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Home , Biot number, Deborah number, Eckert number, Euler number (physics), Grashof number, Lewis number

MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

SIGNIFICANCE OF DIMENSIONLESS NUMBERS IN THE MECHANICS Sobia Sattar, Siddra Rana Department of Mathematics, University of Wah [email protected]

ABSTRACT Dimensionless numbers have high importance in the field of as they determine behavior of fluid flow in many aspects. These dimensionless forms provides help in computational work in mathematical model by sealing. Dimensionless numbers have extensive use in various practical fields like economics, physics, mathematics, engineering especially in mechanical and chemical engineering. Segments having size 1, constantly called dimensionless segments, mostly it happens in sciences, and are officially managed inside territory of dimensional examination. We discuss about different dimensionless numbers like , , , and up to so on. Different dimensionless numbers used for transfer and . For example Biot number, Reynolds number, Peclet number, , are used for and other are used for mass transfer calculations. In this paper we study about different dimensionless numbers and the importance of these numbers in different parameters. This description of dimensionless numbers in fluid mechanics can help with understanding of all areas of the including , viscous flow, turbulance, and thermodynamics. Dimensionless methodology normally sums up the issue. Alongside that dimensionless numbers helps in institutionalizing on condition and makes it autonomous of factors sizes of the reactors utilized in various labs, as to state, since various substance labs utilize diverse size and state of hardware, it's essential to utilize conditions characterized in dimensionless amount.

1. INTRODUCTION: is the fluid? All things consider liquid as a Fluid mechanics is that part of applied material which is delicate and effectively mechanics that is concerned with the statics disfigured when yield pressure is connected. and elements of and . The In any scale framework or scale model, assessment of the direct of liquids depends various factors are utilized to structure the absolutely upon the basic laws of connected model or way to deal with the real world so mechanics that identify with the we can get results or end effectively. preservation of mass, vitality and energy. Presently to lessen these factors, to control Presently, the principal question is that what the test information, to control the MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

perplexing condition, genuine task and Engineering. In dimensional assessment, a rearrange model we present dimensionless non-dimensional number (for example numbers. In spite of the fact that these different with the elements of one) is an numbers neither have any physical measures unadulterated amount with none substantial nor measurement yet characterize the units. It doesn't trade in the event that one conduct of liquid on a base of explicit changes one's arrangement of devices of hindrance. Here we examine measurement. Moreover, dimensionless nonmeasurement numbers in fluid administrative work additionally enable us to mechanics which mark effect in the conduct give the arrangement in a minimal manner. of fluid and inform us concerning the sort of Dimensionless shape licenses us to think stream. about the general impact of the few expressions acting inside the conditions. Non-dimensional numbers in fluid Moreover, it grants us to analyze particular mechanics have a significant position inside frameworks the conduct of fluids. Segments having size . 1, constantly called dimensionless segments, 2. WHAT ARE much of the time happen in sciences, and are officially managed inside the territory of DIMENSIONLESS dimensional examination. In the NUMBERS? century, French mathematician Joseph The non-dimensionalization of the Fourier and Scottish physicist James Clerk overseeing conditions of fluid drift is Maxwell drove tremendous inclinations in fundamental for both hypothetical and cutting edge thoughts of measurement and computational thought processes. unit. After that, British physicists Osborne Nondimensional scaling offers a technique Reynolds and Lord Rayleigh added to the for developing dimensionless offices which information of these numbers in material could give physical observation into the science. Expanding on Rayleigh's significance of assorted expressions inside methodology of dimensional investigation, the arrangement of overseeing conditions. Edgar Buckingham demonstrated the pi [1]Non-dimensional numbers in fluid hypothesis to normalize the character of mechanics are a firm of these amounts which those bits. A few diverse dimensionless include an imperative position inside the numbers, typically proportions, have been lead of fluids. With the help of those instituted in the mid-1900s, specifically numbers we can without issues expect the inside the locales of liquid mechanics and float direct of fluid. [2]Computationally, warmth move. dimensionless administrative work have the additional favors of giving numerical scaling Dimensionless numbers are extremely of the machine discrete conditions, thus significant in Mechanical Engineering and providing a substantial connected Chemical Engineering including methodology for improving the Thermodynamics, Fluid Mechanics, Mass unwellmolding of the gadget of conditions switch, warmth switch, solid Mechanics, [1]. Those numbers are the extents of strain Momentum switch and Chemical reaction to drive, uncommon extents grant novel MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

