Dual solutions for unsteady boundary layer flow of nanofluids over stretching/shrinking surfaces and stability analysis

There are five unsteady boundary layer flow problems being considered which involved the regular flow, rotating boundary layer flow, the stagnation-point flow over a linear and an exponential stretching/shrinking surface which the flows pass through a flat or a cylindrical surfaces. Besides, the effects such as constant mass flux, velocity slip, Soret and Dufour are also taken into account. The mathematical models for boundary layer problems by considering different nanoparticles namely Copper, Alumina and Titania are dispersed into the water. The nanofluid model by Tiwari and Das are used to study the effect of nanoparticle volume fraction towards the flow and heat transfer behaviors at the surface. The governing equations in the form of partial differential equations are transformed to the ordinary differential equation using the similarity variables and is solved by using bvp4c function in Matlab software to gain the numerical results which focused on obtaining the dual solutions so that the stability analysis can be performed. The results have shown the dual solutions existed for unsteady accelerating and decelerating flow with the presence of mass suction effect within a certain range of stretching and shrinking surfaces. Increasing the rotation effect, nanoparticle volume fraction, considering different nanoparticles and exponential stretching/shrinking surface is proven can enlarge the range of solutions. Considering Copper-water has resulted in increasing the skin friction coefficient and heat transfer rate at the surface. Performing the stability analysis has found that the first solution is stable solution meanwhile the second solution is unstable solution.

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