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Forced convection approximation

The approximation of all fluid properties as constant, including the complete neglect of any natural convection, is known as the forced convection approximation. We shall adopt it for this chapter, as well as for Chap. 11. Unlike most approximations that are introduced in this book, the forced convection approximation is adopted initially on an ad hoc basis, without a rigorous asymptotic justification.1 We may be reassured that the resultant analysis is relevant to many conditions of practical interest by the fact that it has been adopted almost universally for analysis of heat transfer problems, in which the fluid motion is not due solely to natural convection. [Pg.594]

In the forced convection approximation, with p and p fixed, the Navier-Stokes and continuity equations can be solved (at least in principle) to determine the velocity field u, and this solution is completely independent of the temperature distribution in the fluid. Once the velocity u is known, the thermal problem, represented by (9-1) and (9-2), can then be solved (again, in principle) to determine the temperature field T. Because the boundary values of T are assumed to be constant, we may anticipate that the temperature distribution throughout the fluid will be independent of time (with the exception of some initial period after the heated body is first introduced into the moving fluid). It is the steady-state temperature field that is most often our goal. For this reason, the time derivative in (9-1) will be dropped in subsequent developments. [Pg.595]

After the electrode reaction starts at a potential close to E°, the concentrations of both O and R in a thin layer of solution next to the electrode become different from those in the bulk, cQ and cR. This layer is known as the diffusion layer. Beyond the diffusion layer, the solution is maintained uniform by natural or forced convection. When the reaction continues, the diffusion layer s thickness, /, increases with time until it reaches a steady-state value. This behaviour is also known as the relaxation process and accounts for many features of a voltammogram. Besides the electrode potential, equations (A.3) and (A.4) show that the electrode current output is proportional to the concentration gradient dcourfa /dx or dcRrface/dx. If the concentration distribution in the diffusion layer is almost linear, which is true under a steady state, these gradients can be qualitatively approximated by equation (A.5). [Pg.85]

Let us suppose that there is a layer of solution close to the electrode within which all concentration changes due to electrode reaction occur and that transport within this layer is entirely by diffusion. For hydro-dynamic electrodes, this approximation is reasonable since the diffusion layer is very thin owing to the effects of forced convection. Following Nernst, we assume that the concentration varies linearly within the diffusion layer such that the flux, j, at the electrode is... [Pg.357]

These relationships have been used by Spalding in the dimensionless presentation both of theoretical values obtained in his approximate solution of the boundary layer equations (58) and of the experimental data (51, 55, 60). Emmons (3), who has solved the problem of forced convection past a burning liquid plane surface in a more rigorous fashion, shows graphically the rather close correspondence between values obtained from his exact solution and that of Spalding, and between the calculated values for flat plates and the experimental values for spheres. [Pg.122]

At a hydrodynamic electrode forced convection increases the transport of species to the electrode. However, the fraction of species converted is low. For example, for a ImM aqueous solution of volume 100 cm3 and a rotating disc of area 0.5 cm2 rotating at W = 4 Hz, the quantity electrolysed in 15 minutes is approximately 1 per cent. [Pg.194]

The boundary layer problem is difficult to solve exactly. There are several approximate methods to solve the problem. This chapter looks at external forced convection, that is, flow outside and around a solid body like a plate. The next chapter discusses flows inside a solid structure such as a pipe, or between two plates. [Pg.108]

In some forced convective flows it has been found that the Nusselt number is approximately proportional to the square root of the Reynolds number. If, in such a flow, it is found that h has a value of 15 W/m2K when the forced velocity has a magnitude of 5 m/s, find the heat transfer coefficient if the forced velocity is increased to 40 m/s. [Pg.28]

Compare the heat-transfer coefficients for laminar forced and free convection over vertical flat plates. Develop an approximate relation between the Reynolds and Grashof numbers such that the heat-transfer coefficients for pure forced convection and pure free convection are equal. [Pg.417]

At low Reynolds numbers, the Nusselt number will tend to the constant value that would exist in purely free convection, this being designated as Afa.v, whereas at high Reynolds numbers, when the effects of the buoyancy forces are small, the Nusselt numbers will tend to the values that would exist in purely forced convection at the same Reynolds number as that being considered. These forced convection Nusselt numbers are here designated as Nur- In the combined convection regions between these two limits, the Nusselt number variation can be approximately... [Pg.449]

It will be seen from the results given in the above table that the heat transfer rate is within 1% of its forced convective value when the velocity is greater than approximately 0.2 m/s. [Pg.454]

In forced convective turbulent boundary layer flow over a plate the velocity and temperature distributions are approximately given by ... [Pg.479]

The Grashof number may be interpreted physically as a dimensionless group representing the ratio of the buoyancy forces to the viscous forces in the free-convection flow system. It has a role similar to that played by the Reynolds number in forced-convection systems and is the primary variable used as a criterion for transition from laminar to turbulent boundary-layer flow. For air in free convection on a vertical flat plate, the critical Grashof number has been observed by Eckert and Soehngen [1] to be approximately 4 x 10". Values ranging between 10" and 109 may be observed for different fluids and environment turbulence levels. ... [Pg.328]

A spherical balloon gondola 2.4 m in diameter rises to an altitude where the ambient pressure is 1.4 kPa and the ambient temperature is — 50°C. The outside surface of.the sphere is at approximately 0°C. Estimate the free-convection heat loss from the outside of the sphere. How does this compare with the forced-convection loss from such a sphere with a low free-stream velocity of approximately 30 cm/s ... [Pg.364]

L. Oblate spheroid, forced convection , d0h up j total surface area i perimeter normal to flow e.g., for cube with side length a, d = 1.27a. k ch [E] Used with arithmetic concentration difference. 120 < NRe 6000 standard deviation 2.1%. Eccentricities between 1 1 (spheres) and 3 1. Oblate spheroid is often approximated by drops. [141] p. 284 [142]... [Pg.70]

Boundary-layer theory has been applied to solve the heat-transfer problem in forced convection laminar flow along a heated plate. The method is described in detail in numerous textbooks (El, G5, S3). Some exact solutions and approximate solutions are also obtained (B2, S3). [Pg.249]


See other pages where Forced convection approximation is mentioned: [Pg.595]    [Pg.699]    [Pg.841]    [Pg.245]    [Pg.595]    [Pg.699]    [Pg.841]    [Pg.245]    [Pg.358]    [Pg.695]    [Pg.695]    [Pg.696]    [Pg.371]    [Pg.245]    [Pg.256]    [Pg.378]    [Pg.517]    [Pg.123]    [Pg.245]    [Pg.11]    [Pg.461]    [Pg.476]    [Pg.479]    [Pg.265]    [Pg.14]    [Pg.143]    [Pg.49]    [Pg.512]    [Pg.513]    [Pg.358]    [Pg.15]    [Pg.176]   
See also in sourсe #XX -- [ Pg.593 , Pg.594 ]




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