Isothermal plane

It is also possible to have a combined wave, which has both gradual and abrupt parts. The general rule for an isothermal, trace system is that in passing from the initial condition to the feed point in the isotherm plane, the slope of the path must not decrease, if it does, then a shock chord is taken for that part of the path. Referring to Fig. 16-19, for a transition from (0,0) to (1,1), the dashes indicate shock parts, which are connected by a simple wave part between points Pi and Pg. 

FIG. 16-19 Path in isotherm plane for a combined wave (After Tudge). 

FIG. 16-23 Transition paths in isotherm plane for adiabatic adsorption and thermal regeneration. 

Two dimensional isothermal diagrams which represent isothermal plane intersections with various surfaces (liquidus, solidus, etc). 

The / -value of a wall or roof structure that involves layers of uniform thickness is determined easily by simply adding up the unit thermal resistances of the layers that are in series. But when a structure involves components such as wood studs and metal connectors, then the thermal resistance network involves parallel connections and possible two-dimensional etfects. The overall / -value in this case can be dctcimined by assuming (1) parallel heal flow paths through areas of different construction or (2) isothermal planes normal to the direction of heal transfer. The first approach usually overpredicts the overall thermal resistance, whereas the second approach usually underpredicts it. The parallel heat flow path approach is more suitable for wood frame walls and roofs, whereas the isothermal planes approach is more suitable for inasoiuy or metal frame walls. 

When the solute isotherms cross one another, the situation becomes more complex. It then becomes possible to experience selectivity reversal that is, at one displacer concentration, the solutes elute in the order A first, then B, whereas at another displacer concentration, the order is B first, then A. In a study of this problem, Antia and Horvath showed the existence of the separation gap. This is a region in the isotherm plane, the position of which depends on the ratio of the saturation capacities of the solutes in question. If the operating line is outside the separation gap, displacement occurs in the normal fashion. The elution order of the solutes then depends on the position of the operating line relative to the separation gap. However, if the operating line is within the separation gap, displacement operation does not separate the displaced solutes, but results in the elution of a mixture of the solutes. 

It is rather simple to calculate the resistance to heat conduction between a tube and an isothermal plane as shown in Fig. 2.18 b. With = l and k according to (2.94) we obtain from (2.96)... 

Fig. 2.18 Three arrangements of tubes with isothermal surfaces, a two eccentric tubes, one inside the other, b a tube and an isothermal plane, c two tubes with distance between their centres s > R + R2...

Heat transfer in laminar flow of a power-law fluid over an isothermal plane surface... 

Consider a temperature midway between the melting points of the pure components and the three eutectic temperatures in system ABC, as shown in Figure 17.34. An isothermal plane at this temperature will cut through all three liquidus surfaces. Near each apex, the plane lies below each liquidus surface, so it shows an area of solid plus liquid filled with tie-lines. In the center of the diagram, the plane is everywhere above the liquidus surfaces, and so it shows a blank field of liquid. Sections at successively lower temperatures would show the two-phase fields expanding and coalescing, leaving smaller and smaller liquid fields. 

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