Computer-extended series solution for laminar flow between a fixed impermeable disk and a porous rotating disk

Abstract

Purpose The purpose of this paper is to study the laminar boundary layer flow between a stationary nonporous disk and a porous rotating disk, both being immersed in large amount of fluid. Design/methodology/approach The governing nonlinear momentum equations in cylindrical polar coordinates together with relevant boundary conditions are reduced to a system of coupled nonlinear ordinary differential equations (NODEs) using similarity transformations. The resulting coupled NODEs are solved using computer-extended series solution and homotopy analysis method. Findings The analytical solutions are explicitly expressed in terms of recurrence relation for determining the universal coefficients. The nature and location of singularity which restricts the convergence of series is analyzed by using Domb–Sykes plot. Reversion of series is used for the improvement of series. The region of validity of series is extended for much larger values of Reynolds number (R), i.e. R = 6 to 15. Originality/value The resulting solutions are compared with earlier works in the literature and are found to be in good agreement.

Impacts of magnetic field and thermal radiation on squeezing flow and heat transfer of third grade nanofluid between two disks embedded in a porous medium

“…The results of differential transformation method (DTM) and the developed fifth-order Runge-Kutta Fehlberg method (RKFM) coupled with shooting method are presented in Table 3. Parametric studies are carried out and the influences of various parameters on the flow and heat transfer processes are established as shown in Figures 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, and 18 (see Table 4).…”

“…After substitution of Eqs. ( 9), ( 10), (11), and (12) into above momentum equations in Eqs. ( 7) and ( 8) and expansion of the resulting equations, one arrives at Eqs.…”

“…Hashimi et al [9] utilized the models and obtained analytical solutions to the governing equations with the assumption of no slip and no temperature jump in the solid-liquid interface. Although, there some other studies presented on the magnetohydrodynamics flow of nanofluids [10,11,12,13,14], these studies are based on the assumption of no slip and no temperature jump. However, the two annulled assumptions have to a reasonable extent influence on the flow and heat transfer processes in under investigation.…”