Best Mechanical engineering tutorials HEAT AND MASS TRANSFER

Best Mechanical engineering tutorials HEAT AND MASS TRANSFER

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HEAT AND MASS TRANSFER


Internal Energy:
                  Molecules in a system are in constant motion by mutual forces of attraction.  The molecular motion has Kinetic energy.  The energy of mutual forces of attraction is Potential energy. The sum total of the energy is the internal energy.  This internal energy is dependent upon temperature level of the system.  Higher the temperature, higher the internal energy.  U is the most common symbol used for internal energy.           E.g.. A room temperature glass of water sitting on a table has no apparent energy, either potential or kinetic . But on the microscopic scale it is a seething mass of high speed molecules traveling at hundreds of meters per second.Heat:                      Energy transfer due to temperature difference is called as heat.  This subject studies the rate at which this energy is transferred.  A system might have accepted or rejected heat.  This is reflected by the changes in temperature.  A increase in temperature indicates that the system has accepted heat and a decrease in temperature indicates that the system has rejected heat.  The quantity of heat transferred is given by the product of mass (m), Specific heat ( Cp or Cv ) and the temperature difference ( ∆T ).Difference Between Thermodynamics and Heat Transfer:                      Consider a heated steel bar cooled in water.  Thermodynamics helps to predict the final equilibrium temperature of the composite system.  But heat transfer predicts the time taken to reach the equilibrium temperature or to find what would the temperature be after a certain length of time.  Thus heat transfer helps to predict the temperature of both bar and water as a function of temperature.Modes of Heat Transfer:Conduction:           The thermal energy transfer takes place from a region of high temperature to the low temperature region, between two bodies which are in contact.  The energy transfer takes place by means of electrons, which are free to move. The observable effect is equalization of temperature.  The flow of heat by conduction as given by Fourier law is given by the following formula.  Here K is called the thermal conductivity.  It has the units W/m.KQ  =  - KA ( dT / dX)Convection:           It is possible because of mixing of fluid medium.  This type of heat transfer is possible only in a fluid medium and is directly linked with the transportation of fluid itself. The amount of heat transferred by convection depends largely upon the extent to which the fluids mix with each other.  Thus there exists a mass moment. There are two types of convection, they are
  • Natural Convection:- This results because of the temperature different leading to the differences in density.
  • Forced Convection:- This take place when the flow is caused by external means such as a fan or pump.
Radiation:           Thermal radiation is the form of transmission of heat from one body to another body without a intervening space.  It does not require a material medium, for the transfer of heat.  The heat is transferred in the form of radiant energy or wave energy.  The mechanism of heat transfer consists of three distinct phases.
  • Conversion of thermal energy to photons.
  • Passage of photons in air space.
  • Transformation of photons back to heat.
Stefan Boltzman Law:           The emissive power of a black body is directly proportional to the fourth power of absolute temperature.  T is the absolute temperature, and the value of the Stefan-Boltzmann constant σ is 5.67 x 10 -8E α T4 E = σAT4Planks Law:                      All bodies emit radiation, the quantity and quality of which depends upon the temperature and property of the material.Absorbivity, Reflectivity and Transmissibility:            First consider a distinction between heat and infrared radiation.  Infrared radiation refers to a particular range of wavelengths, while heat refers to the whole range of radiant energy flowing from one body to another.  Consider a radiant heat flux, q falls upon a translucent plate that is not black as shown in the figure                     Then let                   α =Absorbivity or fraction of total energy absorbed by the body.                   ρ =  Fraction of total energy reflected.                   τ = Fraction of total energy transmitted.           Qo = Qa + Qr + Qt                  Qa / Qo  +   Qr / Qo +  Qt / Qo  =  1           α  +  ρ +  τ  =  1 The following are the important conclusions drawn.
  • When α = 1 and  ρ = τ = 0
                       Then it is a Non-reflecting and Non Transmitting surface.  Such a surface is called as black body.  
  • When ρ = 1 and α = τ = 0
                       Then it reflects all radiation and is called a specular of a absolutely white body.
  • When τ = 1 and α = ρ = 0
