Methods of Heat Transfer Introduction to Thermal Physics Temperature and Thermometers Thermometers as Speedometers What is Heat? Methods of Heat Transfer Rates of Heat Transfer If you have been following along since the beginning of this lesson, then you have been developing a progressively sophisticated understanding of temperature and heat. You should be developing a model of matter as consisting of particles which vibrate (wiggle about a fixed position), translate (move from one location to another) and even rotate (revolve about an imaginary axis). These motions give the particles kinetic energy. Temperature is a measure of the average amount of kinetic energy possessed by the particles in a sample of matter. The more the particles vibrate, translate and rotate, the greater the temperature of the object. You have hopefully adopted an understanding of heat as a flow of energy from a higher temperature object to a lower temperature object. It is the temperature difference between the two neighboring objects that causes this heat transfer. The heat transfer continues until the two objects have reached thermal equilibrium and are at the same temperature. The discussion of heat transfer has been structured around some everyday examples such as the cooling of a hot mug of coffee and the warming of a cold can of pop. Finally, we have explored a thought experiment in which a metal can containing hot water is placed within a Styrofoam cup containing cold water. Heat is transferred from the hot water to the cold water until both samples have the same temperature. Now we should probe some of the following questions: What is happening at the particle level when energy is being transferred between two objects? Why is thermal equilibrium always established when two objects transfer heat? How does heat transfer work within the bulk of an object? Is there more than one method of heat transfer? If so, then how are they similar and different than one another? Conduction - A Particle View Let's begin our discussion by returning to our thought experiment in which a metal can containing hot water was placed within a Styrofoam cup containing cold water. Heat is transferred from the hot water to the cold water until both samples have the same temperature. In this instance, the transfer of heat from the hot water through the metal can to the cold water is sometimes referred to as conduction. Conductive heat flow involves the transfer of heat from one location to another in the absence of any material flow. There is nothing physical or material moving from the hot water to the cold water. Only energy is transferred from the hot water to the cold water. Other than the loss of energy, there is nothing else escaping from the hot water. And other than the gain of energy, there is nothing else entering the cold water. How does this happen? What is the mechanism that makes conductive heat flow possible? A question like this is a particle-level question. To understand the answer, we have to think about matter as consisting of tiny particles atoms, molecules and ions. These particles are in constant motion; this gives them kinetic energy. As mentioned previously in this lesson, these particles move throughout the space of a container, colliding with each other and with the walls of their container. This is known as translational kinetic energy and is the main form of kinetic energy for gases and liquids. But these particles can also vibrate about a fixed position. This gives the particles vibrational kinetic energy and is the main form of kinetic energy for solids. To put it more simply, matter consists of little wigglers and little bangers. The wigglers are those particles vibrating about a fixed position. They possess vibrational kinetic energy. The bangers are those particles that move through the container with translational kinetic energy and collide with the container walls. The container walls represent the perimeters of a sample of matter. Just as the perimeter of your property (as in real estate property) is the furthest extension of the property, so the perimeter of an object is the furthest extension of the particles within a sample of matter. At the perimeter, thelittle bangers are colliding with particles of another substance - the particles of the container or even the surrounding air. Even the wigglers that are fixed in a position along the perimeter are doing some banging. Being at the perimeter, their wiggling results in collisions with the particles that are next to them; these are the particles of the container or of the surrounding air. At this perimeter or boundary, the collisions of the little bangers and wigglers are elastic collisions in which the total amount of kinetic energy of all colliding particles is conserved. The net effect of these elastic collisions is that there is a transfer of kinetic energy across the boundary to