Heat Conduction along a Composite Bar
Objective
To study the conduction of heat along a composite bar and evaluate the overall heat transfer coefficient. Theory
Thermal conduction is the mode of heat transfer which occurs in a material by virtue of a temperature gradient within it. A solid is chosen for the demonstration of pure conduction since both liquids and gasses exhibit excessive convective heat transfer. In a practical situation, heat conduction occurs in three detentions, a complexity which often requires extensive computation to analyse. In the laboratory, a single dimensional approach is required to demonstrate the basic law that relates rate of heat flow to temperature gradient and area. For steady flow along the bar, the heat flow through successive slabs is the same for reasons of continuity. Hence, from Fourier’s law QA=kHTHS-THIXH=kSTHI-TCIXS=kCTCI-TCSXC(1)

We may write Eq (1) as
QA=U(THS-TCS)(2)
Where,
1Q=XHkH+XSkS+XCkC(3)
U is overall heat transfer coefficient for the composite wall and IUis the overall resistance to the heat flow.

Apparatus

Figure 1: Front view of calibration unit and transformer

Figure 2: Front view of the test unit

The heat conduction apparatus shown in Figure 1&2 consist of two electricity heated module mounted on a bench support frame. One module contains a cylindrical metal bar arrangement for a variety of linear conduction experiments while the other consists of a disc for radial profile studies. Both test section are equipped with an array of temperature gradient. The instrumentation provided permits accurate measurements of temperature and electrical power supplied to the heater. Fast response temperature probes, with a resolution of 0.1°C, give direct digital readout in °C. The power control circuit provides a continuously variable electrical output of 0-80 Watts nominal (at nominal supply voltage) with direct digital readout having a resolution of 0.1W. The test modules...

...was carried out to study the conduction of heatalong a compositebar and evaluate the overall heat transfer coefficient.
INTRODUCTION
Conduction is defined as the transfer of energy from more energetic particles to adjacent less energetic particles as a result of interactions between the particles. In solids, conduction is the combined result of molecular vibrations and free electron mobility. Metals typically have high free electron mobility, which explains why they are good conductors.
Conduction can be easily understood if we imagine two blocks, one hot and the other cold. If we put these blocks in contact with one another but insulate them from the surroundings, thermal energy will be transferred from the hot block to the cold block. This mode of heat transfer between the two solid blocks is termed as ‘conduction’.
Figure 1: Schematic of a long cylindrical insulated bar
Provided that the heated, intermediate and cooled sections are clamped tightly together, so that the end faces are in good thermal contact, the three sections can be considered to be one continuous wall of uniform cross section and material.
According to Fourier’s law of heatconduction:
If a plane wall of thickness (Δx) and area (A) supports the temperature difference (ΔT) then the...

...of a gas takes place with no flow of heat energy either into or out of the gas - the process is said to be isentropic or adiabatic. The isentropic (adiabatic) process can be expressed with the Ideal Gas Law as:
p / ρk = constant
where
k = cp / cv - the ratio of specific heats - the ratio of specific heat at constant pressure - cp - to the specific heat at constant volume - cv
The isentropic or adiabatic process can also be expressed as
pVk= constant
or
p1V1k = p2V2k
The Second law of thermodynamics states that,
where δQ is the amount of energy the system gains by heating, T is the temperature of the system, and dS is the change in entropy. The equal sign will hold for a reversible process. For a reversible isentropic process, there is no transfer of heat energy and therefore the process is also adiabatic. For an irreversible process, the entropy will increase. Hence removal of heat from the system (cooling) is necessary to maintain a constant internal entropy for an irreversible process in order to make it isentropic. Thus an irreversible isentropic process is not adiabatic. For reversible processes, an isentropic transformation is carried out by thermally "insulating" the system from its surroundings. Temperature is the thermodynamic conjugate variable to entropy, thus the conjugate process would be an isothermal process in which the system is...

...0 TITLE
HeatConduction- Simple Bar
2.0 OBJECTIVES
Investigate Fourier’s law for linear conduction of heatalong simple bar
3.0 THEORY
ConductionHeat Transfer
Conduction is the heat transfer by means of molecular agitation within a material without any motion of the material as a whole. If the one end of the metal rod is at a higher temperature, then energy will be transferred down the rod toward the colder end because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones.
Heat flows from a body of higher temperature to a body of lower temperature. For a controlled conduction, this continues until a “steady-state” where no more heat transfer occurs. A diagram below illustrates the direction of heat transfer and the variables involved in linear heatconduction through a plane wall.
Fourier’s Law of HeatConduction
The law of heatconduction , also known as Fourier’s law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperatures and to the area, at right angles to the gradient, through which the heat is flowing....

