
A system is said to have undergone a cycle if it returns to its initial state
at the end of the process. That is, for a cycle the initial and final states are
identical.
Some closed system processes
• Work in a closed system – PdV
• A path function – depends on the exact process
through which system reaches from initial state to the
final state
• Path functions have inexact differentials designated by
the symbol δ.
• Hence differential amount of work is δW and not dW
• Properties, however, are point functions (i.e., they
depend on the state only, and not on how a system
reaches that state), and they have exact differentials
designated by the symbol d
Free expansion of gas
• Two vessels 1 and 2 interconnected by a short pipe with a valve A,
and perfectly thermally insulated
• Initially let the vessel 1 be filled with a fluid at a certain pressure,
and let 2 be completely evacuated. When the valve A is opened
the fluid in 1 will expand rapidly to fill both vessels 1 and 2. The
pressure finally will be lower than the initial pressure in vessel 1.
This is known as free or unresisted expansion
• The process is highly irreversible ; since the fluid is eddying
continuously during the process.
• No work is done on or by the fluid, since the boundary of the
system does not move. No heat flows to or from the fluid since the
system is well insulated.
• So, the internal energy of the system cannot change and hence
Initial temperature = Final Temperature