numbers which characterize any things of measure which offers a prompt sign of the fluid. Many numbers characterize the drift of overall significance of the conduction and fluid, warmness move, mass switch, etc. in making sense of the Those are numbers which are gotten by history of a casing being methods for dividing the torpidity control warmed or cooled by utilizing through gravity control or gooey control or convection at its surface. [5] 1.1.1 versatile control. As that is the proportion of once weight to various, it'll be a Definition dimensionless amount. Those likewise are A Biot number is defined as alluded to as non-dimensional parameters. [3] Dimensionless amounts are routinely gained Where, as items or proportions of amounts that Heat transfer coefficient aren't dimensionless, anyway whose measurements counteract inside the Characteristic dimension, which is numerical task. A case of this kind of commonly defined as proportion is designing weight, a proportion of substantial distortion. It is characterized as an adjustment long separated through the of the body 1.1.2 starter term, taking into account that the two amounts have the size length, their Lumped System proportion is dimensionless [4]. In warmth move, a number of bodies are Some of the significant dimensionless seen to carry on like "Lump" in which numbers utilized in fluid mechanics and temperature of the body remains same at warmth move are given underneath. unsurpassed during warmth move (isothermal/ uniform temperature 1.1 BIOT NUMBER conveyance). Along these lines, lumped The Biot number ( ), a non-dimensional System is just appropriate if temperature amount is utilized in warmth move conveyance is uniform at unequaled. computations. It is known after the To decide the quantity of bumps, the Biot century French physicist Jean-Baptiste Biot number ( ), a dimensionless parameter of (1774-1862), and offers a straightforward the framework, is utilized. Bi is characterized file of the proportion of the glow switch as the proportion of the conductive warmth protections inward of edge and on the obstruction inside the article to the outside of the body. This proportion decides convective warmth move opposition over if or never again will the go the item's limit with a uniform shower of altogether in space, while the body warms or various temperature. At the point when the cool after some time, from a warm slope warm protection from warmth moved into connected to its surface. The numerical the article is bigger than the protection from expense of Biot wide assortment (Bi) is a MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

warmth being diffused totally inside the (uniformality in temperature). item, the Biot number is under 1. suggests warmth move opposition inside the body is extremely high methods heat conduction inside the body is slower than the warmth convection far from the surface of body. This demonstrates temperature inclination inside the body. suggests warm opposition of body to warm conduction is zero. [6] In Lumped System Analysis, body A tiny copper ball can behave like a Lump, temperature is consistently conveyed for but a roast beef cannot be treated as example isothermal. Thus, when warm Lumped system. obstruction of body to warm conduction is zero different words, , lumped framework investigation is accurate. 1.1.4 Applications of Biot number It is utilized in insecure state (transient) heat move condition. A substance with is marked as thermally dainty, and temperature can be thought consistent all through the volume. The inverse is additionally valid: A (a "thermally thick" substance) shows that 1.1.3 Significance of Biot number one can't make this suspicion [5]. For the most part we can say that Biot 1.2 REYNOLDS NUMBER number is the proportion of inward warm In fluid mechanics, the Reynolds number ( opposition which is heat conduction to outer ) is a non-dimensional sum that is used to warm obstruction which is heat convection assist expect comparable stream plans in different fluid stream circumstances. The thought was displayed by George Gabriel demonstrate the time rate of change of Stokes in 1851 and named by Arnold temperature. Sommerfield in 1908 [7]. suggests warmth move 1.2.1 Definition obstruction inside the body is low than the It is defined as: warmth convection. This demonstrates no temperature slope inside the body

MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

Where, Uncommon practically speaking in frameworks ρ = of fluid (usually lb/ft³ or kg/m³) ѵ = velocity (usually ft/s or m/s) D = characteristic dimension or length (L) of travel (usually ft or m) µ =dynamic of fluid Turbulent Flow:

