Motion - change in relative position among bodies versus time
Material point : mass with negligible sizes (volume)
Trajectory–all points corresponding to the position of the point P
Frequency f – numer of revolution per unit time
Ideal gas – model assumptions:
Volume of a gas molecule is much smaller than the gas volume → gas molecules are material points
Range of forces between two interacting molecules is much smaller than an average distance between molecules
→ intermolecular interactions are negligible and molecules move in straight lines between collisions
Pressure p is a physical value equal to the force acting on a surface of the body along the normal direction to that surface: p=dFn/dS where: Fn is the normal force acting on dS Unit of p: 1 pascal; 1 Pa = 1N / 1m2
Absolute temperature - defined as a value proportional to the average kinetic energy of particles: T=2E/3k
Equation of state of an ideal gas pV = NkT or: pV = nRT
1 mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12.
Avogadro Avogadro`s law `s In the same volume of different gasses under the same pressure, at the same temperature there is the same number of particles.
Principle of thermal equilibrium thermodynamic law If the bodies 1 and 2 are in thermal equilibrium and bodies 2 and 3 are in thermal equilibrium thus bodies 1 and 3 are in the same thermal equilibrium
degree of freedom - an independent coordinate necessary for determination of the position of a body in space
Principle of equipartition of energy - Mean kinetic energy per one degree of freedom is the same for all molecules and equals to kT/2.
First law of thermodynamic - Principle of energy conservation - with energy division into: macroscopic - mechanic energy of a mass centre motion Ek=Mv2‑/2
microscopic - internal energy of particles U=NE=Nm v2/2
When two bodies with different temperatures are in contact then heat ∆ ∆∆ ∆Q flows from the warmer body to colder one.
Heat – associated with a change of the energy content of the body; does not refer to a property or condition of a body
Heat absorbed by the system is equal to the increase of internal energy of the system and the work performed by the system on the surroundings. dQ = dU + dW
HEAT ∆Q – energy exchanged between the system and surroundings due to temperature difference
Energy transfer – as a heat Q or work W (by means of the force acting on the system) Q and W – not a property of the system (contrary to T, p and V)
Difference ∆Q–∆W=∆U is the same for all processes !
Internal energy of the system U
- increases when it takes energy in a form of heat Q
- decreases when it performs work W
Heat capacity of a system C – the quantity of heat required to rise the temperature of a body through one degree 1K (1C):
Specific heat capacity c – heat capacity per unit mass:
Molar heat capacity Cm – heat capacity of unit amount of substance
Kinetic theory of gases Let`s consider a spherical particle with a diameter d.
Condition for a collision – distance between centres of particles is lower than d → particle is a „target” with an effective area
σ = πd2
σ - total cross section of a particle for a collision (m2)
Mean free path λ - average distance that a molecule moves between two successive collisions with other molecules
Maxwell velocity distribution In an ideal gas – characteristic distribution of molecule velocities → dependence on temperature.
ENTROPY & the second law of thermodynamics Reversible and irreversible processes
(1) Fast motion of the piston → p and T are not well determined (not equal in the whole volume) – irreversible process
(2) Slow motion of the piston without friction → p and T are well determined (gas obtained quickly new equilibrium state).For smaller and smaller changes of gas → →→ → in the limit – ideal process → all intermediate states (between initial and final states) are equilibrium ones – reversible process
A process is reversible when the process can be made in the reverse direction at any stage by making an infinitesimal change in the environment of the system, e.g. an infinitesimal change in pressure.
Carnot cycle →determines the limit of possibility of transformation of heat to work
(1) Gas state is p1, V1, T1 (point A). Cylinder is placed on the heat pump → thermal expansion of gas to state p2, V2, T1 (point B). Gas absorbs heat Q1.
(2) Cylinder is placed on the insulation → adiabatic expansion of gasto state p3, V3, T2 (point C). Gas performs the work during moving the piston and temperature decreases to T2.
(3) Cylinder is placed on the refrigerator (T2) → isothermal compression of gas to state p4, V4, T2 (point D). Gas gives heat Q2 to the refrigerator.
(4) Cylinder is placed on the insulator →adiabatic compression of gas to state p1, V1, T1 (point A). External forces perform work and temperature of gas increases to T .
Total change of internal energy is equal to zero, because final state is the same as initial one. From the first law of thermodynamics is then: W = Q1 – Q2
Efficiency of Carnot engine: N=W/Q1=Q1-Q2/Q1=T1-T2/T1
Second econd law of thermodynamics
1) Perpetum mobile of second type (self-acting machine) can not be constructed
2) When two bodies with different temperatures are in contact, then the heat flows from the body with higher temperature to that with lower temperature → directional process
3) Efficiency of every cyclic machine working between temperatures T1 and T2 is not higher than (T1 - T2) / T1.
