HEAT EXCHANGERS

Heat exchangers are devices used to transfer heat energy from one fluid to another. Typical heat exchangers experienced by us in our daily lives include condensers and evaporators used in air conditioning units and refrigerators.Boilers and condensers in thermal power plants are examples of large industrial heat exchangers. There are heat exchangers in our automobiles in the form of radiators and oil coolers. Heat exchangers are also abundant in chemical and process industries. There is a wide variety of heat exchangers for diverse kinds of uses, hence the construction also would differ widely. However, in spite of the variety, most heat exchangers can be classified into some common types based on some fundamental design concepts.

MECHANICAL PROPERTIES OF MATERIALS

1. MECHANICAL PROPERTIES

ØTensile, Compressive, Shear & Bulk Strength

ØDuctility

ØYield Strength

ØToughness

ØAnelasticity

ØViscoelasticity

ØHardness

ØCreep

ØFatigue

ØStress Relaxation

ØImpact Strength

TENSILE, COMPRESSIVE, SHEAR & BULK STRESS

ØUnder Tensile Stress, load increases length of material, whereas under Compressive Stress, load decreases length of material. In both cases, nature of stress-strain curve remains same

ØShear Stress is force per unit area parallel to surface area of specimen as shown in figure, which is measured in terms of angle of shear

ØShear stress (t) and shear strain (g) are related with each other by ‘Shear Modulus of Rigidity (G)’ 

   and given as t = G g

ØBulk Stress is force per unit area applied on material uniformly in all directions (hydrostatic pressure), so that material changes its volume without changing its shape

ØRatio of bulk stress to bulk strain is known as ‘Bulk Modulus’   [-dp / (dV/V)], where negative sign implies that as pressure increases, volume decreases

ØReciprocal of bulk modulus is known as ‘Compressibility’

ØPoisson’s Ratio is ratio of strains in x or y-directions to that of in z-direction, i.e. u = - (ex / ez) = - (ey / ez) (normally lies in range of 0.25 – 0.35 for metals)

ØElongation in one direction (z-direction) produces compression in other two directions (x and y-directions)

DUCTILITY

ØMaximum percentage elongation for a material or maximum percentage reduction in cross-sectional area (normal to tensile stress) for a material without fracture

ØDuctility = % EL = [(change in length / original length) * 100]

ØDuctility = [(change in diameter / original diameter) * 100]

ØPure metals generally have ductility in range of 35 – 50 %

YIELD STRENGTH

ØStrength of material after which it starts yielding plastically without any appreciable increase in applied stress (perfectly plastic material)

ØDue to strain hardening, yield strength / stress of material goes on increasing up to maximum tensile / compressive strength after which, necking and subsequently fracture takes place

GENERALISED GAS EQUATION

An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces.

Ideal gas law is a generalization containing both Boyle's law and Charles's law as special cases and states that:

In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature. An ideal gas can be characterized by three state variables:

absolute pressure (P), volume (V), and absolute temperature (T).

The relationship between them may be deduced from kinetic theory and is called the Ideal gas law.

PV = kT = nRT

where

n is the total number of moles, NA = Avogadro's Number = 6.02217 · 1023 molecules/mole, R = Universal gas constant = 8.314 J/K · mol , k = Boltzmann Constant = R/NA = 1.380622 · 10-23 J/K.

The ideal gas law can be viewed as arising from the kinetic pressure of gas molecules colliding with the walls of a container in accordance with Newton's laws. But there is also a statistical element in the determination of the average kinetic energy of those molecules. The temperature is taken to be proportional to this average kinetic energy; this invokes the idea of kinetic temperature.

ARCHIMEDES PRINCIPLE

Any body completely or partially submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

Everyone has experienced Archimedes' principle. As an example of a common experience, recall that it is relatively easy to lift someone if the person is in a swimming pool whereas lifting that same individual on dry land is much harder. Evidently, water provides partial support to any object placed in it. The upward force that the fluid exerts on an object submerged in it is called the buoyant force. According to the Archimedes' principle, The magnitude of the buoyant force always equals the weight of the fluid displaced by the object. The buoyant force acts vertically upward through what was the center of gravity of the displaced fluid.

B = W

Where B is the buoyant force and W is the weight of the displaced fluid. The units of the buoyant force and weight are newton ( N ) in SI and "pound force" ( lbf) in British Engineering units. The buoyant force acting on the steel is the same as the buoyant force acting on a cube of fluid of the same dimensions. This result applies for a submerged object of any shape, size, or density.

HOOK'S LAW OF STRESS & STRAIN

The generalized Hooke's Law can be used to predict the deformations caused in a given material by an arbitrary combination of stresses.

The linear relationship between stress and strain applies for   

where:

E is the Young's Modulus n is the Poisson Ratio

The generalized Hooke's Law also reveals that strain can exist without stress. For example, if the member is experiencing a load in the y-direction (which in turn causes a stress in the y-direction), the Hooke's Law shows that strain in the x-direction does not equal to zero. This is because as material is being pulled outward by the y-plane, the material in the x-plane moves inward to fill in the space once occupied, just like an elastic band becomes thinner as you try to pull it apart. In this situation, the x-plane does not have any external force acting on them but they experience a change in length. Therefore, it is valid to say that strain exist without stress in the x-plane.

NEWTON'S LAW OF COOLING

Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature.

Where  is the rate of change of temperature of an object with respect to time t.  is the ambient temperature and K is the experimental constant  From intial condition,  ,  is obtained as follow

K can experimentally be found easily knowing that ,

VAPOUR COMPRESSION REFRIGERATION CYCLE

Vapor Compression Refrigeration Cycle

One of the applications that involves thermodynamic principles is the refrigerator. The figure below is a schematic diagram of the components found in a typical refrigerator. The refrigerant enters the compressor as a slightly superheated vapor at a low pressure. It then leaves the compressor and enters the condenser as a vapor at some elevated pressure, where the refrigerant is condensed as a result of heat transfer to cooling water or to the surroundings. The refrigerant then leaves the condenser as a high-pressure liquid. The pressure of the liquid is decreased as it flows through the expansion valve and, as a result, some of the liquid flashes into vapor. The remaining liquid, now at a lower pressure, is vaporized in the evaporator as a result of heat transfer from the refrigerated space. This vapor then enters the compressor.