Flat plate laminar boundary layer

I. Turbulent, local flat plate, natural convection, vertical plate Turbulent, average, flat plate, natural convection, vertical plate Nsk. = — = 0.0299Wg=Ws = D x(l + 0.494W ) )- = 0.0249Wg=W2f X (1 + 0.494WE )- [S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. Ncr > 10 " Assumes laminar boundary layer is small fraction of total. D [151] p. 225... 

Continuous Flat Surface Boundaiy layers on continuous surfaces drawn through a stagnant fluid are shown in Fig. 6-48. Figure 6-48 7 shows the continuous flat surface (Saldadis, AIChE J., 7, 26—28, 221-225, 467-472 [1961]). The critical Reynolds number for transition to turbulent flow may be greater than the 500,000 value for the finite flat-plate case discussed previously (Tsou, Sparrow, and Kurtz, J. FluidMech., 26,145—161 [1966]). For a laminar boundary layer, the thickness is given by... 

Fig. 4. Migration contribution to the limiting current in acidified CuS04 solutions, expressed as the ratio of limiting current (iL) to limiting diffusion current (i ) r = h,so4/(( h,so, + cCuS(>4). "Sulfate refers to complete dissociation of HS04 ions. "bisulfate" to undissociated HS04 ions. Forced convection" refers to steady-state laminar boundary layers, as at a rotating disk or flat plate free convection refers to laminar free convection at a vertical electrode penetration to unsteady-state diffusion in a stagnant solution. [F rom Selman (S8).]...

Momentum boundary layer calculations are useful to estimate the skin friction on a number of objects, such as on a ship hull, airplane fuselage and wings, a water surface, and a terrestrial surface. Once we know the boundary layer thickness, occurring where the velocity is 99% of the free-stream velocity, skin friction coefficient and the skin friction drag on the solid surface can be calculated. Estimate the laminar boundary layer thickness of a 1-m-long, thin flat plate moving through a calm atmosphere at 20 m/s. 

The transition to a turbulent boundary layer for a flat plate has been experimentally determined to occur at an Rcx value of between 3 x 10 and 6 x 10. For this example, the transition would occur between 15 and 30 cm after the start of the plate. Thus, the computations for a laminar boundary layer at 0.6 and 1 m are not realistic. However, the Blasius solution helps in the analysis of experimental data for a turbulent boundary layer, because it can tell us which parameters are likely to be important for this analysis, although the equations may take a different form. 

Laminar boundary layer theory assumes that a uniform flow (V = constant) approaches a flat plate. A laminar flow region develops near the plate where the thickness of the laminar boundary layer increases with thickness along the plate, as developed in Example 4.2. If we assign 5 to be the boundary layer thickness, or the distance from the plate where the velocity is equal to 0.99 times the velocity that approached the plate, and 5c to be the concentration boundary layer thickness, then we can see that both 5 and 5c are functions of distance, x, from the leading edge, as shown in Figure 8.11. 

Take into consideration two-dimensional, rectilinear, steady, incompressible, constant-property, laminar boundary layer flow in the x direction along a flat plate. Assume that viscous energy dissipation may be neglected. Write the continuity, momentum and energy equations. 

Laminar Boundary Layer Flow Along a Flat Plate with Radiation Boundary Condition... 

Consider a steady, laminar boundary layer flow of incompressible, transparent fluid along a flat plate, with a constant applied heat flux qw Btu/(hr ft2) at the wall surface. The properties of the fluid are assumed constant. The main considerations are conduction to the fluid, and radiation from the plate to the environment at Te. Surface of the plate is opaque and gray, and the uniform emissivity is 8. The fluid which is at a temperature of T,, flows at a uniform velocity of Uo. Flow velocities are sufficiently small so that viscous dissipation may be neglected. 

VISCOUS DISSIPATION EFFECTS ON LAMINAR BOUNDARY LAYER FLOW OVER A FLAT PLATE... 

J0. Show how die numerical method for solving die laminar boundary layer equations discussed in this chapter can be modified to allow for viscous dissipation. Use a computer program based on this modified procedure to estimate the importance of this dissipation on the heat transfer rate along an isothermal flat plate in low speed flow. 

In order to measure the velocity of a stream of air, a flat plate of length 2 cm in the flow direction is placed in the flow. This plate is electrically heated, the heat dissipation rate being uniform over the plate surface. The plate is wide so a two-dimensional laminar boundary layer flow can be assumed to exist The velocity is to be deduced by measuring the temperature of the plate at its trailing edge. If this temperature is to be at least 40°C when the air temperature is 20 C and the air velocity is 3 m/s, find the required rate of teat dissipation in the plate per unit surface area. 

Consider transition in the boundary layer flow over a flat plate. Using the expression for the thickness of a laminar boundary layer on a flat plate given in Chapter 3, find the value of the Reynolds number based on the boundary layer thickness at which transition begins. 

