Pembentukan lapisan sempadan halaju dan terma yang dirangsang oleh aliran bebas bersebelahan plat tegak dengan suhu permukaan malar dikaji. Persamaan-persamaan menakluk dalam bentuk persamaan pembezaan separa diturunkan kepada persamaan-persamaan pembezaan biasa dengan penjelmaan keserupaan, sebelum diselesaikan secara berangka. Kedua-dua aliran membantu dan aliran menentang dipertimbangkan. Didapati bahawa penyelesaian adalah unik bagi aliran membantu, manakala penyelesaian dual wujud bagi aliran menentang. Kadar pemindahan haba pada permukaan didapati meningkat dengan peningkatan kedua-dua daya keapungan dan nombor Prandtl.
The effect of radiation on magnetohydrodynamic (MHD) boundary layer flow of a viscous fluid over an exponentially stretching sheet was studied. The governing system of partial differential equations was transformed into ordinary differential equations before being solved numerically by an implicit finite-difference method. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. It was found that the local heat transfer rate at the surface decreases with increasing values of the magnetic and radiation parameters.
This paper presents a numerical analysis of a stagnation-point flow towards a nonlinearly stretching/shrinking sheet immersed in a viscous fluid. The stretching/shrinking velocity and the external flow velocity impinges normal to the stretching/shrinking sheet are assumed to be in the form U ~ xm, where m is a constant and x is the distance from the stagnation point. The governing partial differential equations are converted into ordinary ones by a similarity transformation, before being solved numerically. The variations of the skin friction coefficient and the heat transfer rate at the surface with the governing parameters are graphed and tabulated. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique for m > 1/3.
Dalam makalah ini, masalah aliran genangan dalam bendalir mikrokutub terhadap permukaan mencancang yang telap dengan fluks haba boleh ubah dipertimbangkan. Dengan menggunakan penjelmaan keserupaan, persamaan asas yang menakluk aliran bendalir dan pemindahan haba dijelmakan kepada satu set persamaan perbezaan biasa. Persamaan yang dijelmakan tertakluk kepada syarat-syarat sempadan yang berkaitan kemudiannya diselesaikan secara berangka menggunakan kaedah tembakan. Kesan parameter sedutan/semburan fw ke atas profil halaju dan suhu serta pekali geseran kulit dan nombor Nusselt setempat diperoleh dan dibincangkan. Keputusan berangka menunjukkan bahawa penyelesaian dual wujud dalam kedua-dua aliran membantu dan aliran menentang.
The steady, two-dimensional laminar flow of a power-law fluid over a permeable shrinking sheet of constant surface temperature is investigated. The governing partial differential equations were transformed into a system of nonlinear ordinary differential equations using a similarity transformation, before being solved numerically by the Runge-Kutta- Fehlberg method with shooting technique. The results are presented graphically and the effects of the power-law index n, suction parameter fw and Prandtl number Pr were discussed. It was found that stronger suction is necessary for the solution to exist for a pseudoplastic fluid (n<1) compared to a dilatant fluid (n>1).
The problem of stagnation point flow over a stretching/shrinking sheet immersed in a micropolar fluid is analyzed
numerically. The governing partial differential equations are transformed into a system of ordinary (similarity) differential
equation and are then solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The
effects of various parameters on the velocity and the angular velocity as well as the skin friction coefficient and the couple
stress are shown in tables and graphs. The noticeable results are found that the micropolar and the slip parameters
decrease the skin friction coefficient and the couple stress in the existence of magnetic field. Dual solutions appear for
certain range of the shrinking strength. A stability analysis is performed to determine which one of the solutions is stable.
Practical applications include polymer extrusion, where one deals with stretching of plastic sheets and in metallurgy
that involves the cooling of continuous strips.
A steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of a viscous and electrically conducting fluid over a permeable shrinking sheet has been studied. The governing partial differential equations are reduced to the nonlinear ordinary differential equations by a similarity transformation. The resulting differential equations are then solved numerically using an implicit finite difference method. It is found that the solutions are non-unique for weak magnetic field, strong suction and large velocity ratio between free stream velocity and wall shrinking velocity.
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 heat transfer behaviour of a viscous fluid over a stretching/shrinking sheet driven by a uniform shear in the far field with a convective surface boundary condition is studied. The boundary layer equations governing the flow are reduced to ordinary differential equations using a similarity transformation. Using a numerical technique, these equations are then solved to obtain the temperature distributions and the heat transfer rate at the surface for various values of Prandtl number, stretching/shrinking parameter and convective parameter. Dual solutions are found to exist for the shrinking case, whereas for the stretching case, the solution is unique.
The unsteady laminar boundary layer flow of a nanofluid and heat transfer over a permeable shrinking cylinder using the Buongiorno’s nanofluid model is investigated. Using a similarity transformation, the governing partial differential equations are transformed into a system of ordinary differential equations and then solved numerically using a shooting method. The numerical results are obtained for velocity, temperature and concentration profiles as well as the skin friction coefficient, the local Nusselt number and the local Sherwood number. Dual solutions are found to exist in a certain range of the suction and unsteadiness parameters. It is observed that suction parameter increase both the skin friction coefficient and the heat transfer rate at the surface, whereas the opposite trend is obtained for the Sherwood number. It is also observed that suction widens the range of the unsteadiness parameter for which the solution exists.
In this paper, the problem of free convection boundary layer flow on a horizontal circular cylinder in a nanofluid with viscous dissipation and constant wall temperature is investigated. The transformed boundary layer equations are solved numerically using finite difference scheme namely the Keller-box method. Numerical solutions were obtained for the reduced skin friction coefficient, Nusselt number and Sherwood number as well as the velocity and temperature profiles.The features of the flow and heat transfer characteristics for various values of the Brownian motion parameter, thermophoresis parameter, Lewis number and Eckert number were analyzed and discussed.
In this study, the numerical solution of stagnation point flow over a stretching surface, generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature is considered. The transformed boundary layer equations are solved numerically using the shooting method. Numerical solutions are obtained for the local heat transfer coefficient, the surface temperature and the temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number, stretching parameter and conjugate parameter are analyzed and discussed.