Magnetohydrodynamic Three-Dimensional Flow and Heat Transfer over a Stretching Surface in a Viscoelastic Fluid

In this paper, the problem of steady laminar three-dimensional magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a stretching surface in a viscoelastic fluid is investigated. The equations which govern the flow are coupled nonlinear ordinary differential equations, which are solved numerically using a finite-difference scheme known as the Keller-box method. Various physical governing parameters such as the magnetic parameter M, the material or viscoelastic parameter K and the Prandtl number Pr are considered and the effects of these parameters are investigated. It is found that the material parameter K and the magnetic parameter M present opposite effects on the fluid flow and heat transfer characteristics. The numerical results obtained for the skin friction coefficient and the local Nusselt number are presented in tables. The features and profiles of the flow and heat transfer characteristics are illustrated in the forms of graphs

Falkner-skan solution for gravity-driven film flow of a micropolar fluid

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

Boundary layer flow and heat transfer adjacent to a stretching vertical sheet with prescribed surface heat flux

The steady two-dimensional flow adjacent to a vertical, continuously stretching sheet in a viscous and incompressible fluid is studied. It is assumed that the sheet is stretched with a power-law velocity and is subjected to a variable surface heat flux. The governing partial differential equations are reduced to nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by the Keller-box method. Results showed that the heat transfer rate at the surface increases as the velocity exponent parameter, mixed convection parameter and the Prandtl number are increased

Three-dimensional flow of a nanofluid over a permeable stretching/shrinking surface with velocity slip: A revised model

A reformulation of the three-dimensional flow of a nanofluid by employing Buongiorno’s model is presented. A new boundary condition is implemented in this study with the assumption of nanoparticle mass flux at the surface is zero. This condition is practically more realistic since the nanoparticle fraction at the boundary is latently controlled. This study is devoted to investigate the impact of the velocity slip and suction to the flow and heat transfer characteristics of nanofluid. The governing partial differential equations corresponding to the momentum, energy, and concentration are reduced to the ordinary differential equations by utilizing the appropriate transformation. Numerical solutions of the ordinary differential equations are obtained by using the built-in bvp4c function in Matlab. Graphical illustrations displaying the physical influence of the several nanofluid parameters on the flow velocity, temperature, and nanoparticle volume fraction profiles, as well as the skin friction coefficient and the local Nusselt number are provided. The present study discovers the existence of dual solutions at a certain range of parameters. Surprisingly, both of the solutions merge at the stretching sheet indicating that the presence of the velocity slip affects the skin friction coefficients. Stability analysis is carried out to determine the stability and reliability of the solutions. It is found that the first solution is stable while the second solution is not stable

MHD viscous flow and heat transfer induced by a permeable shrinking sheet with prescribed surface heat flux

The problem of magnetohydrodynamic (MHD) boundary layer flow and heat transfer due to a permeable shrinking sheet with prescribed surface heat flux is studied. The viscous fluid is electrically conducting in the presence of a uniform applied magnetic field and the induced magnetic field is neglected. The transformed nonlinear ordinary differential equations are solved numerically via the implicit finite-difference scheme known as the Keller-box method. Both two-dimensional and axisymmetric cases are considered. The results for the skin friction coefficient and the wall temperature, as well as the velocity and temperature profiles are presented and discussed for various parameters. Dual solutions exist for certain range of the suction parameter and Hartmann number. It is found that the boundary layer separation is delayed with Hartmann number

Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid with prescribed surface heat flux.

The unsteady laminar flow of an incompressible micropolar fluid over a stretching sheet with prescribed surface heat flux is investigated. The governing partial differential boundary layer equations are first transformed into ordinary differential equations before being solved numerically by a finite-difference m 'hod. The effects of the unsteadiness parameter and Prandtl number on the flow and heat transfer characteristics are studied. It is found that the surface shear stress and the heat transfer rate at the surface are higher for micropolar fluids compared to Newtonian fluids

Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid.

The unsteady laminar flow of an incompressible micropolar fluid over a stretching sheet is investigated. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. Effects of the unsteadiness parameter, material parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined

Similarity solution of marangoni convection boundary layer flow over a flat surface in a nanofluid

The problem of steady Marangoni boundary layer flow and heat transfer over a flat plate in a nanofluid is studied using different types of nanoparticles. The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta-Fehlberg (RKF) method. Three different types of nanoparticles are considered, namely, Cu, Al2O3, and TiO2, by using water as a base fluid with Prandtl number Pr=6.2. The effects of the nanoparticle volume fraction φ and the constant exponent m on the flow and heat transfer characteristics are obtained and discussed

Feedback Control of the Marangoni–Bénard Instability in a Fluid Layer with a Free-Slip Bottom

Feedback control was applied to the steady Marangoni–Bénard convection in a horizontal layer of fluid with a free-slip bottom heated from below and cooled from above. The critical values of the Marangoni numbers for the onset of steady convection are calculated and the latter is found to be critically dependent on the Crispation and Bond numbers. It is shown that the onset of instability can be delayed and the critical Marangoni number can be increased through the use of feedback control

Marangoni driven boundary layer flow past a flat plate in nanofluid with suction/injection

The problem of Marangoni convection boundary layer flow past a flat plate in a nanofluid when the wall is permeable, where there is suction or injection effect, is studied using different types of nanoparticles. The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge‐Kutta‐Fehlberg (RKF) method. Three different types of nanoparticles, namely Cu, Al2O3 and TiO2 are considered by using water as a base fluid with Prandtl number Pr = 6.2. The effects of the suction or injection parameter on the flow and heat transfer characteristics are discussed