A vertical flat plate is maintained at a uniform surface temperature and is exposed to air at standard ambient pressure. At a distance of 10 cm from the leading edge of the plate the boundary layer thickness is 2 cm. Estimate the thickness of the boundary layer at a distance of 25 cm from the leading edge. Assume a laminar boundary layer flow. 

Consider laminar free-conveqtive flow over a vertical flat plate at whose surface the heat transfer rate per unit area, qw, is constant. Show that a similarity solution to the two-dimensional laminar boundary layer equations can be derived for this case. 

Consider mixed convective laminar boundary layer flow over a horizontal flat plate that is heated to a uniform surface temperature. In such a flow there will be a pressure change across the boundary induced by the buoyancy forces, i.e. ... 

This is the momentum equation of the laminar boundary layer with constant properties. The equation may be solved exactly for many boundary conditions, and the reader is referred to the treatise by Schlichting ll] for details of the various methods employed in the solutions. In Appendix B we have included the classical method for obtaining an exact solution to Eq. (5-13) for laminar flow over a flat plate. For the development in this chapter we shall be satisfied with an approximate analysis which furnishes an easier solution without a loss in physical understanding of the processes involved. The approximate method is due to von Karman [2],... 

The average-friction coefficient for a flat plate with a laminar boundary layer up to Recrii and turbulent thereafter can be calculated from... 

What is the momentum equation for the laminar boundary layer on a flat plate What assumptions are involved in the derivation of this equation ... 

Using the linear-velocity profile in Prob. 5-2 and a cubic-parabola temperature distribution [Eq. (5-30)], obtain an expression for heat-transfer coefficient as a function of the Reynolds number for a laminar boundary layer on a flat plate. 

Show that d3u/dy3 = 0 at y = 0 for an incompressible laminar boundary layer on a flat plate with zero-pressure gradient. 

We further observed that the ratio via, the Prandtl number, was the connecting link between the velocity and temperature field and was thus an important parameter in all convection heat-transfer problems. If we considered a laminar boundary layer on a flat plate in which diffusion was occurring as a result of... 

Lim, T.T., Sengupta, T.K. and Chattopadhyay, M. (2004). A visual study of vortex-induced subcritical instability on a flat plate laminar boundary layer. Expts. In Fluids. 37, 47-55. 

A laminar boundary layer develops on the upwind side of a cylinder (Fig. 7-8). This layer is analogous to the laminar sublayer for flat plates (Fig. 7-6), and air movements in it can be described analytically. On the downwind side of the cylinder, the airflow becomes turbulent, can be opposite in direction to the wind, and in general is quite difficult to analyze. Nevertheless, an effective boundary layer thickness can be estimated for the whole cylinder (to avoid end effects, the cylinder is assumed to be infinitely long). For turbulence intensities appropriate to field conditions, in mm can be represented as follows for a cylinder ... 

Knowledge of the temperature field in the fluid is a prerequisite for the calculation of the heat transfer coefficient using (1.25). This, in turn, can only be determined when the velocity field is known. Only in relatively simple cases, exact values for the heat transfer coefficient can be found by solving the fundamental partial differential equations for the temperature and velocity. Examples of this include heat transfer in fully developed, laminar flow in tubes and parallel flow over a flat plate with a laminar boundary layer. Simplified models are required for turbulent... 

When air is heated to between 2000-6000 K and passed over a PTFE surface, carbonyl difluoride is detected by its emission infrared spectrum in the PTFE/air boundary layer [2239]. COF j has also been detected in an ablating flat plate air-PTFE laminar boundary layer [820,821] generated with a subsonic free stream of air (1 atm, 3000-6000 K) produced by an arc jet CO, COj, and NO were also observed in this experiment. 

It is noted that the integral method gives only approximate values for the mass transfer coefficient as the model derivation is based on several simplifying assumptions regarding the concentration and velocity profiles. Nevertheless, the given relation has been confirmed by experiments for laminar boundary layer flows over a flat plate (e.g., [134], p 80 and p 201 [27], p 345). 

A mathematical analysis has been carried out for the laminar boundary layer on a vertical flat plate with gas properties independent of temperature, and the results have been verified experimentally (Schlichting, 1979, pp. 315 ff). The temperature gradient at the wall is... 

Problem 10-9. Translating Flat Plate. Consider the high-Reynolds-number laminar boundary-layer flow over a semi-infinite flat plate that is moving parallel to its surface at a constant speed (7 in an otherwise quiescent fluid. Obtain the boundary-layer equations and the similarity transformation for f (r ). Is the solution the same as for uniform flow past a semi-infinite stationary plate Why or why not Obtain the solution for f (this must be done numerically). If the plate were truly semi-infinite, would there be a steady solution at any finite time (Hint. If you go far downstream from the leading edge of the flat plate, the problem looks like the Rayleigh problem from Chap. 3). For an arbitrarily chosen time T, what is the regime of validity of the boundary-layer solution ... 

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