Positive temperature gradient

Let us consider a family of curves which correspond to the condition given at the hot wall 6 = 0 for = 0 (Fig. 4). We may assert that it is precisely the curve for which the point 6 = 0, = 0 is a maximum (curve 0 in Fig. 4), that is least steep and higher than all the other curves over a large distance. Indeed, curve 1 with a positive temperature gradient near the wall reaches a maximum at > 0, 0max > 0. 

There are other important differences between the stratosphere and troposphere. Whereas the troposphere is heated from the bottom (i.e. the earth s surface), the stratosphere heats from the top (i. e. by incoming solar radiation). This positive temperature gradient results in an extremely stable layering. Therefore, mixing and transport are much weaker than in the troposphere. At the bottom of the stratosphere, close to the tropopause, the lowest temperatures are found (200-220 K and at the poles down to 180 K), whereas temperature rises up to 270 K can be found at 50 km altitude. At each point of the stratosphere the temperature is determined by adiabatic radiation processes O3 absorbs UV radiation and heats the air and CO2 absorbs IR radiation and cools the air. The chemical composition (mixing... 

Inversion Positive temperature gradient or increase in temperature with elevation, resulting in adverse conditions for dispersion of pollutants. 

In contrast, convection currents are not possible in the stratosphere, because of the positive temperature gradient. Mixing there is caused by differential solar heating of the stratospheric gas across the latitudes and is known as advection. Air heated at the equator expands and moves towards the poles. Displaced air tends to rise at the poles and comes back down to replace the sinking heated air at the equator. An important point is that air on either side of the tropopause, moves horizontally and parallel, which makes mixing across the boundary difficult. The stratospheric air mass is therefore, partially isolated from that of the troposphere. Thus, whereas effective mixing within the troposphere may take only a few days or weeks, effective mixing across the boundary may take many months. 

Fig. 4.4 (a) Area ct wlUi and liquid adjacent to the interface showing a negative temperature gradient in the liquid and a positive temperature gradient in the soiid (schematic), (b) Schematic sequence showing the formation and stabilisation of a protuberance on the interface when it projects into a region where the iocai tip temperature is beiow the meiting temperature. 

Van den Akker (1978) carried out a Hnear stabflity analysis for a liquid-liquid spray column operated with a positive temperature gradient. The leading idea was that local differences in mixture density would give rise to a multiple circulation pattern in a way similar to the multicellular natural convection mode in a vertical slot heated from one side (Elder, 1965 Lee and Korpela, 1983). The only way to find in the Hquid—Hquid spray colurrm... 

Van den Akker HEA, Rietema K Plow patterns and axial mixing in liquid-liquid spray columns— part 3. The reduction of axial mixing by applying a positive temperature gradient, Trans Inst Chem Eng 57 84—93, 1979a. 

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