Entropy is a measure of the system disorder
Macrostate – a given configuration of particles in boxes
Microstate – distribution of particles corresponding to a macrostate
Definition of entropy S of the system: S = k · lnw
2nd nd law of thermodynamics law of thermodynamics : :4) In the isolated system, the entropy does not decrease.
Entropy S depends only on the state of the system and
not on the path by which that state was reached.
Adiabatic process: dQ = 0 For reversible process: dS = 0 Entropy of the adiabatically isolated system in which the reversible process takes place, is constant.
In irreversible adiabatic process entropy increases.
1st thermodynamic law:
∆Q = ∆U +p∆V
T∆S = ∆V + p∆V
ENTALPHY For a process with p=const – definition of enthalpy H=U+pV
FREE ENERGY (Helmholtz Helmholtz function) F=U-TS
FREE ENTALPHY (Gibbs function) G=H-TS
Importance of G – in chemical reactions and two phase cases (e.g. solid and liquid)
Thermodynamic function p, V, T , A function of V and p: f=f(V,p) A small change in f resulting from small changes in p and V:
Thermodynamics deals with the amount of heat transfer as a system undergoes from one
equilibrium state to another. • Driving force - difference of temperature
Heat transfer deals with the rate of heat transfer as well as the temperature distribution
within the system at a specified time.
Energy balance for closed stationary system (fixed mass) Ein-Eout=∆U=mcv∆T
Energy balance for steady - flow systems (mass flow) →engineering devices (e.g. water heaters, car radiators
Steady flow - no change in time at a specified location
Uniform flow - no change with position thorough the surface or region at a specified time (1D case)
The change in the total energy of the control volume during a process ∆Ecv=0
Assumption: changes in kinetic and potential energy are negligible
The rate of net heat transfer into or out of the control volume : Q=E
The mechanisms of HEAT TRANSFER
Conduction – energy transfer from the more energetic particles of a substance to the adjacent less energetic ones → a result of interactions between the particles.
In gases and liquids -collisions of the molecules during their random motion.
In solids: - vibrations of the molecules in a lattice - energy transport by free electrons
SURFACE ENERGY BALANCE
A surface contains no volume or mass, thus no energy → a fictitious system with E = const
during the process (steady-state system)Surface energy balance both for steady and transient
conditions: Ein=Eout
Energy balance for the outer surface of the wall: Q=Q1+Q2
The rating problems deal with the determination of the heat transfer rate for an existing system at a specified temperature difference.
The sizing problems deal with the determination of the size of a system in order to transfer heat at a specified rate for a specified temperature difference.
The parameters that effect the rate of heat conduction through a windowless wall:
- geometry (surface area and thickness) of the wall
- material of the wall
- temperature difference across the wall.
HEAT FLUX - the rate of heat transfer per unit surface area
The flux of heat flow through a solid is directly proportional to its thermal conductivity
Convection - energy transfer between a solid surface and the adjacent liquid or gas which is in motion → it involves combined effects of conduction and fluid motion.
In forced convection the fluid is forced to move by xternal means such as a fan, pump, or the wind.
The fluid motion in natural convection is due to buoyancy effects only
Radiation - energy emitted by matter in the form of electromagnetic waves (or photons) → a result of the changes in the electronic configurations of the atoms or molecules.
Stefan-Boltzmann law for a black – body Qrad=εσAs(Ts4-Tsurr4)
Emissivity is the ratio of the radiation (energy flux) emitted by a surface to the radiation emitted by a blackbody at the same temperature.
Black-body radiation represents the maximum amount of radiation that can be emitted from a
surface at a specified temperature
Real bodies emit and absorb less radiation than a blackbody at the same temperature
The Kirchhoff's law of radiation: The emissivity and the absorptivity of a surface are equal at the same temperature and wavelength.
Heat transfer has direction and magnitude → vector character
Rate of heat conduction in a specified direction:
- proportional to the temperature gradient
- three-dimensional (3D)
Heat conduction in a medium:
- steady (T = const with time at any point within the medium) or unsteady (transient) (T≠ ≠≠ ≠ const)
- one-dimensional (when conduction is significant only in 1D) or 2D / 3D
Heat transfer has direction and magnitude → vector character
HEAT TRANSFER – HEAT CONDUCTION EQUATIONHeat transfer has vector features → direction and magnitude at a point.
HEAT GENERATION
- Conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy in solid
Fuel elements of nuclear reactors → nuclear fission → heat source for the nuclear power plants Sun → nuclear reactor (fusion of hydrogen to helium)
Technology of insulation
Ordinary insulations - by mixing fibers, powders, or flakes of insulating materials with air.
