This document discusses heat transfer mechanisms including conduction, convection, and radiation. It then describes various heat transfer equipment used in pharmaceutical industries like heat exchangers and heat interchangers. Specifically, it provides details on single pass tubular heaters, floating head two-pass heaters, multipass heaters, and double pipe heat interchangers. It explains how each type of equipment works and transfers heat between fluids through conduction across metal walls.
Definition of drying
Importance of drying
Difference between drying and evaporation
Drying is defined as removal of the liquid from a material by application of heat & is accomplished by transfer of a liquid from the surface into an unsaturated vapor phase .
Drying is the final removal of water from material (usually by heat)
Drying is commonly the last stage in a manufacture process
Non-thermal drying
1- As Squeezing wetted sponge
2- Adsorption by desiccant (desiccation)
3- Extraction.
Preservation of drug products
Preparation of bulk drugs
Improved handling
Improved characteristics
Equipments
Drying is necessary in order to avoid deterioration. A few examples are…
--blood products, tissues… undergo microbial growth
--effervescent tablets, synthetic & semi synthetic drugs undergo…. chemical decomposition.
Definition of drying
Importance of drying
Difference between drying and evaporation
Drying is defined as removal of the liquid from a material by application of heat & is accomplished by transfer of a liquid from the surface into an unsaturated vapor phase .
Drying is the final removal of water from material (usually by heat)
Drying is commonly the last stage in a manufacture process
Non-thermal drying
1- As Squeezing wetted sponge
2- Adsorption by desiccant (desiccation)
3- Extraction.
Preservation of drug products
Preparation of bulk drugs
Improved handling
Improved characteristics
Equipments
Drying is necessary in order to avoid deterioration. A few examples are…
--blood products, tissues… undergo microbial growth
--effervescent tablets, synthetic & semi synthetic drugs undergo…. chemical decomposition.
Pharmaceutical Engineering Unit- 1 Chapter -1 Flow of fluid.pptxNikita Gupta
Here's a short way to understand the concept of pharmaceutical engineering . Take a look of this amazing ppt who describes the Chapter -1 of Pharmaceutical engineering i.e. Flow of Fluid.
Introduction
Mechanism of Heat Flow
Conduction
Heat Flow through a Cylinder-Conduction
Conduction through fluids
Convection
Film type condensation
Cold liquid-boiling of liquids
Modes of Feed-Heat Transfer
Thermal Radiation
Black Body
Grey body
Equipments
References
2.1 Heat
Heat is a form of energy. According to the principle of thermodynamics whenever a physical or chemical transformation occurs heat flow into or leaves the system.
A number of sources of heat are used for industrial scale operations steam and electric power is the chief sources to transfer heat. It is essential to cover steam without any loses to the apparatus in which it is used. The study of heat transfer processes helps in be signing the plant efficiently and economically
2.2 Heat Transfer:-
Work is one of the basic modes of energy transfer in machines the action of force on a moving body is identified as work. The work is done by a force as it acts upon a body moving in the direction of the force.
Work transfer is considered as occurring between the system and the surroundings work is said to be done by a system is the sole effect on things external to the system can be reduced to the raising of a weight.
If a system has a non-adiabatic boundary its temperature is not independent of the temperature of the surroundings and for the system between the states 1 and 2 the work w depends on path and the differential d-w is inexact. The work depends on the terminal state 1 and 2 as well as non-adiabatic path connecting them. For consistency with the principle of conservation of energy. Some type of energy transfer must have occurred because of the temperature difference between the system and its surroundings and it is identified as heat thus when an effect in a system occurs solely as result of temperature difference between the system and some other system the process in which the effect occur shall be called a transfer of heat from the system at the higher temperature to the system at the lower temperature.
1.1 Evaporation
1.2 Distillation
1.3 Drying
1.4 Crystallization
1.5 Sterilization
Application of Heat Transfer in Pharmaceuticals Industries
This presentation will help the students of Pharmacy in subjects like Pharmaceutics and industrial pharmacy. Hope you will find it better and helpful.
Regards
Amjad Anwar
email: amjadanwar77@gmail.com
Department of Pharmacy, University Of Malakand
A multiple-effect evaporator, as defined in chemical engineering, is an equipment for efficiently using the heat from steam to evaporate water.
Steam is mostly used as heating medium in Multiple effect evaporator.
Multiple Effect Evaporation remains one of the popular method for the concentration of aqueous solutions.