the particles on the opposite side. The more energetic particles will lose a little kinetic energy and the less energetic particles will gain a little kinetic energy. Temperature is a measure of the average amount of kinetic energy possessed by the particles in a sample of matter. So on average, there are more particles in the higher temperature object with greater kinetic energy than there are in the lower temperature object. So when we average all the collisions together and apply the principles associated with elastic collisions to the particles within a sample of matter, it is logical to conclude that the higher temperature object will lose some kinetic energy and the lower temperature object will gain some kinetic energy. The collisions of our little bangers and wigglers will continue to transfer energy until the temperatures of the two objects are identical. When this state of thermal equilibrium has been reached, the average kinetic energy of both objects' particles is equal. At thermal equilibrium, there are an equal number of collisions resulting in an energy gain as there are collisions resulting in an energy loss. On average, there is no net energy transfer resulting from the collisions of particles at the perimeter. At the macroscopic level, heat is the transfer of energy from the high temperature object to the low temperature object. At the particle level, heat flow can be explained in terms of the net effect of the collisions of a whole bunch of little bangers. Warming and cooling is the macroscopic result of this particle-level phenomenon. Now let's apply this particle view to the scenario of the metal can with the hot water positioned inside of a Styrofoam cup containing cold water. On average, the particles with the greatest kinetic energy are the particles of the hot water. Being a fluid, those particles move about with translational kinetic energy and bang upon the particles of the metal can. As the hot water particles bang upon the particles of the metal can, they transfer energy to the metal can. This warms the metal can up. Most metals are good thermal conductors so they warm up quite quickly throughout the bulk of the can. The can assumes nearly the same temperature as the hot water. Being a solid, the metal can consists of little wigglers. The wigglers at the outer perimeter of the metal can bang upon particles in the cold water. The collisions between the particles of the metal can and the particles of the cold water result in the transfer of energy to the cold water. This slowly warms the cold water up. The interaction between the particles of the hot water, the metal can and the cold water results in a transfer of energy outward from the hot water to the cold water. The average kinetic energy of the hot water particles gradually decreases; the average kinetic energy of the cold-water particles gradually increases; and eventually, thermal equilibrium would be reached at the point that the particles of the hot water and the cold water have the same average kinetic energy. At the macroscopic level, one would observe a decrease in temperature of the hot water and an increase in temperature of the cold water. The mechanism in which heat is transferred from one object to another object through particle collisions is known as conduction. In conduction, there is no net transfer of physical stuff between the objects. Nothing material moves across the boundary. The changes in temperature are wholly explained as the result of the gains and losses of kinetic energy during collisions. Conduction Through The Bulk of an Object We have discussed how heat transfers from one object to another through conduction. But how does it transfer through the bulk of an object? For instance, suppose we pull a ceramic coffee mug out of the cupboard and place it on the countertop. The mug is at room temperature - maybe at 26°C. Then suppose we fill the ceramic coffee mug with hot coffee at a temperature of 80°C. The mug quickly warms up. Energy first flows into the particles at the boundary between the hot coffee and the ceramic mug. But then it flows through the bulk of the ceramic to all parts of the ceramic mug. How does heat conduction occur in the ceramic itself? The mechanism of heat transfer through the bulk of the ceramic mug is described in a similar manner as it before. The ceramic mug consists of a collection of orderly arranged wigglers. These are particles that wiggle about a fixed position. As the ceramic particles at the boundary between the hot coffee and the mug warm up, they attain a kinetic energy that is much higher than their neighbors. As they wiggle more vigorously, they bang into their neighbors and increase their vibrational kinetic energy. These particles in turn begin to wiggle more vigorously and their collisions with their neighbors increase their vibrational kinetic energy. The process of energy