The unsteady mixed convection boundary layer flow near the forward stagnation point of a two-dimensional symmetric body prescribed by a uniform heat flux rate is studied in this paper. The main aim of the investigation is to identify situations in which dual solutions for the steady-state flow can be determined when the flow is opposing. It is also shown that there is a smooth transition from the unsteady initial flow (short time) to the final steady state flow (large time).
Penyelesaian berangka bagi masalah aliran lapisan sempadan olakan bebas mantap terhadap silinder bulat mengufuk yang dijanakan oleh pemanasan Newtonan, iaitu pemindahan haba dari permukaan berkadar langsung dengan suhu permukaan setempat, dipertimbangkan. Persamaan lapisan sempadan terjelma diselesaikan secara berangka dengan suatu skim berangka beza terhingga tersirat yang dikenali sebagai kaedah kotak Keller. Penyelesaian berangka diperoleh bagi pekali geseran kulit, pekali pemindahan haba setempat, suhu dinding serta profil halaju dan suhu. Ciri-ciri aliran dan pemindahan haba bagi suatu julat nilai nombor Prandtl yang besar dianalisis dan dibincangkan.
This study offers the numerical solutions for the problem of mixed convection stagnation-point flow along a permeable
vertical flat plate in an Oldroyd-B fluid. The present investigation considers the effects of thermal radiation and heat
generation/absorption in the fluid flow. The similarity transformation simplifies the complex model and the bvp4c function
generates the numerical solutions according to the variations in the governing parameters. A higher degree of shrinking
hastens flow separations. The dual solutions are visible in the range of buoyancy opposing flow. The results from this study
may be useful for the scientist to understand the behaviour of the dilute polymer solutions in the industrial applications,
for example, the drag reduction in pipe flows.
In this study, the effects of suction and injection on the mixed convection flow of a nanofluid, over a moving permeable
vertical plate were discussed. A similarity variable was used to transform the governing equations to the ordinary
differential equations, which were then solved numerically using the bvp4c programme from MATLAB. Dual solutions
(upper and lower branches) were found within a certain range of the mixed convection parameter in assisting and
opposing flow regions. A stability analysis was implemented to confirm that the upper branch solution was stable, while
the lower branch solution was unstable.
In this paper, the steady Falkner-Skan solution for gravity-driven film flow of a micropolar fluid is theoretically investigated. The resulting nonlinear ordinary differential equations are solved numerically using an implicit finite-difference scheme. The results obtained for the skin friction coefficient as well as the velocity and microrotation or angular velocity profiles are shown in table and figures for different values of the material or micropolar parameter K.
The steady two-dimensional stagnation point flow of an incompressible viscous and electrically conducting fluid, subject to a transverse uniform magnetic field, towards a stretching sheet is investigated. The governing system of partial differential equations are transformed to ordinary differential equations, which are then solved numerically using a finite difference scheme known as the Keller-box method. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases with the magnetic parameter when the free stream velocity exceeds the stretching velocity, i.e. ε>1, and the opposite is observed when ε<1.
The classical problems of forced convection boundary layer flow and heat transfer near the stagnation point on a permeable stretching/shrinking surface in a nanofluid is studied theoretically. The similarity equations were solved numerically for two types of nanoparticles, namely copper and silver in the base fluid of water with the Prandtl number Pr = 6.7850 to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter φ of the nanofluid. Also the case of conventional or regular fluid (φ = 0) with Pr = 0.7 is considered for comparison with previously known results from the open literature. The comparison showed excellent agreement. The skin friction coefficient, the Nusselt number and the velocity and temperature profiles were presented and discussed in detail. It was found that the nanoparticle volume fraction substantially affects the fluid flow and heat transfer characteristics.