Fourier numbers

Fig. 5.23 show the solution to Fourier s equation in terms of the temperature gradient at the centre line of section considered and the Fourier Number for... 

The above analysis illustrates how to estimate the cooling time using the relationship between the temperature gradient AT and the Fouriers Number... 

From Fig. S.23 it may be seen that the centre line temperature gradient at this Fourier Number is almost 1. 

This equation is the first term of an infinite series which appears in the rigorous solution of the quasi-diffusion. This equation describes the regular process of quasi-diffusion. For the low values of the Fourier number (irregular quasi-diffusion) it is necessary to use Eq. (5.1) or Boyd-Barrer approximation [105, 106] for the first term in Eq. (5.1)... 

Figures 9.14-9.16 enable the temperature 9C at the centre of the solid (centre-plane, centre-line or centre-point) to be obtained as a function of the Fourier number, and hence of time, with the reciprocal of the Biot number (Bil) as parameter.

Figures 9.17-9.19 clearly show that, as the Biot number approaches zero, the temperature becomes uniform within the solid, and the lumped capacity method may be used for calculating the unsteady-state heating of the particles, as discussed in section (2). The charts are applicable for Fourier numbers greater than about 0.2.

Kato et al. have used electric stepwise heating of a thin metal layer to measure thermal diffusivity of molten salts. The ratio of the temperatures with time and 2/i at distance x below tlie heating plate was evaluated as a function of the Fourier number ... 

In addihon to the CFD results, estimates of the mixing length based on the Fourier number ... 

For heat transfer the Fourier number is cct/a. The heat transfer analogs of the mass transfer dimensionless groups can be found by making the substitutions described in Chapter 1. 

Fo being the Fourier number and d the diameter of the disk. The mass transfer coefficient k can be considered as interpolating between the steady-state convective diffusion at large times (t - oo) and unsteady-state diffusion at short times (t — 0 and v = 0). The constants A and B of Eq. (147) follow from the solutions for these two limiting cases. For these two limiting cases... 

In the theory of heat transfer, 112 is known as the Fourier number. Therefore, the baking procedure can be presented in a two-dimensional frame ... 

The dimensionless temperature profile is described as a function of the Biot number and Fourier numbers [3, 5]. 

A conservative estimate of the disc s mass transfer performance may be obtained from the Nusselt model, assuming that there is no film mixing as it proceeds to the edge of the disc. For unsteady diffusion into a finite stagnant slab, the plot shown in Figure 8 from (8) gives the relative concentration distribution within the slab at various times, with a zero initial concentration and a surface concentration C0 imposed at time t = 0. The parameter on the curves is the Fourier number, Fo, where... 

---