transfer by means of the little bangers continues from the particles at the inside of the mug (in contact with the coffee particles) to the outside of the mug (in contact with the surrounding air). Soon the entire coffee mug is warm and your hand feels it. This mechanism of conduction by particle-to-particle interaction is very common in ceramic materials such as a coffee mug. Does it work the same in metal objects? For instance, you likely have noticed the high temperatures attained by the metal handle of a skillet when placed upon a stovetop. The burners on the stove transfer heat to the metal skillet. If the handle of the skillet is metallic, it too attains a high temperature, certainly high enough to cause a bad burn. The transfer of heat from the skillet to the skillet handle occurs by conduction. But in metals, the conduction mechanism is slightly more complicated. In a manner similar to electrical conductivity, thermal conductivity in metals occurs by the movement of free electrons. Outer shell electrons of metal atoms are shared among atoms and are free to move throughout the bulk of the metal. These electrons carry the energy from the skillet to the skillet handle. The details of this mechanism of thermal conduction in metals are considerably more complex than the discussion given here. The main point to grasp is that heat transfer through metals occurs without any movement of atoms from the skillet to the skillet handle. This qualifies the heat transfer as being categorized as thermal conduction. Heat Transfer by Convection Is conduction the only means of heat transfer? Can heat be transferred through the bulk of an object in methods other than conduction? The answer is yes. The model of heat transfer through the ceramic coffee mug and the metal skillet involved conduction. The ceramic of the coffee mug and the metal of the skillet are both solids. Heat transfer through solids occurs by conduction. This is primarily due to the fact that solids have orderly arrangements of particles that are fixed in place. Liquids and gases are not very good conductors of heat. In fact, they are considered good thermal insulators. Heat typically does not flow through liquids and gases by means of conduction. Liquids and gases are fluids; their particles are not fixed in place; they move about the bulk of the sample of matter. The model used for explaining heat transfer through the bulk of liquids and gases involves convection. Convectionis the process of heat transfer from one location to the next by the movement of fluids. The moving fluid carries energy with it. The fluid flows from a high temperature location to a low temperature location. To understand convection in fluids, let's consider the heat transfer through the water that is being heated in a pot on a stove. Of course the source of the heat is the stove burner. The metal pot that holds the water is heated by the stove burner. As the metal becomes hot, it begins to conduct heat to the water. The water at the boundary with the metal pan becomes hot. Fluids expand when heated and become less dense. So as the water at the bottom of the pot becomes hot, its density decreases. Differences in water density between the bottom of the pot and the top of the pot results in the gradual formation of circulation currents. Hot water begins to rise to the top of the pot displacing the colder water that was originally there. And the colder water that was present at the top of the pot moves towards the bottom of the pot where it is heated and begins to rise. These circulation currents slowly develop over time, providing the pathway for heated water to transfer energy from the bottom of the pot to the surface. Convection also explains how an electric heater placed on the floor of a cold room warms up the air in the room. Air present near the coils of the heater warm up. As the air warms up, it expands, becomes less dense and begins to rise. As the hot air rises, it pushes some of the cold air near the top of the room out of the way. The cold air moves towards the bottom of the room to replace the hot air that has risen. As the colder air approaches the heater at the bottom of the room, it becomes warmed by the heater and begins to rise. Once more, convection currents are slowly formed. Air travels along these pathways, carrying energy with it from the heater throughout the room. Convection is the main method of heat transfer in fluids such as water and air. It is often said thatheat rises in these situations. The more appropriate explanation is to say that heated fluid rises. For instance, as the heated air rises from the heater on a floor, it carries more energetic particles with it. As the more energetic particles of the heated air mix with the cooler air near the ceiling, the average kinetic energy of the air near the top of the room increases. This increase in the average kinetic