1.2.2 Significance of Reynolds number . is the proportion of inertial forces to the Speed of fluid is high viscous forces. The stream is portrayed by the sporadic Basically utilized for analyzation of different development of particles of the fluid. types of flow. Smooth movement is toward the stream When viscous forces are superior (i.e. low The stream speed profile for fierce stream is value of ) then the flow is laminar. genuinely level over the inside segment of a When inertial forces are superior (i.e. high pipe and drops quickly very near the dividers. value of ) then the flow is turbulent. [8]. The usual speed of fluid is almost equal to Laminar vs. Turbulent Flow speed at center of pipe. : Numerical investigation is troublesome. . Most regular kind of stream. [9] Speed of fluid is low At Reynolds numbers between around 2000 and 4000 the stream is unsteady because of Liquid particles move in straight lines the beginning of choppiness. Stream lines more than each other at various velocities with essentially no These streams are now and again alluded to blending within the layers. as transitional streams. The stream speed profile for laminar stream in roundabout funnels is illustrative fit as a fiddle, with a most extreme stream in the center of the pipe and a base stream at the pipe dividers. 1.2.3 Applications of Reynolds number The normal speed of stream is roughly one Utilized in warmth move condition part of the most extreme speed. 1) Reynolds number has a significant Straightforward numerical examination is influence in fluid mechanics. conceivable. MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

2) It is utilized when displaying the where, development of living beings swimming = relaxation time. through water. = for the "time of observation" 3) Atmospheric air is viewed as a fluid. Thus, the Reynolds number can be 1.3.2 Significance of determined for it. Proportion of the unwinding time (relaxation 4) It is significant in determination of time) of a material to the perception or trial wind on air ship. time or observation time. 5) By separating between the streams Materials can show both fluid like and strong routines, we know which exact co-relations like conduct, conditioned on unwinding and to be utilized to have a precise estimation of perception time. grinding misfortunes in the channels. This is one of the straightforward utilization of the The more noteworthy the Deborah number, Reynolds number in the field of fluid the more strong the material; the littler the mechanics. [10] Deborah number, the more fluid the material. 1.3 DEBORAH NUMBER For instance, for a Hookean versatile strong, The Deborah Number is a non-dimension the unwinding time will be unbounded. For number, regularly utilized in to fluid water, is regularly sec describe the smoothness of objects beneath [11] explicit stream conditions. The Deborah number was given by Markus Reiner. He 1.3.3 Application of Deborah number named it by a verse of Bible "The The Deborah number is especially valuable in Mountains streamed before the Lord" [11] time - temperature superposition rule. Time- The littler the Deborah number, the material temperature superposition maintains a carries on progressively fluid like with a strategic distance from the wastefulness of related Newtonian gooey stream. At higher estimating a polymer's conduct over the value of Deborah numbers, the material extensive stretches of time at a conduct changes to nonNewtonian routine, predetermined temperature by using the progressively commanded by flexibility, Deborah number. [12] achieving strong like conduct with high 1.4 Deborah numbers. [12] The Eckert number is a non-dimensional number, named after Ernst R. G. Eckert. The 1.3.1 Definition Eckert number gives a proportion of the The Deborah number is defined as: motor vitality of the stream with respect to the enthalpy distinction over the warm limit layer. It is utilized to describe heat dispersal in fast streams for which gooey MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

dissemination is noteworthy. [13] 1.4.1 1.4.3 Application of Eckert number

Definition Eckert number decides if the job of the force vitality is transfered to warm vitality is The Eckert number is characterized as the noteworthy to influence the stream. This proportion of the advective mass exchange impact is significant in circumstances where to the warmth dissemination potential. It rapid is included. This reality proposes that communicates the connection between a Eckert number is identified with Mach stream's motor vitality and enthalpy, and is number. [14] utilized to describe dissemination. 1.5 MACH NUMBER

