Dimensionless number Prandtl

American engineers are probably more familiar with the magnitude of physical entities in U.S. customary units than in SI units. Consequently, errors made in the conversion from one set of units to the other may go undetected. The following six examples will show how to convert the elements in six dimensionless groups. Proper conversions will result in the same numerical value for the dimensionless number. The dimensionless numbers used as examples are the Reynolds, Prandtl, Nusselt, Grashof, Schmidt, and Archimedes numbers. 

Other dimensionless parameters, namely the Reynolds number, Prandtl number, and Nusselt number ean be represented as follows ... 

Sc = Schmidt number, dimensionless Pr = Prandtl number, dimensionless Cg = gas specific heat, Btu/lb-°F a = interfacial area, fti/fti Q, = sensible heat transfer duty, Btu/hr Qj. = total heat transfer duty, Btu/hr... 

L/pj-A)(S/psA), liquid-solids velocity ratio, dimensionless Number of heat-transfer stages, dimensionless = hdp/kg, Nusselt number, dimensionless Pressure drop, gm-wt/cm2 = Cpu kg, Prandtl number, dimensionless = dpiipj U, Reynolds number, dimensionless S Mass velocity of solids, gm/cirf sec... 

It is seen that we are comparing kinematic viscosity, thermal diffusivity, and diffu-sivity of the medium for both air and water. In air, these numbers are all of the same order of magnitude, meaning that air provides a similar resistance to the transport of momentum, heat, and mass. In fact, there are two dimensionless numbers that will tell us these ratios the Prandtl number (Pr = pCpv/kj = v/a) and the Schmidt number (Sc = v/D). The Prandtl number for air at 20°C is 0.7. The Schmidt number for air is between 0.2 and 2 for helium and hexane, respectively. The magnitude of both of these numbers are on the order of 1, meaning that whether it is momentum transport, heat transport, or mass transport that we are concerned with, the results will be on the same order once the boundary conditions have been made dimensionless. 

Dijfusional dimensionless numbers The Peclet, Prandtl, Schmidt, Sherwood, and Nusselt number are the most common ones. 

Total Prandtl number, dimensionless Eddy Prandtl number, dimensionless Thermal flux in r direction, B.t.u./(sq. ft.)(sec.)... 

PRANDTL NUMBER. A dimensionless number equal to the ratio of llie kinematic viscosity to the tlienuoiiielric conductivity (or thermal diffusivity), For gases, it is rather under one and is nearly independent of pressure and temperature, but for liquids the variation is rapid, Its significance is as a measure of the relative rates of diffusion of momentum and heat m a flow and it is important m the study of compressible flow and heat convection. See also Heat Transfer. 

Dimensionless numbers help in convection heat transfer engineering Used to compare relative values in the practice of engineering In convection, there is the Eckert number and the Prandtl number, There is also the Reynolds number, Peclet number and Nusselt number. 

NGt = Grashof number = L3p2gfi At/p2, dimensionless NPr = Prandtl number = cp(i/k, dimensionless Nr = number of rows of tubes across which shell fluid flows, dimensionless NRe = Reynolds number = DG/fi, dimensionless N, = total number of tubes in exchanger = number of tubes per pass X np, dimensionless... 

Re - Reynolds number, dimensionless Pr - Prandtl, number, dimensionless... 

As explained earlier, with respect to the heat and mass transfer analogies, the Schmidt number is the Prandtl number analogue. Both dimensionless numbers can be appreciated as dimensionless material properties (they only contain transport media properties). For gases, the Sc number is unity, for normal liquids it is 600-1800. The refined metals and salts can have a Sc number over 10 000. 

B Gain a working knowledge of the dimensionless Reynolds, Prandtl, and Nusselt numbers, B Distinguish betvreen laminar and turbulent llovrs, and gain an understanding of the mechanisms of momentum and heat transfer In turbulent flow,... 

Incidentally, Bowes discussed in his book, Self-Heating Evaluating and Controlling the Hazards , some dimensionless numbers, such as the Grashof number, the Reynolds number and the Prandtl number, which are all used in order to discuss the convective flow in fluid mechanics. 

If these Peclet numbers are divided by the Reynolds number, the resulting dimensionless numbers are called the Pradtl number, Pr and Schmidt number. Sc, respectively. The Prandtl number (Pr) is the ratio of momentum diffusivity and thermal diffusivity. The Schmidt number (Sc) is the ratio of momentum diffusivity and mass diffusivity. These five dimensionless numbers can convey very useful information about the relative contributions of convective and molecular transport and relative magnitudes of momentum, heat and mass transfer. 

The Prandtl number is a dimensionless number named after Ludwig Prandtl. It is defined as the ratio of momentum diffusivity (kinematic viscosity) to the thermal diffusivity, as well as the ratio of viscous diffusion rate to thermal diffusion rate ... 

The introduction of different parameterizations for the turbulent viscosity parameter leads to different modifications of the correlations for the dimensionless numbers. By setting the viscous Prandtl and Schmidt number equal to unity and noting that the integral term in the denominator is simply the velocity (5.276) that can also be expressed by = = we get... 

In Chapter 5, following some dimensional arguments, we learned that the independent dimensionless numbers characterizing buoyancy driven flows are the Rayleigh number and the Prandtl number (Ra, Pr), and the heat transfer in (Nusselt number Nu for) natural convection is governed by... 

Define and interpret the following dimensionless numbers Schmidt, Prandtl, and Lewis. 

When the gas is motionless, the free convection is desoibed by three dimensionless numbers the Niisselt number, the Grashof (Gr) number, and the Prandtl (Pr) number ... 

To correlate these data for heat-transfer coefficients, dimensionless numbers such as the Reynolds and Prandtl numbers are used. The Prandtl number is the ratio of the shear component of diffusivity for momentum p/p to the diffusivity for heat k/pc and physically relates the relative thickness of the hydrodynamic layer and thermal boundary layer. 

The Nusselt number is basically a dimensionless temperature gradient averaged over the heat transfer surface. The Nusselt number represents the ratio of the heat transfer resistance estimated from the characteristic dimension of the object (L/k) to the real heat transfer resistance (f/h). In many convective heat transfer problems, the Nusselt number is expressed as a function of other dimensionless numbers, e.g., the Reynolds number and the Prandtl number. 

Reynolds, Prandtl, and Nusselt dimensionless numbers can be obtained as defined previously for the calculation of the tube side heat coefficient, applying the corresponding shell parameters. 

The present problem is governed by a total of 8 dimensionless numbers droplet length to channel width ratio iJi/W), density ratio p /pi), viscosity ratio (jiilpii), thermal diffusivity ratio ai/ai), Prandtl number (Pr), Reynolds number (Re), Capillary number (Ca) and Marangoni number (Ma). Pr, Re, Ca and Ma are defined respectively as... 

Peles et al. [22] investigated heat transfer and pressure drop phenomena over a bank of micro-pin fins in a micro-heat sink. The dimensionless total thermal resistance was expressed as a function of Re)molds number, Prandtl number and the geometrical configuration of the pin-fin microheat sink. They compared their theoretical model with their experimental results and concluded that very high heat fluxes can be dissipated at a low wall terr5>erature rise using a microscale pin-fin heat sink. Thus, forced convection over shrouded pin-fin arrays is a very effective cooling device. In many cases, the primary cause for the rise in wall temperature is the increase of the fluid tempera-... 

The hD/k term is a dimensionless number defined as the Nusselt number. Further analysis shows that the dimensionless temperature is a function of various groups including r, 0, z, the Reynolds number. Re, the Brinkman number, Br (Example 5-6), and another dimensionless group the Prandtl number, Pr. 

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