Three-Dimensional Magnetohydrodynamic Mixed Convection Flow of Nanofluids over a Nonlinearly Permeable Stretching/Shrinking Sheet with Velocity and Thermal Slip

Abstract

In this paper, the steady three-dimensional magnetohydrodynamic (MHD) mixed convection flow of nanofluids over a permeable vertical stretching/shrinking sheet with slip conditions is investigated in a numerical manner. As such, two types of nanofluids, Cu-water and Ag-water, had been considered. A similarity transformation was employed to reduce the governing equations to ordinary differential equations, which were then solved numerically using the MATLAB (Matlab R2015a, MathWorks, Natick, MA, USA, 1984) programme bvp4c. The numerical solutions derived from the ordinary differential equations subjected to the associated boundary conditions, were obtained to represent the values of the mixed convection parameter. Dual (upper and lower branch) solutions were discovered in the opposing flow region of the mixed convection parameter. A stability analysis was carried out to prove that the upper branch solution was indeed stable, while the lower branch solution was unstable. The significant effects of the governing parameters on the reduced skin friction coefficients, the reduced local Nusselt number, as well as the velocity and temperature profiles, were presented graphically and discussed in detail.

Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

“…Figure 15 illustrated the smallest eigenvalue σ 1 of both solutions towards ε where σ 1 act as a determinant of the stability solutions. Positive σ 1 implies that the flow is stable whereas negative σ 1 indicates an initial growth of disturbances which resulting that the flow is unstable [55][56][57][58][59][60][61][62][63][64][65]. It is validated from Figure 15 that the first and second solutions have positive and negative σ 1 , respectively which indicates that the first solution is the real solution.…”

“…The execution of the stability analysis is mathematically performed to verify the physical or real solution among all the solutions. There has been much current literature that discussed the importance, formulation and execution of the stability analysis (see Ismail et al [55][56][57], Bakar et al [58,59], Anuar et al [60], Salleh et al [61,62], Najib et al [63], Jamaludin et al [64] and Yahaya et al [65]).…”

Special Issue on Nanofluids and Their Applications

“…Jamaludin, R. Nazar, and I. Pop [11] performed a numerical study considering two types of nanofluids, Cu-water and Ag-water, for the problem of magnetohydrodynamic mixed convection flow of nanofluids over a permeable vertical stretching/shrinking sheet with slip conditions. It was revealed that Ag-water nanofluid displayed better enhancement for heat transfer when compared to that for Cu-water nanofluid.…”

Nonlinear mixed convection flow of a tangent hyperbolic fluid with activation energy

“…Accordingly, Hayat et al 10 and Khan et al 11 have investigated the mixed convection flow of a non‐Newtonian fluid, such as Jeffrey and Eyring‐Powell fluids with thermal radiation and nonuniform heat sink/source with nanoparticles past a plate, cone, and stretching cylinder. Moreover, Jamaludin et al 12 and Matin et al 13 have investigated numerically the influence of magnetic field and nanoparticles over a stretching/shrinking surface with slip and viscous dissipation conditions.…”