Mach number, in fluid mechanics, proportion of the speed of a liquid to the Where speed of sound in that fluid, named after = the local velocity of flow [m/s] Ernst Mach (1838- - 1916). In the instance of = the constant-pressure [m²/K.s⁻²] an item traveling through air or a fluid, for example, a flying machine in flight, the Mach ΔT = the temperature difference between number is equivalent to the speed of the wall and local temperatures [K]. article in respect to the fluid separated by the speed of sound in that fluid. [19] It is 1.4.2 Significance of Eckert number usually used to speak to the speed of an item The Eckert number links the motor vitality to when it is making a trip near or over the the enthalpy of a fluid. The is utilized to speed of sound. 1.5.1 Definition:- describe the impact of self-warming of a fluid It is defined as: as a result of dispersal impacts. At high stream speeds, the fluidic temperature framework isn't simply commanded by the temperature angles that are available in the where, framework, yet additionally be impacts of U= the velocity of moving object in fluid. c= dissemination because of inward grating of the fluid. [14] speed of sound in the medium. 1.5.2 Significance of Mach number For instance, streaming with a Mach number of under three-tenths might be viewed as incompressible, or of consistent thickness, an estimate that incredibly rearranges the investigation of its conduct. For Mach numbers more noteworthy than

one, streamlining reduces stun wave impacts. MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

• On the off chance that , the nearby weight drop brought about by a stream speed is less than the sound limitation and the dynamic vitality per speed - and there will be subsonic volume of the stream, and is utilized to speed. portray vitality misfortunes in the stream, • On the off chance that the , the where an ideal frictionless stream relates to stream speed is roughly similar to the an of 1.[16] sound speed - and the speed will be 1.6.1 Definition transonic. • On the off chance that the , the It is defined as: stream speed is around like the sound speed - and there will be

transonic speed. • On the off chance that the , Where, the stream speed is greater than the p=characteristic pressure. speed of sound - and there will be supersonic speed. ρ=the density of fluid. • On the off chance that the , U=velocity of fluid flow. the stream speed is a lot greater than the speed of sound - and there will be 1.6.2 Significance of Euler number . [20] It communicates the connection between a 1.5.3 Applications of Mach number nearby weight drop brought about by a Mach number is generally utilized both with confinement and the dynamic vitality per articles going at rapid in a fluid, and with fast volume of the stream, and is utilized to fluid streams inside channels, for example, describe vitality misfortunes in the stream, spouts, diffusers or wind burrows. As it is where an ideal frictionless stream compares characterized as a proportion of two rates, it to an Euler number of 1. The opposite of the is a non-dimensional number. The speed Euler number is alluded to as the Ruark spoken to by Mach 1 is anything but a steady; Number with the image . [17] for instance, it is for the most part subject to 1.6.3 Application of Euler number temperature and barometrical creation and generally autonomous of weight. Hydrodynamics (stream weight versus idleness powers) In Chemical Engineering, the Mach number is usually utilized in computations including The Euler Number is a dimensionless worth high speed gas stream. utilized for breaking down fluid stream elements issues where the weight contrast 1.6 EULER NUMBER between two is significant. Portrayal of The Euler number ( ) is a non-dimensional vitality misfortunes in fluid streams. number utilized in liquid stream counts. It communicates the connection between a MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

1.7 The significant power that opposes the movement is the thick power. [13] The Grashof number ( ) is a nondimensional number in fluid elements and warmth move When Gr >> 1, the gooey power is irrelevant which are the proportion of the lightness to contrasted with the lightness and inertial thick power following up on a fluid. It was powers. At the point when light powers beat termed after Franz Grashof the thick powers, the stream begins a [18]. progress to the fierce routine [18].

1.7.1 Definition It is defined as:

Where, g= gravity β= thermal expansion 1.7.3 Application of Grashof number coefficient Grashof number is utilized when convective = temperature of hot wall warmth move is occurring between the bodies. = reference temperature The Grashof number is a dimensionless L= characteristic length ν = amount utilized in investigating the speed the kinematic viscosity dispersion in free convection frameworks. Free convection is the normal inclination of a 1.7.2 Significance of Grashof number substance to move because of some main Proportion of power to thick thrust. In free convection, the main impetus power in characteristic convection. is a lightness power brought about by a temperature inclination, as the fluid would Reynolds number is utilized in constrained be very still without temperature varieties. convection of fluid stream. Grashof number The Grashof number is closely resembling is critical in instances of liquid stream the Reynolds number in constrained because of regular convection. convection. The Grashof number gives the In the event that this movement and primary paradigm in deciding if the fluid blending is brought about by thickness stream is laminar or tempestuous in varieties coming about because of common convection. [19] temperature contrasts inside the fluid. 1.8 PRANDTL NUMBER Generally the thickness diminishes because of an expansion in temperature and makes The Prandtl number is a non-dimensional the fluid ascent. This movement is brought number, its named was given after its about by the light (lightness power) power. innovator, a German architect Ludwig MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

Prandtl, who additionally recognized the limit layer.

