Thermal entry flow problem for Rabinowitsch fluid subject to circular tube and flat channel with uniform heat flux boundary conditions

The heat exchangers, chemical reactors, cooling/heating systems and haemodialysis are specific areas due to which Graetz thermal problem is considered as fundamental flow in the duct along with heat and mass transfer aspects. Owing to its importance we examine the thermal entry flow problem for Rabinowitsch liquid in the pipe and channel ducts along with heat transfer aspects. The heat equation with uniform heat flux conditions is tackled via the superposition principle and separation of variable approach due to the involvement of non-homogeneous boundary condi-tions. The transformed boundary value problem is solved with the MATLAB algorithm for the calculation of eigenvalues and related eigenfunctions. The special cases for simplified Phan-Thien-Tanner (SPTT) fluid and finite extendable non-linear elastic peterline (FENE-P) fluids are also discussed. For SPTT and FENE-P models the controlling parameter can only take positive values and hence these models can only predict shear-thinning effects. The graphical illustrations of fully developed temperature, local and mean Nusselt numbers are displayed through the main effect brought by the controlling parameter.

Automated summary

This study solves the heat conduction equation problem with non-homogeneous boundary conditions using the superposition principle and separation of variable approach. The MATLAB algorithm is used to calculate eigenvalues and related eigenfunctions. The simplified Phan-Thien-Tanner (SPTT) fluid and finite extendable non-linear elastic peterline (FENE-P) fluid models are also discussed.