Flat plates, flow over, heat transfer

Moutsoglu, A., Chen, T.S. and Cheng, K.C. (1981). Vortex instability of mixed convection flow over a horizontal flat plate, ASME J. Heat Transfer 103 257-261. 

Air at standard atmospheric pressure and a temperature of 30°C flows over a flat plate at a velocity of 20 m/s. The plate is 60 cm square and is maintained at uniform temperature of 90°C. The flow is normal to a sule of the plate. Calculate the heat transfer from the plate assuming that the flow is two-dimensional. 

T. C. Chen and A. Mucoglu, Wave Instability of Mixed Convection Flow Over a Horizontal Flat Plate, Int. J. Heat Mass Transfer (22) 185-196,1979. 

Air flows at a velocity of 9 m/s over a wide flat plate that has a length of 6 cm in the flow direction. The air ahead of the plate has a temperature of 10°C while the surface of the plate is kept at 70°C. Using the similarity solution results given in this chapter, plot the variation of local heat transfer rate in W/m2 along the plate and the velocity and temperature profiles in the boundary layer on the plate at a distance of 4 cm from the leading edge of the plate. Also calculate the mean heat transfer rate from the plate. 

J. Glycerin at a temperature of 30°C flows over a 30-cm long flat plate at a velocity of 1 m/sj The surface of the plate is kept at a temperature of 20°C. Find the mean heat transfer rate per unit area to the plate. 

Consider laminar forced convective flow over a flat plate at whose surface the heat transfer rate per unit area, qw is constant. Assuming a Prandtl number of 1, use the integral equation method to derive an expression for the variation of surface temperature. Assume two-dimensional flow. 

Air at a pressure of S kPa and a temperature of —30°C flows at a Mach number of 2.5 over a flat plate that is aligned with die flow. The plate is kept at a uniform temperature of 5°C. Find the heat transfer from the plate surface to the air. 

As discussed in the previous chapter, most early efforts at trying to theoretically predict heat transfer rates in turbulent flow concentrated on trying to relate the wall heat transfer rate to the wall shear stress [1],[2],[3],[41. The reason for this is that a considerable body of experimental and semi-theoretical knowledge concerning the shear stress in various flow situations is available and that the mechanism of heat transfer in turbulent flow is obviously similar to the mechanism of momentum transfer. In the present section an attempt will be made to outline some of the simpler such analogy solutions for boundary layer flows, attention mainly being restricted to flow over a flat plate. 

The effects of fluid property variations on heat transfer in turbulent boundary layer flow over a flat plate have also been numerically evaluated. This evaluation indicates that if the properties are as with If minar boundary layers evaluated at ... 

Air at a temperature of 20°C flows at a velocity of 100 m/s over a 3-m long wide flat plate which is aligned with the flow. The first fifth of the plate is unheated and the remainder of thie plate is maintained at a uniform wall temperature of 60°C. Plot the variation of the local heat transfer rate along the heated section of the plate. Evaluate the air... 

Air flows over a 3-m long flat plate which has a uniform surface temperature of 60°C, the temperature of the air ahead of the plate being 20°C. The air velocity is 60 m/s. Numerically determine the variation of the local heat transfer rate from the wall. qw, with x assuming that boundary layer transition occurs at Rej of 106. 

Because, for flow over a heated surface. r>ulc>x is positive and ST/ y is negative. S will normally be a negative. Hence, in assisting flow, the buoyancy forces will tend to decrease e and e, i.e., to damp the turbulence, and thus to decrease the heat transfer rate below the purely forced convective flow value. However, the buoyancy force in the momentum equation tends to increase thle mean velocity and, therefore, to increase the heat transfer rate. In turbulent assisting flow over a flat plate, this can lead to a Nusselt number variation with Reynolds number that resembles that shown in Fig. 9.22. 

It turns out that Eq. (5-56) can also be applied to turbulent flow over a flat plate and in a modified way to turbulent flow in a tube. It does not apply to laminar tube flow. In general, a more rigorous treatment of the governing equations is necessary when embarking on new applications of the heat-trans-fer-fluid-friction analogy, and the results do not always take the simple form of Eq. (5-56). The interested reader may consult the references at the end of the chapter for more information on this important subject. At this point, the simple analogy developed above has served to amplify ouf understanding of the physical processes in convection and to reinforce the notion that heat-transfer and viscous-transport processes are related at both the microscopic and macroscopic levels. 

Most of this chapter has been concerned with flow over flat plates and the associated heat transfer. For convenience to the reader we have summarized the equations in Table 5-2 along with restrictions which apply. The general procedure then is to ... 

Derive an expression for the heat transfer in a laminar boundary layer on a flat plate under the condition = w, = constant. Assume that the temperature distribution is given by the cubic-parabola relation in Eq. (5-30). This solution approximates the condition observed in the flow of a liquid metal over a flat plate. 

An experiment is to be designed to demonstrate measurement of heat loss for water flowing over a flat plate. The plate is 30 cm square and it will be maintained nearly constant in temperature at 50°C while the water temperature will be about 10°C. (a) Calculate the flow velocities necessary to study a range of Reynolds numbers from 104 to 107. (b) Estimate the heat-transfer coefficients and heat-transfer rates for several points in the specified range. 

Plot hj versus x for air at 1 atm and 300 K flowing at a velocity of 30 m/s across a flat plate. Take Reonl = 5 x 10s and use semilog plotting paper. Extend the plot to an x value equivalent to Re 10. Also plot the average heat-transfer coefficient over this same range. 

Air flows over an isothermal flat plate maintained at a constant temperature of 65°C. The velocity of the air is 600 m/s at static properties of 15°C and 7 kPa. Calculate the average heat-transfer coefficient for a plate 1 m long. 

Churchill, S. W., and H. Ozoe Correlations for Laminar Forced Convection in Flow over an Isothermal Flat Plate and in Developing and Fully Developed Flow in an Isothermal Tube, J. Heat Transfer, vol. 95, p. 46, 1973. 

While the engineer may frequently be interested in the heat-transfer characteristics of flow systems inside tubes or over flat plates, equal importance must be placed on the heat transfer which may be achieved by a cylinder in cross flow, as shown in Fig. 6-7. As would be expected, the boundary-layer development on the cylinder determines the heat-transfer characteristics. As long as the boundary layer remains laminar and well behaved, it is possible to compute the heat transfer by a method similar to the boundary-layer analysis of Chap. 5. It is necessary, however, to include the pressure gradient in the analysis because this influences the boundary-layer velocity profile to an appreciable extent. In fact, it is this pressure gradient which causes a separated-flow region to develop on the back side of the cylinder when the free-stream velocity is sufficiently large. 

Let us first consider the simple flat plate with a liquid metal flowing across it. The Prandtl number for liquid metals is very low, of the order of 0.01. so that the thermal-boundary-layer thickness should be substantially larger than the hydrodynamic-boundary-layer-thickness. The situation results from the high values of thermal conductivity for liquid metals and is depicted in Fig. 6-15. Since the ratio of 8/8, is small, the velocity profile has a very blunt shape over most of the thermal boundary layer. As a first approximation, then, we might assume a slug-flow model for calculation of the heat transfer i.e., we take... 

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