Multiple Solutions for Stagnation-Point Flow of Unsteady Carreau Fluid along a Permeable Stretching/Shrinking Sheet with Non-Uniform Heat Generation

Abstract

The aim of the present study was to explore the effect of a non-uniform heat source/sink on the unsteady stagnation point flow of Carreau fluid past a permeable stretching/shrinking sheet. The novelty of the flow model was enhanced with additional effects of magnetohydrodynamics, joule heating, and viscous dissipation. The nonlinear partial differential equations were converted into ordinary differential equations with the assistance of appropriate similarity relations and were then tackled by employing the Runge-Kutta-Fehlberg technique with the shooting method. The impacts of pertinent parameters on the dimensionless velocity and temperature profiles along with the friction factor and local Nusselt number were extensively discussed by means of graphical depictions and tables. The current results were compared to the previous findings under certain conditions to determine the precision and validity of the present study. The fluid flow velocity of Carreau fluid increased with the value of the magnetic parameter in the case of the first solution, and the opposite behavior was noticed for the second solution. It was seen that temperature of the Carreau fluid expanded with the higher values of unsteadiness and magnetic parameters. It was visualized from multiple branches that the local Nusselt number declined with the Eckert number parameter for both the upper and lower branch.

Convective Heat Transfer in Magneto-Hydrodynamic Carreau Fluid with Temperature Dependent Viscosity and Thermal Conductivity

“…In addition, the values N 1 and N 2 are set to 1. The associated boundary conditions are taken as [52,55]:…”

“…Hussain et al [54] studied non-uniform heat generation in Carreau fluid across nonlinear elongating cylinder utilizing shooting method. Yang et al [55] examined multiple solution stagnation point flow of Carreau fluid with non-uniform heat generation using RK-4 and shooting method. Mandal and Pal [56,57] analyze entropy generation with magneto-hydrodynamic effect in hybrid nanofluids, carbon nanotubes flow nonlinear radiation effect and variable thermophysical properties.…”

“…Hussain et al [54] examined Carreau fluid over nonlinear elongating cylinder for thermal characterization. Yang et al [55] introduced stagnation point multiple solutions of unsteady Carreau fluid. The novelty of this work is to investigate convective heat transfer over permeable nonlinear stretching/shrinking sheet.…”

Unsteady slip flow of special second-grade fluid induced by Fe3O4 particles past a movable sheet with magnetic and nonlinear heat source/sink

“…Al-Amri and Muthtamilselvan (2020) focused on the magneto SPF of nanofluid along with microorganisms across a stretching sheet subjected to radiation effect. The unsteady dissipative flow of Carreau fluid toward an stagnaton-point (SP) across a stretching/shrinking sheet with irregular heat source/sink and magnetic effects was inspected by Yang et al (2021). They found that the velocity distribution increases due to the magnetic number for the stable outcome and declines for the second branch outcome.…”

Effect of an inclined magnetic field on unsteady mixed convective stagnation point flow over a permeable stretching sheet with radiative heat transfer

“…The well-known 4th order Runge-Kutta derived shooting approach is utilized to examine the influences of numerous prominent flow factors and various kinds of nanomaterials on the velocity curve, energy estimation, drag friction coefficient and heat flux. Since, the 4th order Runge-Kutta scheme has been utilized in numerous examinations as a strong computational approach (Rahman et al [20], and Yang et al [21] utilized this scheme to analyze the thermal and mass transport in the boundary layer scheme with various prominent conditions). The graphical results are displayed and explain for the several influencing factors in details.…”