...16: Heatconduction
Introduction
In this laboratory you will study heat flow across a temperature gradient. By comparing the temperature difference across one material to the temperature difference across a second material of known thermal conductivity, when both are conducting heat at a steady rate, you will be able to calculate the thermal conductivity of the first material. You will then compare the experimental value of the calculated thermal conductivity to the known value for that material. Thermal conductivity is an important concept in the earth sciences, with applications including estimating of cooling rates of magma chambers, geothermal explorations, and estimates of the age of the Earth. It is also important in regard to heat transport in air, to understanding the properties of insulating material (including the walls and windows of your house), and in many other areas. The objective of this laboratory experiment is to apply the concepts of heat flow to measure the thermal conductivity of various materials.
Theory
Temperature is a measure of the kinetic energy of the random motion of molecules with a material. As the temperature of a material increases, the random motion of its molecules increases, and the material absorbs and stores a quantity which we call heat. The material is said to be hotter. Heat, once thought to be a fundamental quantity...

...
HEAT AND MASS TRANSFER
REPORT ON
TRANSIENT HEATCONDUCTION
Submitted by
CDT ARSHAD ALI
CDT NIKHIL BHATIA
Submitted to
Associate Proffessor Pradeep Kumar Singh
Indian Naval Academy
Knowledge Begets immortality
Certificate
This is to certify that this project report entitiled “TRANSIENT HEATCONDUCTION” by CDT ARSHAD ALI and CDT NIKHIL BHATIA during the academic year 2010-2014, is a bonafide record of work carried out under my guidance and supervision.
- Associate Proffessor Pradeep Kumar Singh
Acknowledgement
We would like to express our sincere gratitude to our project guide “Associate Proffessor Pradeep Kumar Singh” for giving us the opportuity to work on this topic .It would never have been possible for us to take the project to the level without his innovative ideas and his continuous support and encouragement.
CDT ARSHAD ALI
CDT NIKHIL BHATIA
Abstract
Table of Contents
Chapter 1 -Introduction
Chapter 2 -Lumped System Analysis
Chapter 3 -Transient HeatConduction in Large Plane Walls, Long Cylinders, and Spheres with Spatial Effects
Chapter 4 -Transient HeatConduction in Semi-Infinite Solids
Chapter 5 -Transient Heat...

...nductioIn heat transfer, conduction (or heatconduction) is the transfer of heat energy by microscopic diffusion and collisions of particles or quasi-particles within a body due to a temperature gradient. The microscopically diffusing and colliding objects include molecules, electrons, atoms, and phonons. They transfer microscopically disorganized kinetic and potential energy, which are jointly known as internal energy.Conduction takes place in all forms of ponderable matter, such as solids, liquids, gases and plasmas.
By conduction, as well as by thermal radiation, heat spontaneously flows from a body at a higher temperature to a body at a lower temperature. In the absence of external driving fluxes, temperature differences disappear over time, and the body approaches thermal equilibrium.
During conduction, the heat flows through the body itself, as opposed to its transfer by the bulk motion of the matter as in convection, and by thermal radiation. In solids, it is due to the combination of vibrations of the molecules in a lattice or phonons and diffusion of free electrons. In gases and liquids, conduction is due to the collisions and diffusion of the molecules during their random motion. Photons in this context do not collide with one another, and heat transport by electromagnetic radiation is...

...fundamental modes of heat transfer are:
Conduction or diffusion
The transfer of energy between objects that are in physical contact
Convection
The transfer of energy between an object and its environment, due to fluid motion
Radiation
The transfer of energy to or from a body by means of the emission or absorption of electromagnetic radiation
Mass transfer
The transfer of energy from one location to another as a side effect of physically moving an object containing that energy
Conduction
On a microscopic scale, heatconduction occurs as hot, rapidly moving or vibrating atoms and molecules interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring particles. In other words, heat is transferred by conduction when adjacent atoms vibrate against one another, or as electrons move from one atom to another. Conduction is the most significant means of heat transfer within a solid or between solid objects in thermal contact. Fluids—especially gases—are less conductive. Thermal contact conductance is the study of heatconduction between solid bodies in contact.
Steady state conduction is a form of conduction that happens when the temperature difference driving the conduction is constant, so that after an...

...Conduction Through A Thick-Walled Tube
This problem is important in the process industries, but we do need to make the distinction between thick and thin walled pipes. In general thin walled pipes can be considered by the previous analysis – but assuming that the pipe wall is effectively unwrapped so that it looks like a flat plate, with the process fluid on one side and the ambient condition on the other. The situation for thick pipes is, however, more complex.
[pic]
The figure shown above represents the condition in a thick walled pipe. The area for heat flow is proportional to the radius – as may be seen, the area at the outside wall of the pipe is much greater than the middle. As a result the temperature gradient is inversely proportional to the radius.
The heat flow ‘per unit length of pipe’ at any radius r, is
[pic]
cf. [pic]
Note: Area,[pic]
Note there is no length of pipe (l) in this equation as we choose to deal with loss per unit length of pipe instead – later we shall introduce the length again, to calculate the total heat loss.
Integration the above equation between r1 and r2 gives
[pic]
or
[pic]
Which, if we define rm as a logarithmic mean radius then
[pic]
[pic]
In Coulson and Richardson Vol 1 it is said that for thin walled pipes it is sufficient to use the arithmetic mean radius ra giving:
[pic] (Used for thin cylinder)
Compare this equation with the...

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