how to set barcode in rdlc report using c# Forced and natural convection Natural convection Forced convection; dynamic similarity Mass transfer in Software

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Forced and natural convection Natural convection Forced convection; dynamic similarity Mass transfer
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Summary of the Chief Dimensionless Groups* (Continued ) Physical signi cance (interpretation) Ratio of convection mass transfer to diffusion in a slab of thickness L Ratio of the velocity of vibration L to the velocity of the uid h cpV hD V Dimensionless heat transfer coef cient (ratio of heat transfer at the surface to that transported by uid by its thermal capacity) Dimensionless mass transfer coef cient Ratio of inertia force to surface tension force Main area of use Convective mass transfer Flow past tube (shedding of eddies) Forced convection
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Sherwood number
Strouhal number
Stanton number
hDL D L V Nu Re Pr
Stanton number (mass transfer)
Weber number
Sh Re Sc V 2L
Convective mass transfer Droplet breakup; thin- lm ow
* In these dimensionless groups, L designates characteristic dimension (eg, tube diameter, hydraulic diameter, length of the tube or plate, slab thickness, radius of a cylinder or sphere, droplet diameter, thin- lm thickness, etc) Physical properties are usually evaluated at mean temperature unless otherwise speci ed Note: D D12 (D12 is also a commonly used symbol for binary diffusion coef cient; Di is theh multicomponent diffusion coef cient) When species 1 is in very small concentration, the symbol D1m is occasionally used,7 representing an effective binary diffusion coef cient for species 1 diffusing through the mixture In some engineering texts, the symbol St is also used for this group
CONSERVATION EQUATIONS AND DIMENSIONLESS GROUPS
m* y*
y* 0
(1048)
This parameter, termed the Sherwood number, is equal to the dimensionless mass fraction (ie, concentration) gradient at the surface, and it provides a measure of the convection mass transfer occurring at the surface Following the same argument as before [but now for Eq (1041)), we have Sh 4(Re, Sc) (forced convection, mass transfer) (1049)
The signi cance of expressions such as Eqs (1044) to (1046) and (1049) should be appreciated For example, Eq (1045) states that convection heat-transfer results, whether obtained theoretically or experimentally, can be represented in terms of three dimensionless groups, instead of seven parameters (h, L, V, k, cp , , and ) The convenience is evident Once the form of the functional dependence of Eq (1045) is obtained for a particular surface geometry (eg, from laboratory experiments on a small model), it is known to be universally applicable; ie, it may be applied to different uids, velocities, temperatures, and length scales, as long as the assumptions associated with the original equations are satis ed (eg, negligible viscous dissipation and body forces) Note that the relations of Eqs (1044) and (1049) are derived without actually solving the system of Eqs (1028) and (1031) References 7 to 12 cover the preceding procedure with more details and also include many different cases It is important to mention here that once the conservation equations are put in dimensionless form, it is also convenient to make an order-of-magnitude assessment of all terms in the equations Often a problem can be simpli ed by discovering that a term that would be very dif cult to handle if large is in fact negligibly small7,8 Even if the primary thrust of the investigation is experimental, making the equations dimensionless and estimating the orders of magnitude of the terms are good practice It is usually not possible for an experimental test to include (simulate) all conditions exactly; a good engineer will focus on the most important conditions The same applies to performing an order-of-magnitude analysis For example, for boundary-layer ows, allowance is made for the fact that lengths transverse to the main ow scale with a much shorter length than those measured in the direction of main ow References 7, 11, and 13 cover many examples of the order-ofmagnitude analysis When the governing equations of a problem are unknown, an alternative approach of deriving dimensionless groups is based on use of dimensional analysis in the form of the Buckingham pi theorem3,5,9,12,14 The Buckingham pi theorem proves that in a physical problem including n quantities in which there are m dimensions, the quantities can be arranged into n m independent dimensionless parameters The success of this method depends on our ability to select, largely from intuition, the parameters that in uence the problem The procedure is best illustrated by an example
Example 101 The discharge through a horizontal capillary tube is thought to depend on the pressure drop per unit length, the diameter, and the viscosity Find the form of the equation The quantities with their dimensions are as follows:
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