Heat transfer; Objectives; Applications; Heat transfer mechanism; Fourier's Law; Heat transfer by conduction, convection and radiation; Heat interchangers and exchangers
Pharmaceutical Engineering Unit- 1 Chapter -1 Flow of fluid.pptxNikita Gupta
Here's a short way to understand the concept of pharmaceutical engineering . Take a look of this amazing ppt who describes the Chapter -1 of Pharmaceutical engineering i.e. Flow of Fluid.
Introduction
Mechanism of Heat Flow
Conduction
Heat Flow through a Cylinder-Conduction
Conduction through fluids
Convection
Film type condensation
Cold liquid-boiling of liquids
Modes of Feed-Heat Transfer
Thermal Radiation
Black Body
Grey body
Equipments
References
2.1 Heat
Heat is a form of energy. According to the principle of thermodynamics whenever a physical or chemical transformation occurs heat flow into or leaves the system.
A number of sources of heat are used for industrial scale operations steam and electric power is the chief sources to transfer heat. It is essential to cover steam without any loses to the apparatus in which it is used. The study of heat transfer processes helps in be signing the plant efficiently and economically
2.2 Heat Transfer:-
Work is one of the basic modes of energy transfer in machines the action of force on a moving body is identified as work. The work is done by a force as it acts upon a body moving in the direction of the force.
Work transfer is considered as occurring between the system and the surroundings work is said to be done by a system is the sole effect on things external to the system can be reduced to the raising of a weight.
If a system has a non-adiabatic boundary its temperature is not independent of the temperature of the surroundings and for the system between the states 1 and 2 the work w depends on path and the differential d-w is inexact. The work depends on the terminal state 1 and 2 as well as non-adiabatic path connecting them. For consistency with the principle of conservation of energy. Some type of energy transfer must have occurred because of the temperature difference between the system and its surroundings and it is identified as heat thus when an effect in a system occurs solely as result of temperature difference between the system and some other system the process in which the effect occur shall be called a transfer of heat from the system at the higher temperature to the system at the lower temperature.
1.1 Evaporation
1.2 Distillation
1.3 Drying
1.4 Crystallization
1.5 Sterilization
Application of Heat Transfer in Pharmaceuticals Industries
This presentation will help the students of Pharmacy in subjects like Pharmaceutics and industrial pharmacy. Hope you will find it better and helpful.
Regards
Amjad Anwar
email: amjadanwar77@gmail.com
Department of Pharmacy, University Of Malakand
A multiple-effect evaporator, as defined in chemical engineering, is an equipment for efficiently using the heat from steam to evaporate water.
Steam is mostly used as heating medium in Multiple effect evaporator.
Multiple Effect Evaporation remains one of the popular method for the concentration of aqueous solutions.
Heat transfer; Objectives; Applications; Heat transfer mechanism; Fourier's Law; Heat transfer by conduction, convection and radiation; Heat interchangers and exchangers
Heat exchangers are devices that transfer heat from one medium to another. The purpose of the heat transfer typically is to lower or raise temperatures in a device.
Objectives, applications & mechanisms of Heat transferAkankshaPatel55
Heat transfer: This is the general scientific term for the movement of thermal energy from one object to another. It can occur through three main mechanisms: conduction, convection, and radiation.
Mechanisms of heat exchange:
Conduction: Direct contact between objects allows heat transfer through vibrations of their atoms or molecules. Metals are good conductors, while wood and plastic are poor conductors.
Convection: Heat transfer occurs through the movement of a fluid (liquid or gas). For example, hot air rises in a room, carrying heat upwards.
Radiation: All objects emit electromagnetic waves based on their temperature. Hotter objects emit more intense radiation, which can be absorbed by other objects, transferring heat. This is how the sun warms the Earth.
Applications of heat exchange:
Power generation: In power plants, heat from burning fuel boils water, creating steam that drives turbines to generate electricity.
Heating and cooling: Heat exchangers transfer heat from furnaces, boilers, or geothermal sources to air or water for heating buildings. Conversely, air conditioners use them to remove heat from indoor air.
Chemical processing: Many chemical reactions require specific temperatures, and heat exchangers maintain those temperatures by transferring heat in or out of reaction vessels.
Car engines: Coolant circulates through the engine, absorbing heat and transferring it to the radiator, where it's dissipated to the air.
Human body: Sweat evaporation and blood circulation are examples of heat exchange mechanisms that help regulate our body temperature.
Types of heat exchangers:
There are various types of examples include:
Shell and tube: Two fluids flow through separate channels separated by a wall, allowing heat transfer without mixing.
Plate: Thin metal plates allow efficient heat transfer between fluids in close contact.
