Natural convection, laminar number

Equation 9.215 is valid for Reynolds Numbers in excess of 10,000. Where the Reynolds Number is less than 2000, the flow will be laminar and, provided natural convection effects... 

Below a Reynolds number of about 2000 the flow in pipes will be laminar. Providing the natural convection effects are small, which will normally be so in forced convection, the following equation can be used to estimate the film heat-transfer coefficient ... 

In the forced convection heat transfer, the heat-transfer coefficient, hy mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, hy on fluid velocity, IT, which has been observed empirically (1—3), for laminar flow inside tubes, is h V1//3 for turbulent flow inside tubes, h V3//4 and for flow outside tubes, h V2/73. Flow may be classified as laminar or turbulent. Laminar flow is generally characterized by low velocities and turbulent flow by high velocities. It is customary to use the Reynolds number, Rtf, to identify whether a flow is laminar or turbulent. 

In order to. illustrate how natural convection in a vertical channel can be analyzed, attention will be given to flow through a wide rectangular channel, i.e., to laminar, two-dimensional flow in a plane channel as shown in Fig. 8.15. This type of flow is a good model of a number of flows of practical importance. 

Ihe role played by the Reynolds number in forced convection is played by the Grashof number in natural convection. As such, the Grashof number provides the main criterion in determining whether the fluid flow is laminar or turbulent in natural convection. For vertical plates, for e.Kample, the critical... 

Water is heated from 15 to 65°C in a steam-heated horizontal 50-mm-ID tube. The steam temperature is 120 C. The average Reynolds number of the water is 450, The individual coefficient of the water is controlling. By what percentage would natural convection increase the total rate of heat transfer over that predicted for purely laminar flow Compare your answer with the increase indicated in Example 12.4. 

The equation for the laminar Nusselt number Nut is obtained in a two-step procedure. In the first step, not only is the flow idealized as everywhere laminar, but the boundary layer is treated as thin. There results from this idealization the equation for the laminar thin-layer Nusselt number Nur. As already explained, natural convection boundary layers are generally not thin, so the second step is to correct Nur to account for thick boundary layers. This correction uses the method of Langmuir [175]. The corrected Nusselt number is the laminar Nusselt number Nuc. 

The intersection points of the pure natural convection and pure forced convection equation also provide valuable information on the conditions for which forced and natural convection are equally important. For example, for laminar flow along the heated isothermal vertical plate in Fig. 4.6 if Eq. 4.33a for NulV is equated to the forced convection Nusselt number given by... 

Horizontal Flow. For laminar flow over the upper surface of a horizontal heated plate (or over the bottom surface of a cooled plate), the center of the mixed convection regime can again be estimated by equating the forced convection Nusselt number from Eq. 4.154 to that for natural convection from Eq. 4.39c (for detached turbulent convection). This results in... 

Uniform Heat Flux. For laminar flow in a horizontal tube where uniform heat flux is applied at the outer boundary of the tube, the bulk temperature Tb, increases linearly in the axial direction. To maintain the heat flow to the fluid, the wall temperature must remain higher than the fluid temperature, and under these conditions a fully developed natural convection motion becomes established in which velocity and temperature gradients become independent of the axial location. Because the fully developed Nusselt number for laminar pure forced convection is small (Nuf —> 4.36), the buoyancy-induced mixing motion can greatly enhance the heat transfer. 

Isothermal Wall. Natural convection also affects the laminar thermal development in a tube with an isothermal wall. In this case the temperature differences in the fluid near the tube inlet initiate a natural convection motion, but as the fluid temperature approaches the wall temperature far downstream, the motion slows and the fully developed Nusselt number (Nujr = 3.66) is approached. 

M. M. Yovanovich and K. Jafarpur, Bounds on Laminar Natural Convection From Isothermal Disks and Finite Plates of Arbitrary Shape From All Orientations and Prandtl Numbers, ASME HTD (264) 93-110,1993. 

As the film thickens further, turbulence will develop in the condensate film, and the heat transfer mechanism then undergoes a significant change, since the heat is transferred across the condensate film by turbulent mixing as well as by molecular conduction. For gravity-dominated flow (i.e., natural convection), the transition from laminar-wavy flow to turbulent flow occurs at film Reynolds numbers of about 1600 [18]. 

Mass and heat transfer with laminar flow in parallel-plate and cylindrical geometries is a well-known theoretical problem which has been treated by a large number of Investigators Cl-9). Perhaps the first papers in this area were those by L vtque Cl) and Graetz C2) who studied the heat transfer problem. In the absence of natural convection and for dilute systems, the heat and mass transfer problems are analogous. 

In heat transfer in a fluid in laminar flow, the mechanism is one of primarily conduction. However, for low flow rates and low viscosities, natural convection effects can be present. Since many non-Newtonian fluids are quite viscous, natural convection effects are reduced substantially. For laminar flow inside circular tubes of power-law fluids, the equation of Metzner and Gluck (M2) can be used with highly viscous non-Newtonian fluids with negligible natural convection for horizontal or vertical tubes for the Graetz number Nq, > 20 and n > 0.10. 

All of these might occur under natural convection, mixed convection, or natural-circulation conditions and each of these as laminar or turbulent flow. At the same time, detailed descriptions of the wall-to-fluid friction must also consider the states of the fluid near the wall and in the bulk. The number of empirical correlations needed to cover all possibilities for heat transfer and wall friction is large. 

From measurements of the local heat transfer from heated vertical surfaces to cryogens in the natural convection regime, it appears that the laminar boundary layer flow undergoes a transition to turbulence when the modified Grashof number (Gr ) is of the order of 10. This agrees with experiments performed with water. For a heat flux of 100 W/m, the wall boundary layer can be expected to be turbulent above a liquid height of 0.3 m in LNG, with an increase in heat transfer coefficient for wall/liquid heat transfer [ 1 ]. 

As highlighted by Shah and London [2], a natural tendency exists to use in convection problems a large number of different sets of dimensionless groups based on the analyst s particular normalization of the differential equations and boundary conditions. An effort to standardize the definitions of dimensionless groups for laminar flows through channels was made by Shah and London [2] some years ago. In this section, the normalization of the convection problems proposed by Shah and London will be followed. 

A flow field is broadly classified as laminar or turbulent. Pressure, velocity, and temperature information are used to characterize a flow field. In turbulent flows, these flow variables are random functions of space and time. The coherent and random flow structures/vortices and interactions between them influence the overall behavior of the turbulent flow field. The location of the wall surface, Reynolds number, Mach number, buoyancy force due to temperature, and concentration gradients, etc. influence the turbulent flow field characteristics. The nature of flow field also depends on the convective or absolute instability mechanism leading to turbulent flow. 

The heat-transfer phenomena for forced convection over exterior surfaces are closely related to the nature of the flow. The heat transfer in flow over tube bundles depends largely on the flow pattern and the degree of turbulence, which in turn are functions of the velocity of the fluid and the size and arrangement of the tubes. The equations available for the calculation of heat transfer coefficients in flow over tube banks are based entirely on experimental data because the flow Is too complex to be treated analytically. Experiments have shown that, in flow over staggered tube banks, the transition from laminar to turbulent flow Is more gradual than in flow through a pipe, whereas for in-line tube bundles the transition phenomena resemble those observed in pipe flow. In either case the transition from laminar to turbulent flow begins at a Reynolds number based on the velocity in the minimum flow area of about 100, and the flow becomes fully turbulent at a Reynolds number of about 3,000. The equation below can be used to predict heat transfer for flow across ideal tube banks. 

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