Methods of calculating heat transfer in metallurgical plants and control models

  • V. G. Lisienko
Article
  • 25 Downloads

Abstract

Modern deterministic approaches to constructing mathematical models and strategic and tactical control models for a production process with reference to metallurgy and labor activity are considered. Examples of using complete and simplified mathematical models to evaluate optimal conditions of production and technological processes are presented.

Keywords

Heat Transfer Mathematical Model Statistical Physic Optimal Condition Production Process 

Notation

p

medium density

t

time

i

medium enthalpy

λ

thermal conductivity

T, Θ

temperature

qv

intensity of internal heat sources

qrad

vector of heat transferred by radiation; m and n, number of volume and surface zones

AΣ

radiation transfer coefficient

g

convective transfer coefficient

Qj

heat sources

c

heat capacity per unit volume

wl.s

velocity along the x-axis

x, y, z

coordinates

qs.t.

source term

s

layer thickness

u, v

gas velocity components

cp

gas heat capacity at constant pressure

μt

turbulent viscosity

Prt

turbulent Prandtl number

qch

heat release power due to chemical reactions

qr

heat by radiation

σ

number of nodes

V

volume of a zone or node

AjΣj

radiation to answer coefficient proportional to the intrinsic radiation flow leaving the zone h

C

concentration of a reagent to be treated

C2

equilibrium concentration

Cj

initial concentration of a reagent in a treating medium

υ

relative initial potential

L0

theoretical reagent flow rate necessary for complete reaction

η

efficiency (effectiveness)

ηs

heat transfer efficiency

ηch

physicochemical efficiency

W

flow heat capacity

G

mass flow

Fx

surface

kch and kΣ

total heat and mass transfer coefficients

Zch and Zenh

enhancement density centers of heat and mass transfer processes

QL

relative potential of the physicochemical and thermal interaction

ηΣ

generalized chemical-thermal efficiency

ηt.ch. andηt

final physicochemical and thermal efficiencies

Δqch and Δqu

useful energy expenditures for chemical and thermal processes

βch andβt

effective resistances determined by the extent of using chemical-thermal regeneration, thermal efficiency of an extra modulus and other factors

bd.r.

energy expenditures for direct use of a reagent

Fopt

complex optimality criterion

Qres

resultant heat flux

Knon

degree of heating nonuniformity

A, B

weight coefficients

ηloss andηloss

coefficients of heat losses by the working space and under chemical and mechanical incomplete combustion

ηr

regeneration degree

JηF

optimality criterion with respect to heat flow rate and capital expenses

bf

specific fuel flow rate

Q

output (commercial products)

V0 and V1

effective labor potential and current potential per labor product

K

labor activity intensity

Fe

extensive factor of the labor activity (last labor)

gout

output

β=N

labor activity capacity

N

pure products (national income)

q1

relative magnitude of useful products

Q

useful products

C

cost

ηac

labor activity effectiveness

ϰΣ

complex coefficient of the labor potential effectiveness

μ

complex extensive factor of the labor activity

Δp.r.

profit rate. Indices

i, j, s, m,l.s.

zones transferring and absorbing the heat, surface, material, and lining-setting

b

liquid or solid body (lining-setting material)

l

laminar boundary layer at the zone-surface boundary

Lf, 1, 2, 0, ′, ″

inlet temperature parameters of the heating medium, the medium to be treated, the treating medium and the surrounding medium at the inlet and outlet

ch

chemical potential

fix

assigned potential

βλ

node

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Copyright information

© Plenum Publishing Corporation 1994

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  • V. G. Lisienko

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