Air-cooled: Fins increase surface area for heat transfer between air and a fluid flowing through tubes.
Heat exchangers
TUBE AND SHELL
PLATE HEAT EXCHANGER
FLOW OF ARRANGEMENT
REGENERATIVE HEAT EXCHANGER
log mean temperature difference (LMTD)
Number of Transfer Units (NTU) Method
EFFECTIVENESS OF HEAT EXCHANGER
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
1. HEAT TRANSFER
Ms. Mandakini Sampat Holkar
(M. Pharm.)
For Second Year B. Pharm. Program as
per PCI syllabus, New Delhi
Unit-II
2. Syllabus
Objectives, applications & Heat
transfer mechanisms. Fourier’s law,
Heat transfer by conduction,
convection & radiation. Heat
interchangers & heat exchangers.
3. MECHANISMS OF HEAT TRANSFER
Heat flows from a location at higher temperature to a region at low
temperature. The flow can occur either by a single or a combination of
any of the three basic mechanisms.
(a) Conduction:
When the flow of heat takes place in a solid body by the
transference of the momentum of individual particles,
atoms or molecules without actual mixing, the process is
called as conduction. It mainly occurs in solids and those
fluids where the movement is restricted due to high
viscosity. For example, flow of heat through a metal sheet,
wall or shell of boiler, evaporator and heat exchanger.
Conduction also occurs through a very thin layer of liquid
film which is formed just adjacent to the metal wall and is
not moving i.e., static liquid films.
4. (b) Convection:
In this form heat flows in fluid by actual mixing of the higher
temperature portions from one location with the cooler portions
at next location.The moving fluid contains high energy in it,
which is transferred to the particles at lower energy. For example,
heating of water in a vessel and heating of air in a room, fumace
or air oven. The main driving force of circulation of fluid is
considered to be the difference in the density between the two
locations.
5. (c) Radiation:
This involves the transfer of heat by means of
electromagnetic waves through space. Radiate means to
spread from a central location or origin. Thus, radiation
is spread of energy from an origin to the space
surrounding it. This mechanism does not involve any
movement or the interaction of the matter and energy is
purely carried by the electromagnetic waves.
The hotter the body the more it radiates.
The best example of radiation can be the heat
transferred from the sun to earth through space. Some of
the other examples are hot air ovens, infrared heaters,
microwave ovens and sonicator baths etc. Which utilize
radiation for producing heat.
6. Heat Exchangers and heat Interchangers
A wide variety of heat transfer equipments are used in
pharmaceutical industries. They
he used to heat fluids i.e., liquids and gases and sometime even
solids. Heating media
d is generally the hot fluid or steam or direct heating using electric
heated coils. Some of processes which involve heat transfer in
pharmaceutical industry are:
❖Evaporators
❖Distillation
❖Drying
❖Crystallization
❖Preparation of semisolid dosage forms- creams, ointments and
pastes etc.
The equipments used for the transfer of heat are known either as
heat exchangers or
heat interchangers.
7. (a) Heat exchangers: These are the devices used to transfer heat
from one fluid to the other liquid through a metal wall. So,
generally liquids are heated using steam as heating media in
such equipments.
(b) Heat interchangers: These are the devices which transfer the
heat from one liquid to another liquid or from one gas to the
another gas through a metal wall.
The two terms are also used interchangeably as the classification
is not exactly marked. Therefore, it is suggested to better call
them as heat transfer equipments.
8. Heat Exchangers or Heaters
The term heater or heat exchanger covers many
devices that exchange the heat between
two fluids of different temperatures that are separated
by a solid wall.
Some heat transfer equipments under this category
are:
❖Single pass tubular heater (shell and tube heater)
❖Two pass floating head heater
❖Multi-pass heat transfer heater
10. The heater consist of an outer cylindrical shell or casing C,
with an inlet and outlet for the fluid to be heated.
Bundle of relatively thin walled parallel tubes A is enclosed in
this casing.
The ends of these tubes are expanded into tube sheets B1 and
B2.
Two distribution chambers, D1 and D2 are provided at each
end of casing.
Fluid to be heated is allowed to enter in D2 chamber through
an inlet, H, and heated fluid is taken out from D1 chamber
through an outlet.
Steam or any other heated fluid is introduced into the tubes
through an inlet, F.
Non-condensable vapours and the condensate from steam are
allowed to escape/drain from K and G respectively.
Construction
11. Working: Steam is passed through F into the tubular
structure and is allowed to flow down the tubes so that the tubes
get heated up. Vent, K, is opened to escape the non-condensed
gases and condensate from steam is drained out from G.
