TAILIEUCHUNG - Heat Transfer Handbook part 131

Heat Transfer Handbook part 131. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | NOMENCLATURE 1297 Least Squares If N consecutive measurements of the output y i 1 1 N are made at successive sampling periods these can be concatenated in a measured output vector Y as Y y n 1 y n 2 y n N T These will be compared with their respective predictions Y by the ARMA process model in which the corresponding augmented vectors can be assembled in matrix T n T n 1 . T n N - 1 T where the elementary vectors also contain the previously measured outputs y i i 1 n and inputs Q i i 1 n. Thus the ARMA model ofthefiiermal system can be written as Y 0. The least squares method minimizes the quadratic index of hie output deviations e Y- Y . J eTe setting the parameters 0 to 0 t -1Y Y where is the pseudoinverse of . NOMENCLATURE Roman Letter Symbols a grinding cut depth m ARMA output coefficient dimensionless A A1 state matrix dimensionless preexponential frequency factor in cure kinetics model e 1 Ac Ao Ai b s cross-sectional area m2 chip width m grinding width m saturation point dimensionless ARMA input coefficient dimensionless B Bi B2 B3 input matrix dimensionless parameters defined in eqs. - dimensionless Bi c c Biot number dimensionless degree of crystaliization dimensionless specific heat capacity kJ kg K saturation level dimensionless C Ca output matrix dimensionless instantaneous resin concentration in the resin-catalyst mixture at any time t kg m3 Cao initial resin concentration in the resin-catalyst mixture kg m3 d delay dimensionless 1298 HEAT TRANSFER IN MANUFACTURING AND MATERIALS PROCESSING ds D grinding wheel diameter m diameter m differential dimensionless period dimensionless D Db Dh Dic e E direct matrix dimensionless degree of bonding dimensionless degree ofhealing dimensionless degree ofintimate contact dimensionless error dimensionless activation energy for viscosity in the chemorheological model kJ kmol error Laplace transform dimensionless expectation dimensionless Ei E2 f F F g G G h activation energies in .

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