Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis

Abstract

A model of unsteady stagnation-point flow and heat transfer over a permeable exponential stretching/shrinking sheet with the presence of velocity slip is considered in this paper. The nanofluid model proposed by Tiwari and Das is applied where water with Prandtl number 6.2 has been chosen as the base fluid, while three different nanoparticles are taken into consideration, namely Copper, Alumina, and Titania. The ordinary differential equations are solved using boundary value problem with fourth order accuracy (bvp4c) program in Matlab to find the numerical solutions of the skin friction and heat transfer coefficients for different parameters such as stretching/shrinking, velocity slip, nanoparticle volume fraction, suction/injection, and also different nanoparticles, for which the obtained results (dual solutions) are presented graphically. The velocity and temperature profiles are presented to show that the far field boundary conditions are asymptotically fulfilled, and validate the findings of dual solutions as displayed in the variations of the skin friction and heat transfer coefficients. The last part is to perform the stability analysis to determine a stable and physically-realizable solution.

Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip

“…The unsteady two-dimensional stagnation-point flow of a hybrid Al 2 O 3 -Cu/H 2 O nanofluid over a convectively heated stretching/shrinking sheet with the influence of velocity slip is considered in this research work, as illustrated in Figure 1 (see Dzulkifli et al [59]). The stretching/shrinking velocity is denoted by u w (x, t) = bx/(1 − ct), where b denotes a constant corresponds to stretching (b > 0) and shrinking (b < 0) cases while c signifies the unsteadiness problem and u e (x, t) = ax/(1 − ct) is the velocity of the free stream where a > 0 represents the strength of the stagnation flow.…”

Thermal Marangoni Flow Past a Permeable Stretching/Shrinking Sheet in a Hybrid Cu-Al2O3/Water Nanofluid

“…Among the earlier studies on mathematical formulation of stability analysis were examined by Harris et al (2009) Merkin (1986, Roşca and Pop (2013), and Weidman et al (2006). Many recent works also discussed the existence of dual solutions and emphasis on stability analysis (Bakar et al 2018;Dzulkifli et al 2018;Hamid & Nazar 2016;Jamaludin et al 2018;Kamal et al 2019;Naganthran et al 2018;Soid et al 2018). All the reported literatures implemented the bvp4c solver in the MATLAB software to examine the paired and stability solutions.…”

A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip

“…The first non-unique solution which is asymptotically satisfying the boundary conditions will be denoted as the first or upper branch solution. For stability purposes, a time-dependent problem needs to be considered based on study in previous literature [67][68][69][70][71][72][73]. The unsteady form of Equations (2)-(6) is…”

“…The pioneer works on formulation of stability analysis were conducted by Merkin [63], Weidman et al [64], Harris et al [65] and Roşca and Pop [66]. A brief of explanation on stability analysis was also discussed by the following literature [67][68][69][70][71][72][73][74]. To the best of the authors' knowledge, the results are new and have not been published.…”