energy corresponds to an increase in temperature. The net result of the rising hot fluid is the transfer of heat from one location to another location. The convection method of heat transfer always involves the transfer of heat by the movement of matter. This is not to be confused with the caloric theory discussed earlier in this lesson. In caloric theory, heat was the fluid and the fluid that moved was the heat. Our model of convection considers heat to be energy transfer that is simply the result of the movement of more energetic particles. The two examples of convection discussed here - heating water in a pot and heating air in a room - are examples of natural convection. The driving force of the circulation of fluid is natural - differences in density between two locations as the result of fluid being heated at some source. (Some sources introduce the concept of buoyant forces to explain why the heated fluids rise. We will not pursue such explanations here.) Natural convection is common in nature. The earth's oceans and atmosphere are heated by natural convection. In contrast to natural convection,forced convection involves fluid being forced from one location to another by fans, pumps and other devices. Many home heating systems involve force air heating. Air is heated at a furnace and blown by fans through ductwork and released into rooms at vent locations. This is an example of forced convection. The movement of the fluid from the hot location (near the furnace) to the cool location (the rooms throughout the house) is driven or forced by a fan. Some ovens are forced convection ovens; they have fans that blow heated air from a heat source into the oven. Some fireplaces enhance the heating ability of the fire by blowing heated air from the fireplace unit into the adjacent room. This is another example of forced convection. Heat Transfer by Radiation A final method of heat transfer involves radiation. Radiation is the transfer of heat by means ofelectromagnetic waves. To radiate means to send out or spread from a central location. Whether it is light, sound, waves, rays, flower petals, wheel spokes or pain, if something radiates then it protrudes or spreads outward from an origin. The transfer of heat by radiation involves the carrying of energy from an origin to the space surrounding it. The energy is carried by electromagnetic waves and does not involve the movement or the interaction of matter. Thermal radiation can occur through matter or through a region of space that is void of matter (i.e., a vacuum). In fact, the heat received on Earth from the sun is the result of electromagnetic waves traveling through the void of space between the Earth and the sun. All objects radiate energy in the form of electromagnetic waves. The rate at which this energy is released is proportional to the Kelvin temperature (T) raised to the fourth power. Radiation rate = k•T4 The hotter the object, the more it radiates. The sun obviously radiates off more energy than a hot mug of coffee. The temperature also affects the wavelength and frequency of the radiated waves. Objects at typical room temperatures radiate energy as infrared waves. Being invisible to the human eye, we do not see this form of radiation. An infrared camera is capable of detecting such radiation. Perhaps you have seen thermal photographs or videos of the radiation surrounding a person or animal or a hot mug of coffee or the Earth. The energy radiated from an object is usually a collection or range of wavelengths. This is usually referred to as an emission spectrum. As the temperature of an object increases, the wavelengths within the spectra of the emitted radiation also decrease. Hotter objects tend to emit shorter wavelength, higher frequency radiation. The coils of an electric toaster are considerably hotter than room temperature and emit electromagnetic radiation in the visible spectrum. Fortunately, this provides a convenient warning to its users that the coils are hot. The tungsten filament of an incandescent light bulb emits electromagnetic radiation in the visible (and beyond) range. This radiation not only allows us to see, it also warms the glass bulb that contains the filament. Put your hand near the bulb (without touching it) and you will feel the radiation from the bulb as well. Thermal radiation is a form of heat transfer because the electromagnetic radiation emitted from the source carries energy away from the source to surrounding (or distant) objects. This energy is absorbed by those objects, causing the average kinetic energy of their particles to increase and causing the temperatures to rise. In this sense, energy is transferred from one location to another by means of electromagnetic radiation. The image at the right was taken by a thermal imaging camera. The camera detects the radiation emitted by objects and represents it by means of a color photograph. The hotter colors represent areas of objects that are emitting thermal radiation at a more intense rate. (Images courtesy Peter Lewis and Chris West of Standford's SLAC.) Our discussion on this page has pertained to the various methods of heat transfer. Conduction, convection and radiation have been described and illustrated. The macroscopic has been explained in terms of the particulate - an ongoing goal of this chapter of The Physics Classroom Tutorial. The last topic to be discussed in Lesson 1 is more quantitative in nature. On the next page, we will investigate the mathematics associated with the rate of heat transfer.