Heat transfer through such insulations is by conduction through the solid material, and conduction or convection through the air space as well as radiation. Such systems are characterized by apparent thermal conductivity instead of the ordinary thermal conductivity in order to incorporate these convection and radiation effects.
Superinsulations - by using layers of highly reflective sheets separated by glass fibers in an evacuated space. Radiation heat transfer between two surfaces is inversely proportional
to the number of sheets used and thus heat loss by radiation will be very low by using this highly reflective sheets. At the same time, evacuating the space between the layers forms a vacuum under 0.000001 atm pressure which minimize conduction or convection through the air space between the layers.
The rate of heat conduction through a plane wall is proportional to the average thermal conductivity, the wall area, and the temperature difference, but inversely proportional to the wall thickness. thermal resistance of a medium -represents the resistance against heat transfer
Convection heat transfer -from a solid surface of area AS and temperature TS to afluid sufficiently far from the surface of temperature T¥ and a convection heat transfer coefficient h
Radiation heat transfer -between a surface of emissivity e and area AS at temperature TS and the surrounding surfaces at some average temperature Tsurr
Convection and radiation ® total heat transfer
Thermal resistance network
1D heat flow through a plane wall of thickness L, area A, and thermal conductivity L , exposed to convection on both sides to fluids at temperatures T¥ 1 and T¥ 2with heat transfer coefficients h1 and h2, respectively
CONVECTION
Heat transfer through a fluid in the presence of bulk fluid motion
Convection:
- natural (free)
- forced (by external means, as a pump or a fan)
- external (fluid flow over a surface)
- internal (flow in a channel)
• In forced convection the fluid is forced to move by
external means such as a fan, pump, or the wind.
• The fluid motion in natural convection is due to
buoyancy effects only
Convection - heat transfer through a fluid in the presence of bulk fluid motion In fluid – convection and conduction (in the absence of bulk motion) Nusselt number Nu L = C hL Nu - dimensionless convection heat transfer coefficient where: L - the thermal conductivity, LC – the characteristic length
The Nusselt number represents the enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer. The larger Nu value, the more effective convection Nu = 1 means heat transfer across the layer by pure conduction
CLASSIFICATION OF FLUID FLOWS
Convection heat transfer – related to fluid mechanics ®
- behaviour of fluids at rest or in motion
- action of fluids with solids or other fluids at the boundaries
Viscous versus inviscid flow
Viscosity – internal resistance due to motion of fluid layers relative to each other (internal stickiness of the fluid) caused by cohesive forces between the molecules in liquids, and by molecular collisions in gases.
Inviscid (frictionless) flow – idealised flows of zero-viscosity fluids.
Internal flow of water in a pipe and the external flow of air over the pipe. Internal versus external flow
Internal flow – completely bounded by solid surface.
External flow – of unbounded fluid over a surface such
as a plate, a wire, or a pipe.
Compressible versus incompressible flow
Important factor – changes of fluid density during flow
Gases – highly compressible; e.g. atmospheric air: pressure change of just 0.01 atm causes a change of 1 % in the density
Assumption: gas flow incompressible if the density changes
are under ~ 5 % (typical in cases when the flow velocity is less
than 30 % of the sound velocity = 346 m/s)
Liquids – incompressible; e.g. water: a pressure of 210 atm causes the density at 1 atm to change by just 1 %.
Laminar versus turbulent flow
Laminar flow – highly ordered ® smooth streamlines;
typical cases – high-viscosity fluids (i.e. oils) at low velocities.
Turbulent flow – highly disordered ® fluctuations;
typical cases – low-viscosity fluids at high velocities.
Steady versus unsteady (transient) flow
Steady flow – no changes with time (at any fixed point; changes possible for different points).
Devices operating under steady-flow – turbines,
compressors, boilers, condensers, heat exchangers.
Uniform flow – no change with location
Radiation heat transfer – in solids, liquids and vacuum ® does not require the presence of a material medium (energy transfer at c)
Thermal radiation – energy transitions of molecules, atoms and electrons of a substance
Temperature – a measure of the strength of the energy transitions at the microscopic level
Thermal radiation – continuously emitted by all matter whose temperature is above absolute zero.
A blackbody – maximum amount of radiation per unit surface area ® idealised body to serve a standard for comparison of real surfaces ® perfect emitter and adsorber of radiation. A blackbody adsorbs all incident radiation and emits radiation energy uniformly in all directions per unit area normal to direction of emission ® diffuse emitter (independent of direction) The radiation energy emitted by a blackbody per unit time and per surface area:
Eb (T) =σT 4 (W / m2)
where Eb is the blackbody total emissive power σ = 5.67 × 10-8 W/m2·K4 is the Stefan-Boltzmann constant
Spectral blackbody emissive power Ebλ
– the amount of radiation energy emitted by a blackbody
at an absolute T per unit time,per unit surface area, and per
unit wavelength about the wavelength λ.
