Errata

Volume 4, Number 2, pp 136-138: A mathematical model for gas-liquid interaction in turbulent reacting flows by M. M. Abou Ellail and E. E. Khalil, should have included the following:

Nomenclature

c, Cr D dD

dn

; FD

gij

H

p

K L

Tfu mu

Specific heat at constant pressure Constant Diameter, droplet diameter Incremental droplet diameter

Incremental number of droplets whose diameter lies between D and D + dD Rate of dissipation of turbulence Mixture fraction Drag force vector on a single droplet Ratio of time spent by jth size group, during

ith time step, in a particular gas phase control volume to ith time step dti Stagnation enthalpy

Heat of reaction of fuel Kinetic energy of turbulence Thermal conductivity Latent heat of vaporization Fuel mass fraction Evaporation rate

Nu

& SL, T

T, t

th

u(t - th)

u, v, w

x,r,e

Droplet’s Nusselt number Radial distance from centreline Source term in 4 equation Source term due to droplet-gas interaction Mean temperature Liquid fuel saturation temperature Time Heating time Unit step function, = 1 for t > th and = 0 for t < t,, Mean axial, radial and tangential velocity components Axial, radial and tangential distances

Greek symbols

o, P Size indices

r@ Exchange coefficient

P Mean density @J Mean component of a dependent variable,

i.e. U, V, W,f ,...

Subscripts

f Furnace

i,i Denote ith step and jth size group respectively L Liquid phase

G Stands for gas phase variables, i.e. U, V, W, f, H, . . . ) etc.

BOOK REVIEWS Theoretical Systems Ecology: Advances and case studies Efraim Halfon (Ed) Academic Press, New York, 1979, 516 pp. $43.00

In systems ecology, as in other areas of science, there has been a decided lack of communication between theoreti- cians, modellers, and field ecologists. The expressed purpose of this book is twofold: to present recent advances in systems science to theoreticians, and to present aspects of systems ecology in such a manner as to be understand- able to and usable by scientists who are not mathematically oriented. Specific examples are presented at the end of each chapter to demonstrate how theory can be applied to practical problems.

The book is composed of 20 chapters written by different authors and is organized into four major sec- tions. The first section discusses the selection of components of the system model in relation to the aggregation problem or choice of compartments.

The second section deals with model structure, formalisms, and theory of modelling. The emphasis here is placed upon hierarchical models and structure properties. A particularly interesting and thought-provoking chapter is ‘Prediction, chaos, and ecological perspective’ by Ulanowicz, in which the relation between caus- ality and model structures is con- sidered. Ulanowicz considers an opinion contrary to that of most modellers: the results for large deter- ministic ecosystem models are not useful since the system tends to chaos. Another chapter of particular merit is ‘System approach to continental shelf ecosystems’ by Patten and Finn, in which causality theory is emphasized as an aid in model development. The third section deals with system identi- fication, ‘. . formally defined as the process of determining coefficients, parameters, and structure of a mathe- matical model in such as way as to describe a physical process in accord- ance with some predetermined criteria.’ This entire section should

be interesting to modellers at all levels, especially with respect to opti- mization and parameter estimation. The last section includes model analysis, and answers the final ques- tion ~ Now what do we do with the model? The emphasis is on the extrac- tion of information from a model after it has been developed and executed.

In general, the entire book is well written and essentially free of typo- graphical errors. The editor has managed to collect a wide variety of papers and to organize them skilfully into this volume. It is not a book which can be glossed over because a large amount of information is presented. It is a valuable reference which can be studied in detail, and the examples should prove particularly instructive, although it would be diffi- cult for readers with non-mathematical backgrounds to extract useful proce- dures from the more theoretical portions of the text. In all, this is a book of high quality which should be placed on the recommended reading list.

R. A. Walters

316 Appl. Math. Modelling, 1980, Vol 4, August