Laminar heat transfer internal flow

The water evaporation takes place below the evaporator in a substantial laminar flow. Because the entire phenomenon is driven by the heat transfer rate, in order to preserve the quality of the end product it is of the utmost importance to avoid any buildup of product on the wall of the evaporator this action is assured by the internal mechanical features of the evaporator, consisting of a rotating shaft holding a series of movable blades supported by appropriate frames. These rotating blades provide for a strong eddy effect on the fed prod-... 

Fabbri, G. Heat Transfer Optimization in Internally Finned Tubes Under Laminar Flow Conditions. Int J Heat Mass Transfer 41 (10) 1243-1253 (1998). 

Internal flows of the type here being considered occur in heat exchangers, for example, where the fluid may flow through pipes or between closely spaced plates that effectively form a duct Although laminar duct flows do not occur as extensively as turbulent duct flows, they do occur in a number of important situations in which the size of the duct involved is small or in which the fluid involved has a relatively high viscosity. For example, in an oil cooler the flow is usually laminar. Conventionally, it is usual to assume that a higher heat transfer rate is achieved with turbulent flow than with laminar flow. However, when the restraints on possible solutions to a particular problem are carefully considered, it often turns out that a design that involves laminar flow is the most efficient from a heat transfer viewpoint. 

This chapter has been concerned with flows in wb ch the buoyancy forces that arise due to the temperature difference have an influence on the flow and heat transfer values despite the presence of a forced velocity. In extemai flows it was shown that the deviation of the heat transfer rate from that which would exist in purely forced convection was dependent on the ratio of the Grashof number to the square of the Reynolds number. It was also shown that in such flows the Nusselt number can often be expressed in terms of the Nusselt numbers that would exist under the same conditions in purely forced and purely free convective flows. It was also shown that in turbulent flows, the buoyancy forces can affect the turbulence structure as well as the momentum balance and that in turbulent flows the heat transfer rate can be decreased by the buoyancy forces in assisting flows whereas in laminar flows the buoyancy forces essentially always increase the heat transfer rate in assisting flow. Some consideration was also given to the effect of buoyancy forces on internal flows. 

Equipment designs based on indirect conduction usually transfer the heat from the primary heat transfer fluid to the intermediate wall within some kind of internal duct or channel. Transfer coefficients for these cases depend on the nature of the flow (laminar or turbulent) and the geometry of the duct or channel (short or long). Expressions for evaluating the transfer coefficients for these cases are available in standard texts. An expression for the convective thermal resistance can be generated similar to that derived for the conductive resistance ... 

Prakash and Liu [266] have numerically analyzed laminar flow and heat transfer in the entrance region of an internally finned circular duct. In this study, the fully developed / Re is compared with those reported by Hu and Chang [265] and Masliyah and Nandakumar [267]. The incremental pressure drop K(°°) and hydrodynamic entrance length L+hy together with /Re are given in Table 5.48, in which the term n refers to the number of fins, while / denotes the relative length of the fins. 

An elliptical duct with four internal longitudinal fins mounted on the major and minor axes, as shown in Fig. 5.48, has been analyzed by Dong and Ebadian [275] for fully developed laminar flow and heat transfer. In this analysis, the fins are considered to have zero thickness. The thermal boundary condition is applied to the duct wall, and / is defined as a ratio of Ha a = Hbib. The friction factors and Nusselt numbers for fully developed laminar flow are given in Table 5.52. 

C. Prakash, and Y. Liu, Analysis of Laminar Flow and Heat Transfer in the Entrance Region of an Internally Finned Circular Duct, J. Heat Transfer, (107) 84-91,1985. 

A. P. Watkinson, D. C. Miletti, and G. R. Kubanek, Heat Transfer and Pressure Drop of Internally Finned Tubes in Laminar Oil Flow, ASME Paper 75-HT-41, ASME, New York, 1975. 

W. J. Marner and A. E. Bergles, Augmentation of Tubeside Laminar Flow Heat Transfer by Means of Twisted-Tape Inserts, Static-Mixer Inserts and Internally Finned Tubes, Heat Transfer 1978, Proc. 6th Int. Heat Transfer Conf, Hemisphere, Washington, DC, vol. 2, pp. 583-588,1978. 

J. E. Porter and R. Poulter, Electro-Thermal Convection Effects With Laminar Flow Heat Transfer in an Annulus, in Heat Transfer 1970, Proceedings of the 4th International Heat Transfer Conference, vol. 2, paper FC3.7, Elsevier, Amsterdam, 1970. 

