On the solution of the differential equation occurring in the problem of heat convection in laminar flow through a tube with slip—flow

[摘要] A technique is developed for evaluation of eigenvalues in solution of the differential equationd2y/dr2+(1/r)dy/dr+λ2(β−r2)y=0which occurs in the problem of heat convection in laminar flow through a circular tube with silp-flow(β>1). A series solution requires the expansions of coeffecients involving extremely large numbers. No work has been reported in the case ofβ>1, because of its computational complexity in the evaluation of the eigenvalues. In this paper, a matrix was constructed and a computational algorithm was obtained to calculate the first four eigenvalues. Also, an asymptotic formula was developed to generate the full spectrum of eigenvalues. The computational results for various values ofβwere obtained.

[学科分类] 工程和技术（综合）