Basics of Heat Transfer In the simplest of terms, the discipline of heat transfer is concerned with only two things: temperature, and the flow of heat. Temperature represents the amount of thermal energy available, whereas heat flow represents the movement of thermal energy from place to place. On a microscopic scale, thermal energy is related to the kinetic energy of molecules. The greater a material's temperature, the greater the thermal agitation of its constituent molecules (manifested both in linear motion and vibrational modes). It is natural for regions containing greater molecular kinetic energy to pass this energy to regions with less kinetic energy. Several material properties serve to modulate the heat tranfered between two regions at differing temperatures. Examples include thermal conductivities, specific heats, material densities, fluid velocities, fluid viscosities, surface emissivities, and more. Taken together, these properties serve to make the solution of many heat transfer problems an involved process. Heat Transfer Mechanisms Heat transfer mechanisms can be grouped into 3 broad categories: Conduction: Regions with greater molecular kinetic energy will pass their thermal energy to regions with less molecular energy through direct molecular collisions, a process known as conduction. In metals, a significant portion of the transported thermal energy is also carried by conduction-band electrons. Fourier Law of Heat Conduction When there exists a temperature gradient within a body, heat energy will flow from the region of high temperature to the region of low temperature. This phenomenon is known as conduction heat transfer, and is described by Fourier's Law (named after the French physicist Joseph Fourier), This equation determines the heat flux vector q for a given temperature profile T and thermal conductivityk. The minus sign ensures that heat flows down the temperature gradient. Heat Equation (Temperature Determination) The temperature profile within a body depends upon the rate of its internally-generated heat, its capacity to store some of this heat, and its rate of thermal conduction to its boundaries (where the heat is transfered to the surrounding environment). Mathematically this is stated by the Heat Equation, along with its boundary conditions, equations that prescribe either the temperature T on, or the heat flux qthrough, all of the body boundaries W, In the Heat Equation, the power generated per unit volume is expressed by qgen. The thermal diffusivity a is related to thethermal conductivity k, the specific heat c, and the density rby, For Steady State problems, the Heat Equation simplifies to, Derivation of the Heat Equation The heat equation follows from the conservation of energy for a small element within the body, heat conducted in + heat generated within = heat conducted out + change in energy stored within We can combine the heats conducted in and out into one "net heat conducted out" term to give, net heat conducted out = heat generated within - change in energy stored within Mathematically, this equation is expressed as, The change in internal energy e is related to the body's ability to store heat by raising its temperature, given by, One can substitute for q using Fourier's Law of heat conduction from above to arrive at the Heat Equation, Conductive heat loss through cylinder or pipe walls Conductive heat loss through a cylinder or pipe wall can be expressed as q = 2 π k (ti - to) / ln(ro / ri)        (1) where q = heat transferred per unit time per unit length of cylinder or pipe (W/m, Btu/hr ft) k = thermal conductivity of the material (W/m.K or W/m oC, Btu/(hr oF ft2/ft)) to = temperature outside pipe or cylinder (K or oC, oF) ti = temperature inside pipe or cylinder (K or oC, oF) ln = the natural logarithm ro = cylinder or pipe outside radius (m, ft) ri = cylinder or pipe inside radius(m, ft) Example - Heat Transfer by Conduction A plane wall constructed of solid iron with thermal conductivity 70 W/moC, thickness 50 mm and with surface area 1 m by 1 m, temperature 150 oC on one side and 80 oC on the other. Conductive heat transfer can be calculated as: q = (70 W/moC) (1 m) (1 m) ((150 oC) - (80 oC)) / (0.05 m)     = 98,000 (W)     = 98 (kW) Heat Transfer through Plane Walls In Series Heat conducted through several walls in good thermal contact can be expressed as q = (T1 - Tn) / ((s1/k1A) + (s2/k2A) + ... + (sn/knA))     (2) where  T1 = temperature inside surface (K or oC, oF) Tn = temperature outside surface (K or oC, oF) Example - Heat Transfer through a Furnace Wall  A furnace wall of 1 m2 consist of a 1.2 cm thick stainless steel inner layer covered with a 5 cm this outside insulation layer of asbestos board insulation. The inside surface temperature of the steel is 800 K and the outside surface temperature of the asbestos is 350 K. The thermal conductivity for stainless steel is 19 W/m.K and for asbestos board 0.7 W/m.K.  