Mixed Convective Flow and Heat Transfer of a Dual Stratified Micropolar Fluid Induced by a Permeable Stretching/Shrinking Sheet

Abstract

The present study accentuates the magnetohydrodynamics (MHD) flow and heat transfer characteristics of a dual stratified micropolar fluid over a permeable stretching/shrinking sheet. Thermal and solutal buoyancy forces are also included to incorporate with the stratification effect. Similarity, transformation is applied to reduce the governing model (partial differential equations) into a set of nonlinear ordinary differential equations (ODEs) due to its complexity. Using bvp4c solver in the MATLAB software, numerical results for some limiting cases are in favorable agreement with the earlier published results. Both assisting and opposing buoyancy flows have dual similarity solutions within specific range of suction and stretching/shrinking parameters, whereas only a distinctive solution is observed for pure forced convective flow. The micropolar fluid shows a disparate pattern of flow, heat and mass transfer characteristics between stretching and shrinking cases. Unlike the shrinking flow, the surface velocity gradient, local Nusselt and Sherwood numbers for stretching flow intensify with the increment of the material parameter. The result from stability analysis reveals that the first solution is the real solution, whereas the second solution is virtual.

MHD Flow and Heat Transfer of Double Stratified Micropolar Fluid over a Vertical Permeable Shrinking/Stretching Sheet with Chemical Reaction and Heat Source

“…where H and P are constants whilst 0 T and 0 C are initial ambient temperature and concentration. Under the boundary layer approximations, the corresponding boundary layers equation with the above-mentioned effects is (see Srinivasacharya & Upendar [5], Rashad et al, [6], Khashi'ie et al, [7]):…”

“…Most recently, Khashi'ie et al, [7] investigated suction, magnetic field, and double stratifications effects on the mixed convection boundary layer flow over a stretching/shrinking sheet in micropolar fluid. They reported that dual solution exists in a certain range of suction and stretching/shrinking parameters.…”

Magnetohydrodynamic (MHD) Flow of Micropolar Fluid with Effects of Viscous Dissipation and Joule Heating Over an Exponential Shrinking Sheet: Triple Solutions and Stability Analysis

“…Beneš et al [7] investigated the time-dependent flow of an incompressible micropolar fluid through a pipe using asymptotic analysis. Some interesting results of the micropolar fluid are studied in these papers [8][9][10][11][12][13].…”

Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface

“…Furthermore, they specified that the dual solution depended on the range of the suction parameter. Khashi'ie et al [21] highlighted the importance of the multiple solutions and the stability analysis during the examination of the mixed convection flow of the micropolar fluid. They stated "if the problem has non-unique solutions but the researchers manage to find one solution only, there is a probability that the solution is the lower branch solution (unstable/not real).…”