Unsteady mixed convection on the stagnation-point flow adjacent to a vertical plate with a magnetic field

An analysis is performed to study the unsteady combined forced and free convection flow (mixed convection flow) of a viscous incompressible electrically conducting fluid in the vicinity of an axisymmetric stagnation point adjacent to a heated vertical surface. The unsteadiness in the flow and temperature fields is due to the free stream velocity, which varies arbitrarily with time. Both constant wall temperature and constant heat flux conditions are considered in this analysis. By using suitable transformations, the Navier–Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (, ). These transformations also uncouple the momentum and energy equations resulting in a primary axisymmetric flow, in an energy equation dependent on the primary flow and in a buoyancy-induced secondary flow dependent on both primary flow and energy. The resulting system of partial differential equations has been solved numerically by using both implicit finite-difference scheme and differential-difference method. An interesting result is that for a decelerating free stream velocity, flow reversal occurs in the primary flow after certain instant of time and the magnetic field delays or prevents the flow reversal. The surface heat transfer and the surface shear stress in the primary flow increase with the magnetic field, but the surface shear stress in the buoyancy-induced secondary flow decreases. Further the heat transfer increases with the Prandtl number, but the surface shear stress in the secondary flow decreases.     

Free convection flow over a truncated cone embedded in a porous medium saturated with pure or saline water at low temperatures

Steady free convection boundary layer about a truncated cone embedded in a porous medium saturated with pure or saline water at low temperatures has been studied in this paper. The governing coupled partial differential equations are solved numerically using a very efficient finite-difference method. Several new parameters arise and the results are given for some specific values of these parameters. The obtained results for a Boussinesq fluid are compared with known results from the open literature and it is shown that the agreement between these results is very good.     

MHD mixed convection in a nanofluid filled vertical lid-driven cavity having a flexible fin attached to its upper wall

Journal of Thermal Analysis and Calorimetry - In this study, fluid flow and heat transfer in a vertical lid-driven CuO–water nanofluid filled square cavity with a flexible fin attached to its...     

Effects of two-phase nanofluid model on MHD mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater

Journal of Thermal Analysis and Calorimetry - This paper investigates a steady mixed convection in a lid-driven square cavity subjected to an inclined magnetic field and heated by corner heater...     

Thermo-magneto-hydrodynamical effects on merging flow of TiO2–water nanofluid

Journal of Thermal Analysis and Calorimetry - The steady flow of a nanofluid (mixture of titanium dioxide and water) in a rectangular channel under the influence of an inclined magnetic field is...     

Thermal radiation and surface roughness effects on the thermo-magneto-hydrodynamic stability of alumina–copper oxide hybrid nanofluids utilizing the generalized Buongiorno’s nanofluid model

Journal of Thermal Analysis and Calorimetry - Sequel to the fact that hybrid nanofluidic systems (e.g. scalable micro-/nanofluidic device) exhibit greater thermal resistance with increasing...     

A numerical simulation of mixed convective and arbitrarily oblique radiative stagnation point slip flow of a CNT-water MHD nanofluid

Journal of Thermal Analysis and Calorimetry - Numerical simulation of a non-linear mathematical model governing an arbitrarily oblique slip flow of a nanofluid, with suspended carbon nanotubes in...     

Mixed Convection in a Ventilated Cavity Filled with a Triangular Porous Layer

Accurate prediction of the macroscopic flow parameters needed to describe flow in porous media relies on a good knowledge of flow field distribution at a much smaller scale—in the pore spaces. The extent of the inertial effect in the pore spaces cannot be underestimated yet is often ignored in large-scale simulations of fluid flow. We present a multiscale method for solving Oseen’s approximation of incompressible flow in the pore spaces amid non-periodic grain patterns. The method is based on the multiscale finite element method [MsFEM Hou and Wu in J Comput Phys 134:169–189, 1997)] and is built in the vein of Crouzeix and Raviart elements (Crouzeix and Raviart in Math Model Numer Anal 7:33–75, 1973). Simulations of inertial flow in highly non-periodic settings are conducted and presented. Convergence studies in terms of numerical errors relative to the reference solution are given to demonstrate the accuracy of our method. The weakly enforced continuity across coarse element edges is shown to maintain accurate solutions in the vicinity of the grains without the need for any oversampling methods. The penalisation method is employed to allow a complicated grain pattern to be modelled using a simple Cartesian mesh. This work is a stepping stone towards solving the more complicated Navier–Stokes equations with a nonlinear inertial term.     

Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H2O nanofluid on a flat surface in a porous medium: A stability analysis

The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems. So, here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium is examined. Moreover, the thermal radiation and viscous dissipation effects are considered. The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method. The computed results can reveal many vital findings of practical importance. Firstly, dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows, the solution is unique. The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium. But different shapes of nanoparticles are not disturbing the dual solution existence range, though it has a considerable impact on thermal conductivity of the mixture. Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid, i.e., the water here. On the other hand, the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium. Regarding the cooling rate of the heated surface, it rises with the permeability parameter, shape factor (related to various shapes of Cu-nanoparticles), and radiation parameter. The surface drag force becomes stronger with the permeability parameter. Also, with growing values of nanoparticle volume fraction, the boundary layer thickness (BLT) increases and the thermal BLT becomes thicker with larger values of shape factor. For decelerating unsteady flow, the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed. The thermal BLT is thicker with radiation parameter. Due to the existence of dual solutions, a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.     

Unsteady laminar hydromagnetic fluid–particle flow and heat transfer in channels and circular pipes

The problem of unsteady laminar flow and heat transfer of a particulate suspension in an electrically conducting fluid through channels and circular pipes in the presence of a uniform transverse magnetic field is formulated using a two-phase continuum model. Two different applied pressure gradient (oscillating and ramp) cases are considered. The general governing equations of motions (which include such effects as particulate phase stresses, magnetic force, and finite particle-phase volume fraction) are non-dimensionalized and solved in closed form in terms of Fourier cosine and Bessel functions and the energy equations for both phases are solved numerically since they are non-linear and are difficult to solve analytically. Numerical solutions based on the finite-difference methodology are obtained and graphical results for the fluid-phase volumetric flow rate, the particle-phase volumetric flow rate, the fluid-phase skin-friction coefficient and the particle-phase skin-friction coefficient as well as the wall heat transfer for plane and axisymmetric flows are presented and discussed. In addition, these numerical results are validated by favorable comparisons with the closed-form solutions. A comprehensive parametric study is performed to show the effects of the Hartmann magnetic number, the particle loading, the viscosity ratio, and the temperature inverse Stokes number on the solutions.