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.     

Convective heat transfer performance of hybrid nanofluid in a horizontal pipe considering nanoparticles shapes effect

Journal of Thermal Analysis and Calorimetry - In the present paper, the first and second laws of thermodynamics are utilized to select the optimized position of porous insert to achieve maximum...     

Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects

The problem of steady, laminar, thermosolutal Marangoni convection flow of an electrically-conducting fluid along a vertical permeable surface in the presence of a magnetic field, heat generation or absorption and a first-order chemical reaction effects is studied numerically. The general governing partial differential equations are converted into a set of self-similar equations using unique similarity transformations. Numerical solution of the similarity equations is performed using an implicit, iterative, tri-diagonal finite-difference method. Comparisons with previously published work is performed and the results are found to be in excellent agreement. Approximate analytical results for the temperature and concentration profiles as well as the local Nusselt and sherwood numbers are obtained for the conditions of small and large Prandtl and Schmidt numbers are obtained and favorably compared with the numerical solutions. The effects of Hartmann number, heat generation or absorption coefficient, the suction or injection parameter, the thermo-solutal surface tension ratio and the chemical reaction coefficient on the velocity, temperature and concentration profiles as well as quantitites related to the wall velocity, boundary-layer mass flow rate and the Nusselt and Sherwood numbers are presented in graphical and tabular form and discussed. It is found that a first-order chemical reaction increases all of the wall velocity, Nusselt and Sherwood numbers while it decreases the mass flow rate in the boundary layer. Also, as the thermo-solutal surface tension ratio is increased, all of the wall velocity, boundary-layer mass flow rate and the Nusselt and Sherwood numbers are predicted to increase. However, the exact opposite behavior is predicted as the magnetic field strength is increased.     

Unsteady two-fluid flow and heat transfer in a horizontal channel

The problem of unsteady oscillatory flow and heat transfer of two viscous immiscible fluids through a horizontal channel with isothermal permeable walls has been considered. The partial differential equations governing the flow and heat transfer are solved analytically using two-term harmonic and non-harmonic functions in both fluid regions of the channel. Effects of physical parameters such as viscosity ratio, conductivity ratio, Prandtl number and frequency parameter on the velocity and temperature fields are shown graphically. It is observed that the velocity and temperature decrease as the viscosity ratio increases, while they increase with increases in frequency parameter. The effect of increasing the thermal conductivity ratio also suppresses the temperature in both fluid regions. The effect of periodic frequency on the flow is depicted in tabular form. It is predicted that both the velocity and temperature profiles decrease as the periodic frequency increases.     

Exact analytical solutions for thermosolutal Marangoni convection in the presence of heat and mass generation or consumption

The steady laminar thermosolutal Marangoni convection in the presence of temperature-dependent volumetric heat sources/sinks as well as of a first-order chemical reaction is considered in this paper. Assuming that the surface tension varies linearly with temperature and concentration and that the interface temperature and concentration are quadratic functions of the interface arc length x, exact analytical similarity solutions are obtained for the velocity, temperature and concentration fields. The features of these exact solutions as functions of the physical parameters of the problem are discussed in detail.     

Unsteady compressible boundary layer flow over a circular cone near a plane of symmetry

An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either inflow or outflow in the presence of suction. The flow is assumed to be steady at time t=0 and at t>0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer approximations have been solved by using an implicit finite-difference method. It is found that suction plays an important role in stabilising the fluid motion and in obtaining unique solution of the problem. The effect of the cross flow parameter is found to be more pronounced on the cross flow surface shear stress than on the streamwise surface shear stress and surface heat transfer. Beyond a certain value of the cross flow parameter overshoot in the cross flow velocity occurs and the magnitude of this overshoot increases with the cross flow parameter. The time variation of the streamwise surface shear stress is more significant than that of the cross flow surface shear stress and surface heat transfer. The suction and the total enthalpy at the wall exert strong influence on the streamwise and cross flow surface shear stresses and the surface heat transfer except that the effect of suction on the cross flow surface shear stress is small.