                       Then it allow all radiations to pass throughout it and is called a transparent or diathermanous body.Black body:            Black bodies are perfect thermal radiators.  It is necessary to have a experimental method for making a perfectly black body.  The conventional device for this approach is the hohlraum, which means literally hollow space.  It is a simple device that traps all the energy that reaches the aperture.  The cross section of a hohlraum is shown  below.  The hole has the attributes of a nearly perfect thermal black body.Condensation:           Fluid in gaseous or vapor phase changes to liquid state, with the liberation of heat from the vapor. There are two types of condensation.  They are film condensation and Drop wise condensation.           In film condensation, liquid drop lets cover the surface and further condensation is not possible.  But in drop wise condensation, there is not wetting of cooling surface.  Apart of the condensation film is always exposed to vapor without the formation of liquid film.Heat Exchangers:           It is a equipment designed for the effective heat transfer between two fluids, where one of them is hot and other is cold.  The purpose may be to remove heat or add heat.  Examples of such heat exchangers are Automobile radiators, Air and water coolers & Air and Water Heaters.          Based on the nature of heat exchange process, the following are the classifications.Direct contact - Both heat and mass transfer takes place. Regenerators - The hot fluid flows in a matrix or tube followed by the cold fluid or vice versa. Recuperators - Fluid flows simultaneously on either side of a separating unit.  No physical contact of the fluids.  The heat is transferred as follows. Convection - Hot fluid & Wall. Conduction - Across the wall. Convection - Wall & Cold fluid.Parallel Flow Arrangement - The hot and cold fluids enter and leave the unit in the same direction ( Unidirectional )Counter Flow Arrangement - The two fluids enter the units from opposite ends, and travel in opposite directions.  Maximum heat transfer rate.Cross Flow Arrangement - The fluids travel at right angles to each other.The figure of parallel, counter flow and cross flow arrangement is shown below.
Parallel and cross flow arrangement
Cross flow arrangement
Fins:            The conductive removal of heat from a surface can be substantially improved if we put extensions on that surface to increase its area.  These extensions can take a variety of forms.  The surface of a commercial heat exchanger tubing can be extended with protrusions called as fins.Mass Transfer:           The transfer of one constituent from a region of higher concentration to a region of lower concentrations called mass transfer.  There are two types of mass transfer.  They are diffusive and convective mass transfer.  Examples of mass transfer areEvaporation of petrol in the carburetor of engine.Evaporation of liquid ammonia in the atmosphere of hydrogen in a electro flux refrigerator.Compressors:            A simple definition of a compressor is a device used to pressurize a fluid, including liquids and gases. There are many different kinds of compressors, but typically the main purpose of using a compressor is to raise the pressure of a liquid or gas. Compressors are found in both gas power cycles and vapor compression refrigeration cycles.            A compressor converts shaft power to a rise in enthalpy of a fluid. The fluid, often a gas, enters the compressor at a low pressure (low enthalpy) and exits at a high pressure (high enthalpy). The rotating shaft is attached to a blade assembly. The rotating blades push on the gas and increase the pressure, thereby increasing the enthalpy. Compressors are continuous flow processes, and can be either axial or radial.
NUMERICAL PROBLEMSProblem 1:  The front of a slab of lead ( k = 35 W/m.K ) is kept at 110o C and the back is kept at 50o C.  If the are of the slab is 0.4m2 and it is 0.03m thick, compute the heat flux, q, and the heat transfer rate, Q.Heat flux q = - K (dT / dX) = -35 x ( 50 - 110 ) / 0.03 = 70,000 W/m2Heat transfer rate = qA = 70,000 x 0.4 = 28 Kw.Problem 2:  The heat flux q is 6000 W/m2 at the surface of an electrical heater.  The heater temperature is 120o C, when it is cooled by air at 70o C.  What is the average convective heat transfer coefficient, h?  Convective heat transfer coefficient h = q / dT = 6000 / (120 - 70) = 120 W/m2KHEAT AND MASS TRANSFER BOOKS
  1. Fundamentals of Heat and Mass Transfer, 5th Edition by Frank P. Incropera, David P. Dewitt
  1. The Heat Transfer Problem Solver: A Complete Solution Guide to Any Textbook (Rea's Problem Solvers) by Staff of Research and Education Association, James Ogden
  1. Schaum's Outline of Heat Transfer by Donald R. Pitts, Leighton E. Sissom (Contributor)
  1. Heat Transfer by J. P. Holman
  1. Handbook of Heat Transfer by Warren M. Rohsenow, James P. Hartnett,Young I. Cho. (Editors)
  1. Compact Heat Exchangers by W. M. Kays, A. L. London
  1. Heat Exchangers: Selection, Rating and Thermal Design, Second Edition by Hongtan Liu, Sadik Kaka
HEAT AND MASS TRANSFER

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