# P K Nag Heat And Mass Transfer Pdf

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## Heat and Mass Transfer by p k Nag 0070702535

A fl ux like heat transfer, momentum transfer, mass transfer, electricity and chemical reaction rate is linearly proportional to the respective conjugate force of temperature gradient, velocity gradient, concentration gradient, electric potential gradient and chemical affi nity, the constant of proportionality being a property of the medium, like thermal conductivity, viscosity, diffusion coeffi cient and electrical conductivity.

It is a law of nature phenom enological law which states that a driving force causes the respective fl ux from a higher to a lower potential. The reverse never happens spontaneously. The transfer process indicates the tendency of a system to proceed towards equilibrium.

For example, in a solid body with a nonuniform temperature distribution, energy is transferred so as to establish a uniform temperature distribution in the body. Heat is defi ned as energy transferred by virtue of a temperature difference or gradient. Heat transfer is a vector quantity, fl owing in the direction of decreasing temperature, with a negative temperature gradient.

In the science of thermodynamics, the important parameter is the quantity of heat transferred during a process. In the subject of heat transfer, attention is directed to the rate at which heat is transferred. Thermodynamics is concerned with the transition of a system from one equilibrium state to another, and is based principally on the two laws of nature, the fi rst law and the second law of thermodynamics. It is the science of heat transfer which is concerned with the estimation of the rate at which heat is transferred, the duration of heating and cooling for a certain heat duty and the surface area required to accomplish that heat duty.

When a small amount of perfume vapour is sprayed into a room of air, the mass transfer process causes the perfume vapour to diffuse throughout the room until its concentration is uniform, indicating an equilibrium condition. In an electrically conduct ing material with a nonuniform electrical potential voltage distribution, electric charge will fl ow until a uniform potential distribution is set up. In all transfer processes we are con cerned with rates at which changes in properties of a system occur.

In the fl ow of a viscous fl uid, the viscous frictional stresses may be related to the rate of change of momentum of a system. Heat conduction may be related to the rate of change of internal energy of system. Mass diffusion may be related to the rate of change of composition of a mixture due to transfer of one or more of the component species.

There are three distinct modes in which heat transmission can take place: conduction, radiation and convection. Strictly speaking, only conduction and radiation should be classifi ed as heat transfer processes, because only these two modes depend on the existence of a temperature difference. Convection refers to the mass motion of a fl uid, and the convective heat transfer between a solid wall and a fl uid depends not only on the tempera ture difference, but also on the mass transport of the fl uid.

However, since convection, like conduction and radiation, also accomplishes energy transfer from regions of higher temperature to regions of lower temperature, the term 'heat transfer by convection' has become generally accepted.

Thermodynamics deals with systems in equilibrium and calculates the energy transferred to change a system from one equilibrium state to another. However, it cannot tell the duration for which heat has to fl ow to change that state of equilibrium.

The time depends on various factors such as the temperature of the oil bath, physical properties of the oil, motion of the oil etc. An appropriate heat transfer analysis considers all these factors. Analysis of heat transfer processes requires some concepts of thermodynamics. The fi rst law of thermodynamics states the principle of conservation of energy and it is expressed in the form of an energy balance for a system. A closed system containing a fi xed mass of a solid Fig. There is heat transfer into the system at a rate Q W , and heat may be generated internally within the solid, say, by nuclear fi ssion or electrical current at a rate Q G W.

The principle of energy conservation requires that over a time interval Dt s. Since, all heat transfer processes occur through fi nite tempera ture differences overcoming thermal irreversibility, the heat transfer area or operating variables can be optimized in regard to two or more irreversibilities following the principle of minimization of entropy generation or exergy destruction [3].

The roles of thermodynamics, cost or economics, and heat transfer, simultaneously act upon to yield an energy-effi cient equipment, which is now a concern of the engineers. Fourier's law after the French scientist J. Fourier who proposed it in of heat conduction states that the rate of heat transfer is linearly proportional to the temperature gra dient. It may be noted that temperature can be given in kelvin or degree Celsius in Eq. The magnitude of the thermal conductivity k for a given substance very much depends on its microscopic structure and also tends to vary somewhat with temperature.

For the simple case of steady-state one-dimensional heat fl ow through a plane wall Fig. Resistance ConceptHeat fl ow has an analogy in the fl ow of electricity.

Ohm's law states that the current I Ampere fl owing through a wire Fig. The similarity of Eqs 1. The rate of heat conduction is then 1. Composite WallsFor a composite wall, as shown in Fig. The rate of heat conduction is the same through all sections. The slope of the temperature profi le in each depends on the thermal conductivity k of the material of that section. The lower the k, the more will be the slope and the higher is the temperature difference. The higher the k, the less will be the slope and the lower is the temperature difference.

The total thermal resistance. The walls are assumed to be in good thermal contact, with no contact resis tance. Conduction can occur in a wall with two different materials in parallel Fig. If the temperatures over the left and right faces are uniform at T 1 and T 2 , the equivalent thermal circuit is shown to the right of the physical system.

