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Nusselt numberSource: WikipediaTheNusselt number(Nu) is the ratio ofconvectivetoconductiveheat transfer across (normalto) the boundary. Named afterWilhelm Nusselt, it is adimensionless number. The conductive component is measured under the same conditions as the heat convection but with a (hypothetically)stagnant(or motionless) fluid. A similar non-dimensional parameter isBiot Number, with the difference that thethermal conductivityis of the solid body and not the fluid.A Nusselt number close to one, namely convection and conduction of similar magnitude, is characteristic of "slug flow" orlaminar flow. A larger Nusselt number corresponds to more active convection, withturbulent flowtypically in the 1001000 range.The convection and conduction heat flows areparallelto each other and to the surface normal of the boundary surface, and are allperpendicularto themeanfluid flow in the simple case.

wherehis theconvectiveheat transfer coefficientof the flow,Lis thecharacteristic length,kis thethermal conductivityof the fluid.Selection of the characteristic length should be in the direction of growth (or thickness) of the boundary layer; some examples of characteristic length are: the outer diameter of a cylinder in (external)cross flow(perpendicular to the cylinder axis), the length of a vertical plate undergoingnatural convection, or the diameter of a sphere. For complex shapes, the length may be defined as the volume of the fluid body divided by the surface area.The thermal conductivity of the fluid is typically (but not always) evaluated at thefilm temperature, which for engineering purposes may be calculated as themean-average of the bulk fluid temperature and wall surface temperature.In contrast to the definition given above, known asaverage Nusselt number, local Nusselt number is defined by taking the length to be the distance from the surface boundaryto the local point of interest.

Themean, oraverage, number is obtained by integrating the expression over the range of interest, such as

Biot number

TheBiot number(Bi) is adimensionless quantityused in heat transfer calculations. It is named after the FrenchphysicistJean-Baptiste Biot(17741862), and gives a simple index of the ratio of the heat transfer resistancesinside ofandat the surface ofa body. This ratio determines whether or not the temperatures inside a body will vary significantly in space, while the body heats or cools over time, from a thermal gradient applied to its surface.In general, problems involving small Biot numbers (much smaller than 1) are thermally simple, due to uniform temperature fields inside the body. Biot numbers much larger than 1 signal more difficult problems due to non-uniformity of temperature fields within the object. It should not be confused withNusselt number, which employs the thermal conductivity of the fluid and hence is a comparative measure of conduction and convection, both in the fluid.The Biot number has a variety of applications, including transient heat transfer and use in extended surface heat transfer calculations.The Biot number is defined as:

Where:h= film coefficient orheat transfer coefficientor convective heat transfer coefficientLC=characteristic length, which is commonly defined as the volume of the body divided by the surface area of the body, such thatkb=thermal conductivityof the bodyThe physical significance of Biot number can be understood by imagining the heat flow from a small hot metal sphere suddenly immersed in a pool, to the surrounding fluid. The heat flow experiences two resistances: the first within the solid metal (which is influenced by both the size and composition of the sphere), and the second at the surface of the sphere. If the thermal resistance of the fluid/sphere interface exceeds that thermal resistance offered by the interior of the metal sphere, the Biot number will be less than one. For systems where it is much less than one, the interior of the sphere may be presumed always to have the same temperature, although this temperature may be changing, as heat passes into the sphere from the surface. The equation to describe this change in (relatively uniform) temperature inside the object, is simple exponential one described inNewton's law of cooling.In contrast, the metal sphere may be large, causing the characteristic length to increase to the point that the Biot number is larger than one. Now, thermal gradients within the sphere become important, even though the sphere material is a good conductor. Equivalently, if the sphere is made of a thermally insulating (poorly conductive) material, such as wood or Styrofoam, the interior resistance to heat flow will exceed that of the fluid/sphere boundary, even with a much smaller sphere. In this case, again, the Biot number will be greater than one.Mass transfer analogueAn analogous version of the Biot number (usually called the "mass transfer Biot number", or) is also used in mass diffusion processes:

where:hm- filmmass transfer coefficientLC- characteristic lengthDAB- mass diffusivity.