Kirchhoff`s law ® Gustaw Kirchhoff (1860)
Assumption: A small body of surface area AS, emissivity e, and absorptivity a at temperature T contained in a large isothermal enclosure.
ε(T) =λ(T)
The total emissivity of a surface at temperature T is equal to its total absorptivity for radiation coming from a blackbody at the
same temperature.
Boiling and evaporation - the liquid-to-vapour phase change processes that occur at a solid-liquid interface when the surface is heated above the saturation temperature Tsat of the liquid → convection heat transfer.
Evaporation occurs when the vapour pressure is less than the saturation pressure of the liquid at a given
temperature, and it involves no bubble formation or bubble motion.
Boiling occurs when a liquid is brought into contact with a surface maintained at a temperature TS
sufficiently above the saturation temperature Tsat of the liquid.
Boiling → convection heat transfer → the boiling heat flux from a solid surface to the fluid – Newton`s law of cooling:
Surface tension → bubbles → thermodynamic non- equilibrium conditions → →→ → different temperature in the bubble than in liquid.
The pressure difference between the liquid and the vapour is balanced by the surface tension at the interface → the driving force for heat transfer between two phases.
When the liquid is at a higher T than the bubble, heat will be transferred from the liquid to the bubble → the bubbles grow and rise to the top under influence of buoyancy.
Surface tension in liquids → in an elastic membrane (2D effect) → analogy to tension in an elastic spring (1D effect)
Any line element of the surface of the „membrane” is in equilibrium due to equal and opposite forces exerted perpendicular to ∆ ∆∆ ∆l by the parts of the „membrane” on either side.
Natural convection boiling regime- the fluid motion is governed by natural convection currents, and heat transfer from the heating surface to the fluid is by natural convection.
Nucleate boiling regime - bubbles form at various preferential sites on the heating surface, and rise to the top.
Transition boiling regime - part of the surface is covered by a vapor film.
Film boiling regime - the heater surface is completely covered by a continuous stable vapor film, and heat transfer is by combined convection and radiation.
Condensation on a plate• Influence of gravity.• Ts must be below Tsat of the vapour for condensation to occur.
• Temperature of the condensate is Tsat at the interface and decreases gradually to Ts at the wall.
• The velocity of the condensate at the wall is zero because of the „no- slip” condition.
• Velocity maximum at the liquid – vapour interface.
Dropwise condensation of steam on a vertical surface One of the most effective mechanisms of heat transfer → → extremely large heat transfer coefficients (more than 10 times larger than in case of film condensation) → →→ preferred mode of condensation (efficient condensers) → →→ → adding a promoting chemical into the vapour, treating the surface with a promoter chemical or coating the surface with a polymer (teflon) or a noble metal (gold, platinum, silver)
Mass transfer requires the presence of two regions at different chemical compositions ® movement of chemical species from a
high concentration region toward a lower concentration (nonhomogeneous medium).
An impermeable surface is a surface that does not allow any mass to pass through.
Moisture – influence on the performance and durability of building materials ® importance of moisture transmission Moisture – affects the effective thermal conductivity of porous building materials linear increase of heat transfer
Negative effects due to excess moisture – changes in the
appearance and physical properties of materials:
- corrosion and rusting in metals
- rotting in woods
- peeling of paint on the interior and exterior wall surfaces
- molds grow on wood surfaces at relative humidities above 85%
- damage of the porous material structure due to freezing
The effects of moisture in buildings – migration of water vapour
through the walls and condensation on the inner side, releasing
the heat of vaporisation.
The vapour barriers (thick metal and plastic layers) and retarders
(thin metal, paper and plastic layers) – control of moisture
migration in the walls, floors and ceilings.
Mechanical waves - disturbance in an elastic medium (i.e. acoustic waves) – result of a displacement of an element of the medium from equilibrium ® transport of the oscillations to the succeeding elements (medium does not move but only its
elements oscillate in limited regions of space). Waves transfer energy (kinetic and potential energy of medium particles).
Energy transfer – through matter due to displacement of disturbance not involving translational motion of matter. Travelling of waves – in a medium from the wave source. addition of the disturbances produces a resultant wave of the same frequency as the two component waves but with twice theamplitude -> constructive interference the two waves are out of phase by π. The waves cancel, producing no net disturbance-> destructive interference
Christian Doppler (1842 r) found that when the source and receiver of waves are in relative motion, the wave frequency, as measured by the receiver, is different from the source frequency.
Zero law of ther. – If two thermodynamic systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other
First law of ther.- The increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings.
Second law of ther-entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.