AN ERROR ANALYSIS OF NUMERICAL SOLUTIONS OF THE TRANSIENT HEAT CONDUCTION EQUATION.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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In this investigation the transient temperatures in a semi-infinite slab with a convective boundary layer are determined numerically using the Crank-Nicolson and Crandall Methods. These temperatures are compared with the exact solution to determine if the Crandall technique, as theoretically predicted, has smaller truncation error. A finite difference boundary equation is derived for the convective boundary condition which is consistent with the internal node formula developed by Crandall. The latter formula and the derived boundary equation are used to obtain six node temperatures at six time intervals for values of M inverse Fourier modulus equal to 1, 2, 3, 4, and the square root of 20 and N Nusselt modulus equal to 2, 12, 14, and 18. The results show that these temperatures are always more accurate than those obtained using the Crank-Nicolson Method if the nodes are closely spaced N equal to 18. In addition, the solutions for those values of M and N which permit the boundary equation truncation error to be minimized indicate that the Crandall Method is more accurate if N is less than or equal to 12. The accuracy improvement factors for the two numerical methods are also determined however, the results do not agree with those predicted theoretically and show no consistent trends. Also, the equation required to apply the Crandall technique to bodies with variable thermal properties is derived. Author