Simplified models of the symmetric single-pass parallel-plate counterflow heat exchanger: a tutorial.

The heat exchanger is important in practical thermal processes, especially those of (i) the molten-salt storage schemes, (ii) compressed air energy storage schemes and (iii) other load-shifting thermal storage presumed to undergird a Smart Grid. Such devices, although central to the utilization of energy from sustainable (but intermittent) renewable sources, will be unfamiliar to many scientists, who nevertheless need a working knowledge of them. This tutorial paper provides a largely self-contained introduction for such persons.

A model for leaf initiation: determination of phyllotaxis by waves in the generative circle.

A biophysical model is proposed for how leaf primordia are positioned on the shoot apical: meristem in both spiral and whorl phyllotaxes. Primordia are initiated by signals that propagate: in the epidermis in both azimuthal directions away from the cotyledons or the most recently: specified primordia. The signals are linear waves as inferred from the spatial periodicity of the: divergence angle and a temporal periodicity.

A simplest steady-state Munch-like model of phloem translocation, with source and pathway and sink.

In the 80 years since its introduction by Münch, the pressure-driven mass-flow model of phloem translocation has become hegemonic, and has been mathematically modelled in many different fashions but not, to our knowledge, by one that incorporated the equations of hydrodynamics with those of osmosis and slice-source and slice-sink boundary conditions to yield a system that admits of an analytical steady-state solution for the sap velocity in a single sieve tube. To overcome this situation, we drastically simplified the problem by: (i) justifying a low Peclet number idealisation in which transverse variations could be neglected; (ii) justifying a low viscosity idealisation in which axial pressure drops could be neglected; and (iii) assuming a sink of strength sufficient to lower the photosynthate concentration at the extreme distal end of the sieve tube to levels at which it became unimportant. The resulting ordinary nonlinear second-order differential equation in sap velocity and axial position was of a generalised Liénard form with a single forcing parameter; and this is reason enough for the lack of a known analytic solution.