The conductive heat transport through the wall can be calculated as q =((800 K) - (350 K)) / (((0.012 m) / (19 W/mK) (1 m2)) + ((0.05 m) / (0.7 W/m.K) (1 m2)))           = 6245 (W) Thermal Conductivity and Common Units Btu/(h ft2 oF/ft) Btu/(h ft2 oF/in) Btu/(s ft2 oF/ft) MW/(m2 K/m) kW/(m2 K/m) W/(m2 K/m) W/(m2 K/cm) W/(cm2 oC/cm) W/(in2 oF/in) kJ/(h m2 K/m) J/(s m2 oC/m) kcal/(h m2 oC/m) cal/(s cm2 oC/cm) Convection: When heat conducts into a static fluid it leads to a local volumetric expansion. As a result of gravity-induced pressure gradients, the expanded fluid parcel becomes buoyant and displaces, thereby transporting heat by fluid motion (i.e. convection) in addition to conduction. Such heat-induced fluid motion in initially static fluids is known as free convection. Heat transfer between a solid and a moving fluid is called convection. This is a short tutorial about convective heat transfer Heat energy transferred between a surface and a moving fluid at different temperatures is known as convection. In reality this is a combination of diffusion and bulk motion of molecules. Near the surface the fluid velocity is low, and diffusion dominates. Away from the surface, bulk motion increase the influence and dominates. Convective heat transfer may take the form of either forced or assisted convection natural or free convection Forced or Assisted Convection Forced convection occurs when a fluid flow is induced by an external force, such as a pump, fan or a mixer. Natural or Free Convection Natural convection is caused by buoyancy forces due to dens ity differences caused by temperature variations in the fluid. At heating the density change in the boundary layer will cause the fluid to rise and be replaced by cooler fluid that also will heat and rise. This continues phenomena is called free or natural convection. Boiling or condensing processes are also referred as a convective heat transfer processes. The heat transfer per unit surface through convection was first described by Newton and the relation is known as the Newton's Law of Cooling. The equation for convection can be expressed as: q = hc A dT         (1) where q = heat transferred per unit time (W) A = heat transfer area of the surface (m2) hc= convective heat transfer coefficient of the process (W/(m2K) or W/(m2oC)) dT = temperature difference between the surface and the bulk fluid (K or oC) Heat Transfer Coefficients - Units 1 W/(m2K) = 0.85984 kcal/(h m2 oC) = 0.1761 Btu/(ft2 h oF) 1 Btu/(ft2 h oF) = 5.678 W/(m2 K) = 4.882 kcal/(h m2 oC) 1 kcal/(h m2 oC) = 1.163 W/(m2K) = 0.205 Btu/(ft2 h oF) Convective Heat Transfer Coefficients The convective heat transfer coefficient - hc - is dependent on the type of media, gas or liquid, the flow properties such as velocity, viscosity and other flow and temperature dependent properties. Typical convective heat transfer coefficient for some common fluids: ·         Free Convection - air, gases and dry vapors : 0.5 - 1000 (W/(m2K)) ·         Free Convection - water and liquids: 50 - 3000 (W/(m2K)) ·         Forced Convection - air, gases and dry vapors:  10 - 1000 (W/(m2K)) ·         Forced Convection - water and liquids:  50 - 10000 (W/(m2K)) ·         Forced Convection - liquid metals:  5000 - 40000 (W/(m2K)) ·         Boiling Water : 3.000 - 100.000 (W/(m2K)) ·         Condensing Water Vapor: 5.000 - 100.000 (W/(m2K)) The convective heat transfer coefficient of air is approximately equal to  hc = 10.45 - v + 10 v1/2    (2) where v = the relative speed of the object through the air (m/s) Note! - this is an empirical equation and can be used for velocities - v - from 2 to 20 m/s. Example - Convective Heat Transfer A fluid flows over a plane surface 1 m by 1 m with a bulk temperature of 50oC. The temperature of the surface is 20oC. The convective heat transfer coefficient is 2,000 W/m2oC. q = (2,000 W/(m2oC)) ((1 m) (1 m)) ((50 oC) - (20 oC))     = 60,000 (W)     = 60 (kW) Convective Heat Transfer Calculator Top of Form  A - surface area (m2)  tsurface - surface temperature (oC)  tair  - air temperature (oC)  hc - convective heat transfer coefficient (W/(m2K)) Heat Transfer = 60000 (W) Bottom of Form Convective Heat Transfer Chart Dimensionless