Fluid to be heated is introduced through H to enter distribution
chamber D2. It flows through the heated tubes and reaches the
other distribution chamber D1. The steam and the fluid are
physically separated by the metal wall of the tubes but they are
in thermal contact with each other. Fluid gets heated up due to
conduction of heat across the metal wall of tube and finally
convection occurs to spread the heat to the entire fluid. The total
heat transfer occurs only by single passage of fluid through the
tubes, hence the name, single pass heater.
From Di, the heated fluid leaves the casing through outlet, I
13. In floating head two pass heater, the ends of the tubes are
structurally independent of the shell.The construction of
this heater is similar to that of tubular heater with slight
modifications.
Construction: It consists of a bundle of parallel tubes.
Tubes are enclosed in a shell. The right side of the
distribution chamber is partitioned and opening for inlet
and outlet of cold fluid are connected to the same chamber.
The partitioning is so done that both the sections have
same number of tubes. The left side of the casing has the
distribution chamber,
which is not connected to the shell. Since, it is independent
of the shell structurally, it is known as Floated head. The
left end side of the tubes is embedded into the floating
head.
14. The tubular bundle has openings for inlet of steam or hot
vapour and outlet for draining the
the condensate.
A vent is also provided at the top for the escape of non-
condenšable gases.
15. Woking- Steam or hot vapour is introduced through the
inlet port into the tubes and is allowed to flow down the
tubes so that the tubes get heated up. Vent is opened to
escape the non-condensed gases and condensate from
steam is drained out from the outlet.
The fluid to be heated (cold fluid) is introduced into the
distribution chamber on right side of the heater. The
portion directs the fluid to pass through the heated tubes
and fluid reaches the floating head. The fluid then
changes its direction and moves back to the second part
of the partition chamber on right side. Thus, the fluid
has to flow twice through tubes hence the name two pass.
Fluid gets heated up due to conduction of heat across the
metal wall of tube and finally convection occurs to spread
the heat to the entire fluid. Then the fluid leaves the
shell through the outlet provided in the shell.
17. Heat interchangers
When heat is to be transferred from one liquid to
another or from one gas to another through metal wall
the device is known as heat Interchanger
19. Double-pipe heat interchanger: In this type of heat interchanger, the fluid
to be heated passed single time through the heated tubes before it is
discharged
Construction-
This is a concentric tube construction where two pipes are used ,one is
inserted in to the other.
The inner pipe is carry the fluid to be heated and the outer pipe acts like a
jacket through which hot liquid is circulated.
The outer pipes are connected through the annular spaces.
Generally there are few pipe sections joined and the length of the pipe is
also less.
A proper number of such pipes are connected in parallel
and then stacked vertically. Flow in a double-pipe heat
interchanger can be co-current or counter-current.
Two flow configurations: co-current is when the flow of the
two streams is in the same direction,
counter current is when the flow of the streams is in
opposite directions.
20. Working:
The hot liquid is pumped through the jacketed section
and is allowed
circulate through the annular spaces between them and
passed from one section to the other. In doing so, the
inner pipes get heated up and the hot liquid looses its
heat so that its temperature falls.
The liquid to be heated i.e., the cold fluid is pumped
through the inner pipe in such a way that either its flow
is co-current or counter current to the flow of hot fluid. In
diagram counter-current flow configuration. As the liquid
passes in the pipes, it gets heated up and flows through
the bent tubes into the next section of the pine Incase the
flow is counter current, the fluid gets heated further
every time it reaches the next section. This continues
the fluid is exited from the outlet on right side of the
interchanger.
21. Heat transfer by conduction
Heat can only flow whenever there is a temperature gradient i.e. Hot
and cold regions under steady state conditions, the rate of heat
transfer by condition can be written in the form of basic rate equation
Rate = Driving force/resistance------------------------------1
The driving force is the temperature drop across the solid surface
which is in direct relation to the rate of transfer.
The more is the temperature drop, the more will be the rate of heat
flow. resistance is the impeding factor which obstructs the flow and is
related to the thickness , surface are and thermal conductivity of
material This factor can be quantitatively expresses by Fourier law
Resistance = Thickness of the surface (L)
Mean proportionality constant(km) * surface area (A)
22. R= L/ Km A..............................................1
Fourier's law states that the rate of flow of heat through a uniform
material is proportional to the area and temperature drop and is
inversely proportional to length of path of flow i.e. Thickness of the
surface
Rate of heat flow α (Area * Temperature drop )
Thickness
dQ/dθ =q α (A. ∆t) / L or
q= Km.A. ∆t / L ....................2
Here Q= quantity of heat
Θ=time
A =area
∆t = Temperature drop
L= thickness
q= quantity of heat transferred in unit time
Km=mean proportionally constant
23. Derivation of Fourier’s Law
Consider a flat metal wall of surface area A and thickness L.