1.8.1 Definition It is defined as:

Where, v = viscous 1.8.3 Applications of Prandtl number rate [m²/s] α = thermal Utilized in warmth move conditions diffusivity [m²/s] Prandtl Number of Water and Air 1.8.2 Significance of Prandtl number The value of Prandtl number of air at room temperature is 0.71 and for water its value is Prandtl ( number gives the data about the 7.56 at which implies that the warm sort of liquid. Additionally it gives the data diffusivity is more overwhelming for air than about the thickness of warm and velocity for water. For a Prandtl number of solidarity, limit layer. On the off chance that the energy diffusivity approaches the warm >>1 higher force diffusivity contrasted with diffusivity and the instrument and rate of warmth diffusivity….More thickness of warmth move are like those for force move. speed limit layer. Prandtl Number of Liquid Metals In the event that <<1 higher diffusivity of warmth than energy diffusivity… more For fluid metals the Prandtl number is thickness of the warm limit layer. For extremely little, for the most part in the instance, the ordinary incentive for fluid range from 0.01 to 0.001. This implies the mercury, which is about 0.025, shows that warm diffusivity, which is identified with the the warmth conduction is increasingly huge rate of warmth move by conduction, contrasted with convection, so warm unambiguously rules. This extremely high diffusivity is overwhelming. warm diffusivity results from exceptionally high warm conductivity of metals, which is In contrast with Reynolds number, the around multiple times higher than that of Prandtl number isn't reliant on geometry of water. an article engaged with the issue, however is needy exclusively on the fluid and the fluid Laminar Prandtl Number - Turbulent state. Prandtl Number When managing Prandtl numbers, we need to characterize a laminar piece of Prandtl number and a violent piece of Prandtl number. The condition =ѵ/α MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

indicates us in reality just the laminar part limit layer. The relates to which is legitimate for laminar streams. The the Prandtl number in warmth move. A tempestuous Prandtl number is a Schmidt number of solidarity demonstrates nondimensional term characterized as the that energy and mass exchange by proportion between the energy whirlpool dissemination are tantamount, and speed diffusivity and the warmth move swirl and focus limit layers nearly correspond with diffusivity. It essentially portrays blending one another. Mass dispersion in fluids due to twirling/turn of fluids. [13] develops with temperature, generally conversely corresponding consistency variety with temperature, so the Schmidt number, =ѵ/D, rapidly diminishes with 1.9 SCHMIDT NUMBER temperature. The Schmidt number is a non-dimensional number, it is named was given after the German engineer Ernst Heinrich Wilhelm Schmidt (1892-1975).

1.9.1 Definition

It is defined as 1.9.3 Applications of Schmidt number Turbulent Schmidt Number

Where, Similarly as for the Prandtl number, also Schmidt number has a special formula for Ѵ = kinematic viscosity [m²/s] turbulent flow. It is defined as: = the mass diffusivity [m²/s]

= Prandtl Number Where, = Lewis number 1.9.2 Significance of = the viscosity [m²/s] Schmidt number It is closely related to K = the eddy diffusivity [m²/s][13] Heat Transfer. 1.10 LEWIS NUMBER Utilized in fluid streams in which there is The Lewis number is a non-dimensional concurrent force and mass dissemination. number, its named was given after Warren K. It is additionally the proportion of fluid limit Lewis (1882-1975). The Lewis number can layer to mass exchange limit layer thickness. likewise be communicated regarding the Prandtl number and the Schmidt number as It physically relates the general thickness of the velocity and mass-move / MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

1.10.1 Definition It is defined as:

Where, thermal diffusivity [m²/s]