Vertical Surfaces. If the laminar flow direction is downward and gravity-controlled, heat transfer coefficient for internal condensation inside vertical tubes can be predicted using the correlations for external film condensation—see Table 17.23. The condensation conditions usually occur under annular flow conditions. Discussion of modeling of the downward internal convective condensation is provided in Ref. 76. 

Fairweather, M., Kilham, J. K., and Nawaz, S. "Stagnation Point Heat Transfer from Laminar, High Temperature Methane Flames." International Journal of Heat and Fluid Flow 5, no. 1 (1984) 21-27. 

Internal circulation is generally assumed to cause thinning of the outside boundary layer, thus increasing appreciably the transfer rate between the drop and the ambient fluid (B12, G3). In other words, because of the mobility of the interface, a smaller velocity gradient exists near it that results in larger convective heat transfer. Rumscheidt and Mason (R8) proved the dependence of the streamlines outside and inside spherical drops undergoing laminar shear flow on the viscosity ratio of the fluids. As the exact velocity profiles for normal flow conditions are unknown, the solutions for the transfer rate that account for this effect are only approximate. 

The solution of Eqs. 22 and 23a with the appropriate dynamic and thermal boundary conditions allows one to obtain the velocity and temperature distribution inside the microchannel for laminar fully developed flows. The analytical solution of Eqs. 22 and 23a has been obtained only for a few cross-sectional geometries. The numerical approach enables the calculation of the local and the average Nusselt number by means of which the internal convective heat transfer coefficients in microchannels can be computed. 

The surface to volume ratio for microdevices can be as high as 50 000 m m [4]. For comparison, the specific surface area of typical laboratory and production vessels seldom exceed 100 m m . Moreover, because of the laminar flow regime within microcapillaries, the internal heat transfer coefficient is inversely proportional to the channel diameter. Therefore, overall heat transfer coefficients up to 25000 W m" can be obtained, exceeding those of conventional heat exchangers by at least 1 order of magnitude [5]. Indeed, conventional heat exchangers have overall heat transfer coefficients of less than 2000 W m [6]. 

G. Gamrat, M. Favre-Marinet, D. Asendrych, Conduction and entrance effects on laminar liquid flow and heat transfer in rectangular microcharmels. International Journal of Heat and Mass Tranfer. 2005, 48, 2943-2954. 

Worsoe-Schmidt PM. Heat transfer in the thermal entrance region of circular tubes and annular passages with fully developed laminar flow. International Journal of Heat and Mass Transfer 1967 10 541-551. 

For fully developed laminar flow (Section 3.2.2.1), the average Nu number for the heat transfer to the internal surface of the tube with uniform temperature, length L, and diameter dt is (Schluender, 1970 VDI, 1997, see Example 3.2.1) ... 

The peripheral average heat transfer flux is strongly dependent on the thermal boundary conditions in the laminar regime, typical of microchanneis, while very much less dependent in the turbulent flow regime. For this reason, for microchanneis is very important to classify the thermal boundary conditions in order to model correctly the internal convective heat transfer. 

Solutions exist for a porous channel with two porous walls for laminar channel flow with heat transfer for asymmetric isoflux hoimdaries (Hadim, 1994 Nield et al., 1996, 2003h Kuznetsov and Nield, 2009 Chen and Tso, 2012), with small uniform suction or injection (Doughty, 1971 Raithhy, 1971 Doughty and Perkins, 1972), with arbitrary uniform suction or injection (Lan and Khodadadi, 1993), for non-Newtonian fluid flow (Mahmud and Fraser, 2002), and for internal heat sources included (Vidhya and Kesavan, 2010) with arbitrary uniform suction or injection (Elbashbeshy and Bazid, 2004 Cortell, 2005). 

Performance problems related to maldistribution also exist in cooling applications, especially where viscosity increases as temperature is lowered. At worst, case equipment could become inoperable, due to plugging of all but the center of the flow channel. This condition can be eliminated by the use of static mixer internals, discussed later. Heat transfer coefficients for laminar flow in empty pipe are correlated by... 

Asako, Y., H. Nakamura and M. Fagri. Developing laminar flow and heat transfer in the entrance region of regular polygonal ducts. International Journal of Heat and Mass Transfer 31 2590-2593,1988. 

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