Let one face of the wall be maintained at uniform higher temperature
t1 and other face of the wall be at a uniform lower temperature t2
over the same area.
Since it is a flat wall a does not vary with L.
Heat flows at the right angles to the plan A and is assumed to be at
steady state.
If thin section of the thickness dL parallel to area A is considered at
some intermediate point in the wall and the temprature difference is
dt across this thin section, then Fourier’s law may be applied as
mentioned below:
q= - k. A.dt /dl..........3
K is constant known as thermal conductivity of the solid.
Negative sign indicates that the temperature is decreasing in the
direction of heat flow.
24. The term dt/dl is known as temperature gradient.
The exact value of dt is not known but the temperature of the
two faces of the wall are known.
rewrite the equation 3
q.dl/A =-k.dt.................................................4
Integration equation 4 between the limits
L=0 when t=t1
L=L when t=t2
we get
q 0∫L dL/A = - t1 ∫t2 kdt = t2∫ t1 kdt
qL/A= km (t1-t2) =km ∆t...............................5
Rearranging equation 5
q= km.A.∆t / L
25. q= km.A.∆t / L
q= ∆t / L/km.A
Comparing this equation with 1
shows that ∆t is driving force and
L/km.A is the resistance for rate
of heat flow.
26. Conduction through compound resistance in series
Consider a flat wall constructed of series of three layers of different
materials.
Let the thickness of each layer be L1 ,L2 and L3
And Thermal conductivity be k1 ,k2 and k3 respectively.
Area of the entire wall is A and
the temperature drop across each layer be ∆t1 , ∆t2 , ∆t3.
Resistance offered by each layer be R1,R2and R3.
if ∆t is the overall temperature drop over the entire wall then
∆t = ∆t1 + ∆t2 + ∆t3 .......................................................1
overall resistance R is equal to the sum of individual resistance of
each layer
R= R1+R2+R3..............................................................2
27. According to Fourier’s law
R= L / K.A
R= L1/ k1.A + L2/ k2.A + L3 / k3.A..................................3
Hence
∆t = q1.L1/ k1.A + q2. L2/ k2.A + q3.L3 / k3.A..............................4
Since entire heat must pass through the resistance in series,haet
transfer rate q can be written as
q=q1 + q2 + q3...............................................5
q= ∆t /R1+R2+R3 ....................................................6
Therefore for heat flow through a number of resistances in series
the contribution of temperature difference to the total
temperature and individual thermal resistances to the total
resistance can be expresses as
∆t; ∆t1; ∆t2: ∆t3::R:R1:R2:R3.....................................7
28. Gray Body
I t is defined as that body whose absorptivity remains
constant at all the wavelengths of radiation at a given
temperature.
consider a small cold body with a surface area A and
temperature T2 which is completely enclosed by a hot
body having temperature T1.
The amount of heat transferred for this system can be
obtained by Stefan-Boltzmann law which is
q=A.σ.(T14- T24)
29. Black Body
The amount of radiation energy emitted from a surface at a given
wavelength depends up on the material of the body and condition of its
surface and also surface temperature. Hence different bodies may emit
different amount of radiation per unit surface area through they are at
same temperature.
A blackbody may be defined as a perfect emitter and absorber of radiation.
It absorbs all the radiation falling on it regardless of its wavelength and
direction. also it emits the radiation uniformly in all the directions per unit
area emission. Therefore a blackbody is a diffusion emitter which is
independent of direction.
30. Stefan-Boltzman Law
Amount of themal radiation emitted from the body increases rapidly
with increase in temperature.Both stefan and Boltzman were
physicist.
They found that amount of radiant energy emitted is proportional to
the fourthpower of the absolute temperature of the heat source body.
Eb = σ.( T abs) 4
Eb emission power the gross energy emitted from an ideal surface per
unit area (A) time θ
Eb= Q/A. Θ =q/A
q= A. σ.( T abs) 4
According to this equation rate of heating depends on the temperature and
surface area of the emitter.
31. It also depends up on the absorption capacity of the material to be
heated
Actual bodies do not radiates as much as blackbody
Equation modified for actual bodies
q= E .A. σ.( T abs) 4
E= ENERGY EMITTED BY ACTUAL BODY / ENERGY EMITTED by blackbody