The mass diffusivity [m²/s] 1.10.3 Applications of Lewis number 1.10.2 Significance of Lewis number The Lewis number puts in relationship the Proportion of warm diffusivity to mass mass dissemination and the warm diffusivity. conductivity of a fluid. Like the Prandtl number, which relates energy transport and Fluid stream with synchronous Heat and warm transport properties of a fluid, and mass exchange by convection like the Schmidt number, which It is likewise proportion of Schmidt number corresponds force transport and mass to Prandtl number. transport of a fluid, the Lewis number Correspondingly concerning Schmidt and connects mass transport to warm transport Prandtl number, the Lewis properties of the liquid. [14] number physically relates the overall 1.11 PECLET NUMBER thickness of the warm layer and mass-move (focus) limit layer. The Peclet number ( ) is a class of nondimensional numbers. Its name was A Lewis number of solidarity demonstrates given after the French physicist Jean Claude that warm limit layer and mass exchange by Eugene Peclet. It is defined to be the dispersion are practically identical, and temperature and focus limit layers nearly proportion of the rate of advection harmonize with one another. Mass transport rate to diffusive transport rate. diffusivity or dissemination coefficient is a [22] 1.11.1 Definition proportionality steady between the molar It is defined as: motion because of sub-atomic dispersion A) Peclet Number for Heat Transfer and the angle in the grouping of the species (or the main thrust for dissemination). [13]

B) Peclet Number for Mass Transfer MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

Peclet Number in Heat Transfer In heat transfer problems, the Peclet number is the proportion of the warm energy

convected to the warm energy conducted Where, within the fluid. U=local flow velocity L= characteristic length α, = diffusion rate

1.11.2 Significance of Peclet number

Warmth transported through convection to Heat transported through conduction. 1.11.4 Applications of Peclet number Result of and for (HT) and result of & for (MT). It is used in convective heat transfer calculation. On the off chance that <1, at that point this implies diffusive rate is prevailing and on the It is an important parameter for heat transfer off chance that >1, at that point this within the fluid. implies advective rate is overwhelming. It is related to both the Prandtl number What's more, at 1 then impact is which links momentum transport and heat comparative. transport, as well as the Reynolds number, 1.11.3 Peclet Number in Mass Transfer which links the inertia and viscous forces. [23] In mass exchange issues, the Peclet number is the result of the Reynolds number, which 1.12 NUSSELT NUMBER depicts the stream routine, and the Schmidt The Nusselt number is a non-dimensional number. number, termed after a German engineer Wilhelm Nusselt. The Nusselt number is closely linked to Peclet number and both numbers are used to determine the proportion of the convective heat energy of the fluid to the conductive heat energy within the fluid. [13]

1.12.1 Definition It

is defined as: MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

flow regimes, the Nusselt number and a given correlation can be used to find the convective heat transfer coefficient. [22] Where, h= the convective heat transfer coefficient 1.13 [W/m².K] Richardson number, parameter that can be L=the characteristic dimension used to judge the occurrence of fluid . It was defined by the British = Thermal conductivity of the fluid meteorologist Lewis Fry Richardson, [W/m.K] (18811953) a pioneer in mathematical weather forecasting. The Richardson 1.12.2 Significance of Nusselt number number can be defined as a product of The Nusselt number represents the Grashof number and Reynolds number. increment of heat transfer by a fluid layer. 1.13.1 Definition It If =1, then, than your fluid is at rest position and all heat is transfer through is defined as: conduction. With >1, the motion of the fluid increases the heat energy through advection. [13]

Where, = Grashof number = Reynolds number. g= gravity β= thermal expansion coefficient. 1.12.3 Applications of Nusselt number =temperature of warm wall. Used in heat transfer conditions =reference temperature. Nusselt number is required to find `h' which is convective heat transfer coefficient. L=characteristic length Nusselt Number for Liquid Metal Reactors U= velocity scale Convective heat transfer correlations are 1.13.2 Significance of Richardson number usually presented in terms of Nusselt • If the , buoyancy is number versus Peclet number. Typical Peclet unnecessary in the flow. number for normal operation are from 150 • If , buoyancy is dominant. to 300 in the fuel bundles. As for another MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

