Analysis Of The Research Works In Fluid Mechanics
The main aim of fluid mechanics, as a multiform phenomenon, is to perform modelling of the liquids and gases in their common temperature and pressure ranges. Conservation of mass, momentum and energy can be taken as three basic laws for any engineering problem involving in the boundary layer theory. Recently, the complexity of such problems can be greatly simplified by using the approximate solution methodologies. In this way, Raees et al. proposed a multiple solution for homogeneous-heterogeneous reactions on the Oberbeck-Boussinesq buoyancy-driven flow of dilute nanofluids. They derived the governing nonlinear equations based on the Buongiorno's mathematical model, and showed that the dilute nanofluid gives a higher stability of chemical reactions than a typical fluid. Khoshrouye Ghiasi and Saleh analyzed the Casson type fluid over an unsteady shrinking surface in the presence of Joule heating and magnetic inclination. They showed that the effect of viscous force in their model will be usually negligible for large values of the Hartmann number.
Abdul Gaffar et al. employed the Keller box finite-difference method (FDM) to simulate the thermomechanical behaviour of viscoelastic Jeffery's fluid inside a non-parallel vertical channel so that an excellent consistency with those of Hossain and Paul was obtained. They also proved that the predicted behaviour is quite elastic with large Deborah numbers. Sayyed et al. took the influence of permeability and slip boundary condition into account to study the geothermal aspects of flow over a wedge-shaped configuration. They combined the differential transformation method (DTM) with the Padé approximation, and showed that the suction in this case has the same effect as the injection on the permeability. Besthapu et al. extended the double stratification (i. e. , the stratified medium due to the temperature and nanoparticle concentration fields) to the laminar boundary layer flow along an exponentially stretching surface, which previously was reported by Khan and Pop. Furthermore, they showed that their results are in good agreement with those obtained by Ishak.
Melting heat transfer can be briefly defined as follows: The melt liquid has not been diffused into the ambient liquid. It has found many applications in engineering and physics, for example, to magma solidification, to semiconductor materials, thawing permafrost, etc. However, as we will now see, there exist only a few research studies concerning this issue. Hayat et al. performed a melting heat transfer analysis of Powell-Eyring fluid with convective boundary condition. Sheikholeslami and Rokni used a similar idea applied to the forced convection flows considering the Buongiorno's mathematical model. They showed that the Drag force distribution generated from the magnetic field affects the momentum boundary layer thickness. Valipour et al. investigated the heat and mass transfer characteristics of two-phase nanofluids induced by nonlinearly rotating plates carried out numerically in the standard MAPLE software. They found that the rotational velocity and temperature distributions increase with an increase in the Reynolds number. Hayat et al. employed the perturbation technique to analyze the melting heat transfer of peristaltic flows in the presence of viscous dissipation and Joule heating. They also analyzed the oscillatory heat transfer caused by the sinusoidal traveling wave in a channel.
It is noteworthy to mention that although some sort of solution methodologies has been employed to investigate the melting heat transfer characteristics to date, the homotopy-based methodology, due to its optimization performed in MATHEMATICA package BVPh2. 0 [73], can be developed as an efficient procedure compared to any other one. It is found that this methodology does not suffer from long runs and can provide high accuracy estimates.