Numbers in Heat Transfer It is almost impossible to read an article or listen to a lecture on heat transfer without hearing names like Reynolds. Nusselt, Rayleigh, etc. These names refer to very specific dimensionless numbers that are used to characterize and classify the heat transfer problems. This article attempts to explain the meaning and significance of these numbers and help you to get used to them. But first, why do we need dimensionless numbers anyway? Well, we actually don't need them but they are useful tools. The nature itself does not have a clue about these numbers. It is not like the air says to itself " boy, my Reynolds number is exceeding 2500 and I am in a pipe so I better switch to my turbulent mode or all the fluid dynamics textbooks will be wrong". We have invented dimensionless numbers to be able to take our knowledge from experimenting with one system to learning about another system with different dimensions. If I have come up with some neat formula for calculating the pressure drop in a 2 inch pipe, can I use that formula for a 4 inch pipe? In a way, we are trying to get rid of dimensions in order to extend our knowledge beyond its source of acquisition. Mr. Osborne Reynolds experimented with pipes of different diameters and discovered that, regardless of the pipe diameter, if the ratio of UD/ exceeds 2500 or so, the flow no longer stays nice and laminar. This ratio is what we call Reynolds number and is probably the most commonly used dimensionless group in fluid dynamics. Dimensionless numbers allow us to experiment with model cars, airplanes and ships and predict the behavior of the big thing under actual conditions. All we have to establish is to make sure that there is similarity between the model and the actual thing. But, this is beyond the scope of this article. The Dimensionless numbers we will describe in this article are the most common numbers used in heat transfer: Reynolds Number Nusselt Number Prandtl Number 4.    Grashof Number Rayleigh Number Before getting into the definitions of these numbers, we should define the physical properties of fluids since they show up all over the place in the dimensionless numbers. We are ready now to explore these numbers in more detail. Reynolds Number Reynolds number defined as  (where L is a characteristic length) may be interpreted as the ratio of two forces that influence the behavior of fluid flow in the boundary layer. These two forces are the inertia forces and viscous forces: When the Reynolds number is large, the inertia forces are in command. Viscous forces dominate the boundary layer when the Reynolds number is small. Now, how does this relate to transition from laminar to turbulent flow? Any real flow of fluid contains small disturbances that will grow given enough opportunities. as long as the viscous forces dominate these disturbances are under control. As the inertia forces get bigger, the viscosity can no longer maintain order and these tiny disturbances grow into trouble makers and we transition to turbulent flow. Another important quantity of the boundary layer that is influenced by the Reynolds number is its thickness. As the Reynolds number increases, the viscous layer gets squeezed into a smaller distance from the surface. The value of Reynolds number beyond which the flow is no longer considered laminar is called the critical Reynolds number. For flow over a flat plate, the critical Reynolds number is observed to vary between 1e+5 to 3e+6 depending on the turbulence level in the free stream and the roughness of the surface. We normally use 5e+5 as the critical Reynolds number for flow over flat plates. Calculation of the Reynolds number is easy as long as you: Identify the characteristic length Pick the right velocity Use a consistent set of units For flow over a flat plate, the characteristic length is the length of the plate and the characteristic velocity is the free stream velocity. For pipes the characteristic length is the pipe diameter and the characteristic velocity is the average velocity through the pipe obtained by dividing the volumetric flow rate by the cross-sectional area (we are assuming that the pipe is full, of course). For pipes with a non-circular cross-section, the characteristic length is the Hydraulic Diameter defined as 4A/P, where A is the cross-sectional area of the duct and P is the wetted perimeter. You can easily verify that for a circular pipe the hydraulic diameter equals the pipe diameter. For non-cicular pipes the average velocity is used as the characteristic velocity. The situation gets messy when you are dealing with a problem that has many velocity and length scales such as the flow inside a computer cabinet. You must decide, based on your design objectives, which length and velocity length scales make sense for calculation of the Reynolds number. Nusselt Number Nusselt number is the