• If the , then the flow energy In this thesis we study about different comes from potential energy in the dimensionless numbers and the importance system originally. of these numbers in different parameters. 1.13.3 Applications of Richardson number This description of the dimensionless numbers in fluid mechanics can help with the The Richardson number has extensive use in understanding of all areas of the fluid judging density and turbidity currents in dynamics including compressible flow, oceans, lakes, and reservoirs and in case of viscous floe, turbulence, aerodynamics and weather forecasting. thermodynamics. Dimensionless Flying methodology normally sums up the issue. For fluid mechanics perspective, In flying (air transport), the Richardson arrangement of dimensionless structure is number is utilized as a harsh proportion of the arrangement of a specific issue. Be that expected air disturbance. A lower worth as it may, dimensionless arrangement relies shows a higher level of disturbance. Qualities upon a lot of dimensionless parameters. in the range 10 to 0.1 are average, with Utilizing one dimensionless arrangement qualities underneath solidarity showing one can portray numerous dimensional critical choppiness. arrangement. Warm convection Alongside that dimensionless numbers helps in institutionalizing on condition and makes In warm convection issues, Richardson it autonomous of factors sizes of the reactors number speaks to the significance of characteristic convection with respect to the utilized in various labs, as to state, since various substance labs utilize diverse size constrained convection. Regularly, the and state of hardware, it's essential to utilize common convection is unimportant when <0.1, constrained convection is immaterial conditions characterized in dimensionless amount. when >10, nor is insignificant when 0.1 < < 10. It might be noticed that typically the REFERENCES constrained convection is enormous with respect to characteristic convection aside [1] A.Salih Dept. of Aerospace Engineering from on account of incredibly low IIST, Dimensionless numbers, constrained stream speeds. Thiruvananthapuram Be that as it may, lightness regularly assumes [2] J. Kunes. 2012. Dimensionless physical a noteworthy job in characterizing the quantities in science and engineering. laminar- - fierce progress of a blended [3] Peter J. Mohr and William D. Phillips. convection stream. In the structure of water 2015. Dimensionless units in the SI. filled warm vitality stockpiling tanks, the [4] J. D Huba. 2007. NRL Plasma Formulary: Richardson number can be helpful. Dimensionless Numbers of Fluid Mechanics. 3. CONCLUSION MDSRIC - 2019 Proceedings, 26-27, November 2019 Wah/Pakistan

[5] Frank P. Incropera. 2007. Fundamentals Applications of Euler number. of heat and mass transfer, John Wiley. [17] C. J Sander, Holman. 1972. Franz Grashof [6] Yunus A.Cengel. 2002. Heat Transfer a and the Grashof Number. practical approach, McGraw-Hill (TX); 2nd [18] R. James, Welty. 1976. Fundamentals of edition, vol. 8.3 x 1.5 x 10.3 inches. Momentum, Heat, and Mass Transfer, [7] N. Rott. 1990. Reynolds number, Annual John Wiley. Review of Fluid Mechanics, vol. 22. [19] W. P Graebel. 2001. Engineering Fluid [8] H. Divedi. 2016.A mechanical engineer, Mechanics, Mach number, Taylor & Dimensionless numbers and their Francis. p. 16. physical significance. [20] V. Suhas, Patankar. 1980. Numerical Heat [9] J. R. Lamarsh. 1983. Introduction to Transfer and Fluid Flow, McGraw-Hill. Nuclear Reactor Theory, 2nd ed., [21] Bastian E. Rapp. 2017. Eckert number, in Addison-Wesley. : Modelling, Mechanics and [10] D. Jackson, Brian Launder. 2007. Reynolds Mathematics. number, Volume 39. [22] M. White Frank. 2010. Fluid Mechanics, [11] J. S. Vrentas, C. M. Jarzebski, J. L. Duda. McGraw-Hill Education, 7th edition. 1975. A Deborah number for diffusion in [23] J. S Turner. 1973. Richardson number. polymer-solvent systems, vol. 21. Buoyancy Effects in Fluids. [12] Ed Lachapelle in McCarthy. 2005.

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Microfluidics: Modelling, Mechanics and Mathematics.

[15] G. K Bachelor. 1967. An introduction to fluid dynamics, Euler number.

[16] S. Andreou, J. Lambright. 2004.