Eigenvalue Graetz problem

The problem given by eq.(59) subject to the conditions (60) is referred to as extended Graetz problem in honor of the pioneering work [5]. To solve this problem we need the eigenvalues m and the eigenfunctions y [R] of the eigenproblem ... 

Barron R. F, X. Wang, R. O. Warrington, and T. Ameel, 1996, Evaluation of the eigenvalues for the Graetz problem in slip-flow, Int. Comm. Heat Mass Transfer 23 (4), 1817-1823. 

Mikhailov M. D. and R. M. Cotta, 1997, Eigenvalues for the Graetz Problem in Slip-Flow, Int. Comm. Heat... 

Unsal M., 1990, A solution for the complex eigenvalues and eigenfunctions of periodic Graetz problem, International Communications in Heat Mass Transfer, 25, 4, 585-592. 

Ozisik MN, Sadeghipour MS. Analytic solution for the eigenvalues and coefficients of the Graetz problem with third kind boundary condition. International Journal of Heat and Mass Transfer 1982 25 736-739. 

The above problem is known as Graetz problem and can be solved as an eigenvalue problem. A similar problem is also seen for thermally developing heat transfer. The solution can be obtained for local Nusselt number (Nu(x)). 

The Graetz eigenfunctions and eigenvalues are not widely tabulated. However, Brown (1960) has computed a large number of eigenvalues suitable for most problems. The final result can be written in dimensionless form as... 

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