Search

A numerical study of combined effects of thermal stratification and convective heating for the two-dimensional unsteady flow of hydromagnetic natural convection of nanofluid with buoyancy effects against permeable stretching sheet in presence of electric field is presented. Viscous dissipation and Ohmic heating, as well as radiative heat transfer, are taken into account in the heat convection field. The impact of the chemical reaction due to zero flux of nanoparticle concentration is adopted. The model associated with Brownian motion and thermophoretic diffusion is controlled with slip flow as well as the convective boundary conditions with effects of thermal stratification are employed. Suitable similarity transformations are utilised to transform the governing equations into a couple of ordinary differential equations. The transformed equations systems are then solved numerically using Keller box method. The effects of the pertinent parameters on dimensionless nanofluid velocity, temperature and concentration as well as the skin friction, and Nusselt number are examined. The numerical data obtained in the present investigation are validated and are in good agreement with the previously published data. The numerical computations reveal that that electric and magnetic fields exhibit opposite's flow behaviour due to fluid motion and both enhance the fluid temperature field. The consequence of convective heating intensifies the nanofluid temperature for higher values as thermal stratification reduces the profiles and its associate's thermal boundary layer thickness. [ABSTRACT FROM AUTHOR]

The flow of water over an obstacle is a fundamental problem in fluid mechanics. Transcritical flow means the wave phenomenon near the exact criticality. The transcriti-cal flow cannot be handled by linear solutions as the energy is unable to propagate away from the obstacle. Thus, it is important to carry out a study to identify suitable model to analyse the transcritical flow. The aim of this study is to analyse the transcritical flow over a bump as localized obstacles where the bump consequently generates upstream and downstream flows. Nonlinear shallow water forced Korteweg-de Vries (fKdV) model is used to analyse the flow over the bump. This theoretical model, containing forcing functions represents bottom topography is considered as the simplified model to describe water flows over a bump. The effect of water dispersion over the forcing region is in-vestigated using the fKdV model. Homotopy Analysis Method (HAM) is used to solve this theoretical fKdV model. The HAM solution which is chosen with a special choice of ħ-value describes the physical flow of waves and the significance of dispersion over a bump is elaborated. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to theoretically investigate the steady two-dimensional electrical magnetohydrodynamic (MHD) nanofluid flow over a stretching/shrinking sheet. The effects of stretching and shrinking parameter, as well as electric and magnetic fields, thermal radiation, viscous and Joule heating in the presence of slip, heat and mass convection boundary conditions at the surface, are imposed and studied. The mathematical model governing the flow has been constructed which are partial differential equations and then rehabilitated for a system of ordinary differential equations involving the momentum, energy and concentration equations via suitable similarity transformations. Though various conjectures have been put forward to explain the concept of boundary layer flow, the current investigation employed implicit finite difference scheme indicates good agreement with those of the previously published investigation in the limiting sense. Numerical results of the dual solutions for the velocity, temperature, and concentration as well as heat transfer are elucidated through graphs and tables. The velocity, thermal and solutal boundary layer thickness in the first solutions is smaller than that of the second solutions, the first solution is more stable compared to the second solution. Temperature and nanoparticle concentration fields are augmented by the heat and mass convective boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, Maxwell fluid over a flat plate for convective boundary layer flow with pressure gradient parameter is considered. The aim of this study is to compare and analyze the effects of the presence and absence of λ (relaxation time), and also the effects of m (pressure gradient parameter) and Pr (Prandtl number)on the momentum and thermal boundary layer thicknesses. An approximation technique namely Homotopy Perturbation Method (HPM) has been used with an implementation of Adam and Gear Method's algorithms. The obtained results have been compared for zero relaxation time and also pressure gradient parameter with the published work of Fathizadeh and Rashidi. The current outcomes are found to be in good agreement with the published results. Physical interpretations have been given for the effects of the m, Pr and β (Deborah number) with λ. This study will play an important role in industrial and engineering applications. [ABSTRACT FROM AUTHOR]

In this study, the effect of pressure gradient have been included for heat transfer in the boundary layer flow of Maxwell fluid over a flat plate.The solution of the problem is obtained with an application of algorithms of Adams Method (AM) and Gear Method (GM) with Homotopy Perturbation Method (HPM) as an approximation technique. This technique shows the outcomes of pressure gradient (m), Deborah number (α) and Prandtl number (Pr) in the boundary layer flow on temperature and velocity profiles, also the momentum and thermal boundary layer thickness and discussed. To obtain this objective, the momentum and energy equations of Maxwell are solved. The outcomes of HPM in the absence of relaxation time (λ) or Deborah number (α) and pressure gradient (m) (i.e. λ = α = m = 0) at Prandtl number Pr = 1 are in closed relation with the numerical results having the value of n∞1 is around 5. Also it is found that the system is convergent, as a whole momentum and thermal boundary layer thicknesses becomes thinner and thinner. Importantly, some cooling effects of the Maxwell fluid over a flat plate for energy profile have been observed. [ABSTRACT FROM AUTHOR]

The unsteady magnetohydrodynamic (MHD) natural convection flow and heat transfer of an electrical conducting incompressible viscous nanofluid over a linear permeable shrinking sheet in the presence of electric field, thermal radiation, viscous dissipation, chemical reaction, slip and passively controlled conditions at the wall is studied. The boundary layer governing equations which are partial differential equations are converted into a system of nonlinear ordinary differential equations by applying a suitable similarity transformation. Implicit finite difference scheme is applied to investigate the numerical results how the various physical embedded parameters affect the nanofluid flow and heat transfer with the aid of different graphical presentations and tabular forms. The nanofluid flow is due to a decelerating shrinking sheet as the electric field reduced the nanofluid velocity, and the first solution is stable compared to the second solution. Thermal radiation and viscous dissipation boost the nanofluid temperature whereas thermal slip reduces. Thermal convective parameter and mass convective parameter demonstrated opposite behavior. The magnetic field, unsteadiness parameter, and the suction parameter widen the range for the solution existence. Comparisons with previously published works seen in literature were performed and found to be in excellent agreement. [ABSTRACT FROM AUTHOR]