Design and Optimization of Thermal Systems Episode 3 Part 8 ppsx

THE PROBLEM CONSIDERED IS THE ONE GIVEN IN C EXAMPLE 4.4... C ROOT SOLVING WITH THE SECANT METHODC THE FUNCTION USED IS THE ONE IN EXAMPLE 4.2... OF GRID POINTS IL= , JL= ’ PRINT*,‘ MAX

% Replaced by two first order ODEs: dx/dt = y; dy/dt = 9.8 – 0.05 y

C TO BE SOLVED IS THE ONE GIVEN IN EXAMPLE 4.4

C N IS THE ORDER OF THE TRIDIAGONAL MATRIX

C A IS THE SUBDIAGONAL OF THE TRIDIAGONAL MATRIX

C B IS THE DIAGONAL OF THE TRIDIAGONAL MATRIX

C C IS THE SUPERDIAGONAL OF THE TRIDIAGONAL MATRIX

C F IS THE RIGHT HAND SIDE VECTOR

C T IS THE SOLUTION VECTOR

C CONSTANT DEFINED IN THE PROBLEM AND N IS THE NUMBER OF

C EQUATIONS THE PROBLEM CONSIDERED IS THE ONE GIVEN IN

C EXAMPLE 4.4

C ROOT SOLVING WITH THE SECANT METHOD

C THE FUNCTION USED IS THE ONE IN EXAMPLE 4.2

C CHECK FOR CONVERGENCE

END

A.F.4

C THIS PROGRAM FINDS THE REAL ROOTS OF AN EQUATION F(X)=0

C BY THE NEWTON-RAPHSON METHOD

C

C

C

C HERE X IS THE INDEPENDENT VARIABLE, Y1 THE VALUE OF THE

C DX THE INCREMENT IN X FOR THE NEXT ITERATION, EPS THE

END

A.F.5

C THIS PROGRAM SOLVES THE LAPLACE EQUATION BY EMPLOYING

C THE SUCCESSIVE OVER RELAXATION (SOR) ITERATION METHOD

C

C WHOLE DOMAIN

C EPSI IS THE CONVERGENCE CRITERION

C PHIOL IS THE SOLUTION VARIABLE AT N-1TH TIME STEP.

PRINT *,‘ENTER NO OF GRID POINTS IL= , JL= ’

PRINT*,‘ MAXIMUM POSSIBLE IS 11 FOR BOTH IL AND JL,’

PRINT*,‘UNLESS DIMENSION STATEMENTS ARE CHANGED.’

PRINT*,‘THE INPUT VALUES ARE:’

PRINT*,‘INITIAL GUESS FOR PHI=’,PHIINT

C

C

C AFTER THE PREVIOUS ITERATION AND EPS IS THE CONVERGENCE

C CRITERION APPLIED TO THE TOTAL FLOW RATE C

IF (ABS(C-CO) LE EPS) THEN

Appendix B

Material Properties

B.1: Properties of dry air at atmospheric pressure—SI units

B.2: Property values of gases at atmospheric pressure

B.3: Properties of saturated water

B.4: Properties of common liquids—SI units

B.5: Thermal properties of metals and alloys

B.6: Properties of other materials

B.7: Emissivities En of the radiation in the direction of the normal to the

sur-face and E of the total hemispherical radiation for various materials for

the temperature T

A NOTE ON MATERIAL PROPERTIES

These tables on the properties of common materials are provided for quick ence and convenience However, for detailed design and optimization of practical systems, the various handbooks, encyclopedias, and references cited in the text should be used instead, for the most appropriate and accurate property data.

tempera-k, thermal conductivity, mW/m •K; Pr, Prandtl number, dimensionless; h, enthalpy, KJ/kg; a, sound

N r 10 6 (m 2 /s)

k

(W/m • nC)

A r 10 7 (m 2 /s)

B r 10 3 (1/K) Pr

N r 10 6 (m 2 /s)

k

(W/m • nC)

A r 10 7 (m 2 /s)

B r 10 3 (1/K) Pr

Source: A J Chapman, Heat Transfer, 4th ed., Macmillan, New York, 1984 Reprinted with

permis-sion of Simon & Schuster, copyright¡ 1984