Conjugate Heat Transfer: Analysis Via Integral Transforms and Eigenvalue Problems

An integral transform approach to the solution of the problem on conjugate heat transfer, combining the singledomain formulation with the convective eigenfunction expansion basis within the total integral transformation framework, which leads to a nonclassical eigenvalue problem, is presented. The problem on the conjugate heat transfer in the transient two-dimensional incompressible laminar flow of a Newtonian fluid in a parallel-plate channel is considered to illustrate the hybrid numerical-analytical approach. To demonstrate the improvement of the convergence rate achieved with the methodology proposed, a critical comparison against the traditional total integral transformation solution of the diffusive eigenvalue problem is provided, and results are presented and discussed for three representative situations realized with different Peclet numbers: Pe = 1, 10 and 100. A remarkable improvement of the convergence rate, obtained especially with the large Peclet numbers, offers evidence of the validity of the expansion constructed upon the nonclassical eigenvalue problem proposed.