This resistance is primarily a function of surface The direct contact between the solid surfaces, as shown in the expanded view, takes place at a limited number of spots, and the voids between them usually are fi lled with air or the surrounding fl uid. Heat transfer through the fl uid fi lling the voids is mainly by conduction, since there is no convection in such a thin layer of fl uid and the radiation effects are negligible at normal temperatures.

An increase in contact pressure can reduce the contact resistance signifi cantly. The interfacial fl uid also affects the thermal resistance, as shown in Table 1. Putting a viscous liquid like glycerin on the interface reduces the contact resistance 10 times with respect to air at a given pressure. A thermally conducting liquid called a thermal grease such as silicone oil is applied between the contact surfaces before they are pressed against each other.

It is commonly done when attaching electronic components such as power transistors to heat sinks. Numerous experimental measurements have been made of the contact resistance at the interface between dissimilar metallic surfaces, but no satisfactory correlations have been found [2]. Thermal ConductivityAs defi ned by Fourier's law, Eq. A layer of solid material of known thickness and area can be heated from one side by an electric resistance heater of known output. If the other surface of the heater is perfectly insulated, all the heat generated by the resistance heater will be transferred through the material whose conductivity is to be determined.

Then measuring the two surface temperatures T 1 and T 2 of the layers of material when steady state has been reached, the thermal conductivity can be estimated, as shown in Fig. For engineering purposes, the experimentally measured values of thermal conductivity are gener ally used.

These values can be predicted fairly well for gases with the help of kinetic theory of gases. But in the case of liquids and solids, theories are not adequate to predict thermal conductivity with suffi cient accuracy. Table 1. It may be noted that pure metals are the best conductors and gases are the poorest ones.

The mechanism of thermal conduction in a gas can be explained on a molecular level from basic concepts of the kinetic theory of gases [3]. The kinetic energy KE of a molecule is a function of temperature. Molecules in a high-temperature region have higher KE and hence higher velocities than those in a lower-temperature region.

Since molecules are in continuous random motion, as they collide with one another they exchange energy as well as momentum. When a molecule moves from a higher-temperature region to a lower-temperature region, it transports KE from the higher-to the lower-temperature part of the system.

Upon colli sion with slower molecules, the faster molecule gives up some of its energy. In this manner thermal energy is transferred from higher to lower-temperature regions in gas by molecular motion. The faster the molecules move, the faster they will trans port energy.

Thus, the transport property called thermal conduc tivity depends on the temperature of the gas. At moderate pres sures the space between molecules is large compared to the size of a molecule. Thermal conductivity of gases is therefore essentially independent of pressure and density. Figure 1. The basic mechanism of heat conduction in liquids is quali tatively similar to that in gases.

However, molecular condi tions in liquids are more diffi cult to describe and the details of the conduction mechanisms in liquids are not well understood.

The curves in Fig. For most liquids, the thermal conductivity decreases with temperature, but water is a notable exception. Generally, the thermal conductivity of liquids decreases with increasing molecular weight. Solid materials consist of free electrons and atoms in a periodic lattice arrangement. Heat can be conducted in a solid by two mechanisms: a migration of free electrons k e b lattice vibration k l These two effects are additive, i. Since electrons transport electric charge in a manner similar to the way in which they carry thermal energy from a higher to a lowertemperature region, good electrical conductors are also good heat conductors, whereas good electrical insulators are poor heat conductors.

In non-metallic solids there is little or no electronic transport and the conductivity is therefore determined primarily by lattice vibration.

## Heat Transfer PK Nag PDF

The best ways is to study thermodynamics is through problems, you must know how to apply theoretical concepts through problems and to do so you. Thermodynamics- the Backbone of Mechanical Engineering therefore Mastering Thermodynamics is most important many of the subjects which. Microscopic thermodynamics or statistical thermodynamics Macroscopic thermodynamics or classical thermodynamics A quasi-static process is also called a reversible process. Intensive and Extensive Properties Intensive property: Whose value is independent of the size or extent i. Extensive property: Whose value depends on the size or extent i. If mass is increased, the value of extensive property also increases.

## p k Nag Solution

The best ways is to study thermodynamics is through problems, you must know how to apply theoretical concepts through problems and to do so you must solve these problems. Thermodynamics- the Backbone of Mechanical Engineering thereforeMastering Thermodynamics is most important many of the subjects which come in later like Heat and Mass Transfer, Refrigeration and Air Conditioning, Internal Combustion Engine will require fundamental knowledge of Thermodynamics. Every effort has been made to see that there are no errors typographical or otherwise in the material presented. However, it is still possible that there are a few errors serious or otherwise. Microscopic thermodynamics or statistical thermodynamics Macroscopic thermodynamics or classical thermodynamics A quasi-static process is also called a reversible process.

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Heat and Mass Transfer P. Nag This book on Heat and Mass Transfer provides a highly intuitive and practical understanding of the topics by emphasizing the physics and the underlying physical phenomena involved. Read Online Heat and Mass Transfer

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