Fluid mechanics is the branch of physics that deals with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. A fluid is a substance that cannot resist a shear stress by a static deflection and deforms continuously as long as the shear stress is applied. Fluid mechanics can be divided into fluid statics or the study of fluids at rest; and fluid dynamics or the study of the effect of forces on fluid motion. Fluid mechanics has a wide range of applications, including mechanical engineering, chemical engineering, geophysics, astrophysics, and biology. Fluid mechanics, especially fluid dynamics, is an active field of research with many problems that are partly or wholly unsolved. Commercial code based on numerical methods is used to solve the problems of fluid mechanics. The principles of these methods are developed by computational fluid dynamics (CFD), a modern discipline that is devoted to this approach to solve the aforementioned problems.

A short history of fluid mechanics from the beginning up to now is as follows:

ā¢ The fundamental principles of hydrostatics and dynamics were given by Archimedes (285ā212 BC) in his work On Floating Bodies, around 250 BC. Archimedes has developed the law of buoyancy, also known as Archimedes' Principle [1].

ā¢ Islamicate scientists, particularly Abu Rayhan Biruni (973ā1048) and later Al-Khazini (1115ā30), were the first to apply experimental scientific methods to fluid mechanics, especially in the field of fluid statics, to determine specific weights.

ā¢ In the 9th century, BanÅ« MÅ«sÄ brothers' Book of Ingenious Devices described a number of early automatic controls in fluid mechanics [2]. Two-step level control for fluids, which was an early form of discontinuous variable structure controls, was developed by the BanÅ« MÅ«sÄ brothers [3]. They also described an early feedback controller for fluids.

ā¢ In 1206, Al-Jazari's Book of Knowledge of Ingenious Mechanical Devices described many hydraulic machines [4]. Of particular importance were his water-raising pumps. Al-Jazari also invented a twin-cylinder reciprocating piston suction pump, which included the first suction pipes, suction pumping, and double-action pumping, and made early uses of valves and a crankshaft-connecting rod mechanism.

ā¢ Then, Leonardo da Vinci (1452ā1519) derived the equation of conservation of mass in a one-dimensional steady flow [5].

ā¢ A Frenchman, Edme Mariotte (1620ā84), built the first wind tunnel and tested models in it.

ā¢ The effects of friction and viscosity in diminishing the velocity of running water were noticed in the Principia of Sir Isaac Newton, which threw much light upon several branches of hydromechanics.

ā¢ In 1687, Isaac Newton (1642ā1727) postulated his laws of motion and the law of viscosity of the linear fluids, which is now called newtonian. The theory first yielded to the assumption of a āperfectā or frictionless fluid, and 18th century mathematicians (Daniel Bernoulli, Leonhard Euler, Jean d'Alembert, Joseph-Louis Lagrange, and Pierre-Simon Laplace) introduced many beautiful solutions to frictionless-flow problems. At the end of the 19th century, unification between experimental hydraulics and theoretical hydrodynamics finally began.

ā¢ William Froude (1810ā79) and his son Robert (1846ā1924) developed laws of model testing.

ā¢ Lord Rayleigh (1842ā1919) proposed the technique of dimensional analysis, and Osborne Reynolds (1842ā1912) published the classic pipe experiment in 1883, which showed the importance of the dimensionless Reynolds number named after him.

ā¢ Meanwhile, viscous-flow theory was available but unexploited since Navier (1785ā1836) and Stokes (1819ā1903) had successfully added the newtonian viscous terms to the governing equations of motion. Unfortunately, the resulting NavierāStokes equations were too difficult to analyze arbitrary flows.

ā¢ In 1904 a German engineer, Ludwig Prandtl (1875ā1953), showed that fluid flows with small viscosity (water and air flows) can be divided into a thin viscous layer, or boundary layer, near solid surfaces and interfaces, patched onto a nearly inviscid outer layer, where the Euler and Bernoulli equations apply. Boundary layer theory is the most important tool in modern flow analysis.

### 1.1.2. Heat Transfer

In physics, heat is defined as the transfer of thermal energy across a well-defined boundary around a thermodynamic system. Heat transfer is a process function (or path function). It means that the amount of heat transferred that changes the state of a system depends not only on the net difference between the initial and final states of the process but also on how that process occurs. The rate of heat transfer is dependent on the temperatures of the systems and the properties of the intervening medium through which the heat is transferred. In engineering contexts, the term heat is taken as synonymous to thermal energy. This usage has its origin in the historical interpretation of heat as a fluid (caloric) that can be transferred by various causes. The transport equations for thermal energy (Fourier's law), mechanical momentum (Newton's law for fluids), and mass transfer (Fick's laws of diffusion) are similar, and analogies among these three transport processes have been developed to facilitate prediction of conversion from any one to the others. The fundamental modes of heat transfer are Advection, Conduction or diffusion, Convection, and Radiation. Types of phase transition occurring in the three fundamental states of matter include: deposition, freezing and solid to solid transformation in solid, boiling/evaporation, recombination/deionization, and sublimation in gas, and condensation and melting/fusion in liquid.

The history of heat has a prominent place in the history of science. The ancients viewed heat as related to fire. The ancient Egyptians in 3000 BC viewed heat as related to origin mythologies. It traces its origins to the first hominids to make fire and to speculate on its operation and meaning to modern day physicists who study the microscopic nature of heat. The history of heat is a precursor for developments and theories in the history of thermodynamics.

ā¢ Around 500 BC, the Greek philosopher Heraclitus and Hippocrates proposed the first theory about heat and its principles.

ā¢ In the 11th century AD, AbÅ« RayhÄn BÄ«rÅ«nÄ« cites movement and friction as causes of heat, which, in turn, produces the element of fire, and lack of movement as the cause of cold near the geographical poles [6].

ā¢ Around 1600, the English philosopher and scientist Francis Bacon surmised that heat itself, its essence and quiddity, is motion and nothing else.

ā¢ In 1761, Scottish chemist Joseph Black discovered that ice absorbs heat without changing the temperature when it is melting. Between 1759 and 1763, he formulated a theory of latent heat on which his scientific fame chiefly rests and also showed that different substances have different specific heats.

ā¢ James Watt invented the Watt engine. The ability to use heat transfer to perform work allowed the invention and development of the steam engine by inventors such as Thomas Newcomen and James Watt. In addition, in 1797 a cannon manufacturer Sir Benjamin Thompson, Count Rumford, demonstrated that through the use of friction it was possible to convert work to heat [7].

ā¢ In 1824 the French engineer Sadi Carnot set the importance of heat transfer: āproduction of motive power is due not to an actual consumption of caloric, but to its transportation from a warm body to a cold body, i.e., to its re-establishment of equilibrium.ā According to Carnot, this principle applies to any machine set in motion by heat [7].

ā¢ The work of Joule and Mayer demonstrated that heat and work were equivalent forms of energy, and led to the statement of the principle of the conservation of energy by Hermann von Helmholtz in 1847.

ā¢ In 1850, Clausius demonstrated that caloric theory could be reconciled with kinetic theory provided that the conservation of energy was employed rather than the movement of a substance and stated the First Law of Thermodynamics.