dimensionless heat transfer coefficient and appears when you are dealing with convection. It, therefore, provides a measure of the convection heat transfer at the surface. It is defined as hL/k where, h is the heat transfer coefficient, L is a characteristic length and k is the thermal conductivity. But, what does this grouping mean from a physical standpoint? Let's find out. I am afraid that we have to look at the boundary layer in order to explain the concept of Nusselt number. We will, of course, cover the basics of the boundary layer in a separate tutorial but for now it suffices to say that when a fluid flows over a solid surface, the first layer of the fluid stick to the boundary (we even have a name for this thing called, no slip condition). This causes the flow to retard in the vicinity of the wall. As we move away from the wall the effect of this no slip thing gets smaller and smaller up to a point where it is no longer felt by the fluid. To get to this point, though, we have had to go through a layer of fluid who still knows about the wall. This layer is called the boundary layer. This was the effect of the wall on the velocity (or momentum). A similar argument applies when, for example, a cold fluid flows over a hot surface. The first layer of the fluid (which is now stuck to the surface) gets its heat from the surface through pure conduction. It then gives its newly acquired energy to all of the other fluid molecules that it comes in contact with as they pass by it (this is convection). As we move further and further away from the wall, the effect of the hot wall is felt less and less (it, of course, depends on the thermal conductivity of the fluid). Eventually, there comes a point where the fluid does not have a clue about the hot wall. The layer of fluid between the wall and this point is called the thermal boundary layer. It is where all of the action is taking place (as far as heat transfer between the solid and fluid is concerned). Before continuing with the Nusselt number, let us define another dimensionless property: Prandtl Number Heat transfer gurus have invented another dimensionless number called the Prandtl number which is a grouping of the properties of the fluid but it has a significance to our discussion. Prandtl number is defined as: It is the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It can be related to the thickness of the thermal and velocity boundary layers. It is actually the ratio of velocity boundary layer to thermal boundary layer. When Pr=1, the boundary layers coincide. Typical values of the Prandtl number are: When Pr is small, it means that heat diffuses very quickly compared to the velocity (momentum). This means the thickness of the thermal boundary layer is much bigger than the velocity boundary layer for liquid metals. Now, back to the Nusselt number. Remember that we explained how the first fluid layer stick to the solid surface and the heat is transferred via conduction. Well, let's write this equation: In a boundary layer situation the characteristic length is the thickness of the boundary layer. Consider a fluid layer of thickness L and a temperature difference of across this layer. Heat transfer by convection can be calculated as hwhile heat transfer by conduction is k/L. Dividing the convection heat transfer to the conduction heat transfer, we get: So, the Nusselt number may be viewed as the ratio of convection to conduction for a layer of fluid. If Nu=1, we have pure conduction. Higher values of Nusselt mean that the heat transfer is enhanced by convection. Grashof Number You see this number and you should think of natural or free convection. The Grashof number is the ratio of buoyancy forces to the viscous forces. In natural convection the Grashof number plays the same role the is played by the Reynolds number in forced convection. The buoyant forces are fighting with viscous forces and at some point they overcome the viscous forces and the flow is no longer nice and laminar. For a vertical plate, the flow transitions to turbulent around a Grashof number of 10^9. Rayleigh Number The Rayleigh number is the product of Grashof and Prandtl numbers. It turns out that in natural convection the Nusselt number scales with Rayleigh rather than just Grashof. Most correlations in natural convection are of the form: where . - See more at: http://www.coolingzone.com/library.php?read=481#sthash.2PAV1Lkb.dpuf Radiation: All materials radiate thermal energy in amounts determined by their temperature, where the energy is carried by photons of light in the infrared and visible portions of the electromagnetic spectrum. When temperatures are uniform, the radiative flux between objects is in equilibrium and no net thermal energy is exchanged. The balance is upset when temperatures are not uniform, and thermal energy is transported from surfaces of higher to surfaces of lower temperature.