MHD Flow of a Micropolar Fluid past a Stretched Permeable Surface with Heat Generation or Absorption

This work considers steady, laminar, MHD flow of a micropolar fluid past a stretched semi-infinite, vertical and permeable surface in the presence of temperature dependent heat generation or absorption, magnetic field and thermal radiation effects. A set of similarity parameters is employed to convert the governing partial differential equations into ordinary differential equations. The obtained self-similar equations are solved numerically by an efficient implicit, iterative, finite-difference method. The obtained results are checked against previously published work for special cases of the problem in order to access the accuarcy of the numerical method and found to be in excellent agreement. A parametric study illustrating the influence of the various physical parameters on the skin friction coefficient, microrotaion coefficient or wall couple stress as well as the wall heat transfer coefficient or Nusselt number is conducted. The obtained results are presented graphically and in tabular form and the physical aspects of the problem are discussed

Unsteady natural convective power-law fluid flow past a vertical plate embedded in a non-Darcian porous medium in the presence of a homogeneous chemical reaction

A numerical solution is presented for unsteady coupled heat and mass transfer by natural convection from a non-Newtonian power-law fluid flow past a vertical plate embedded in a non-Darcian porous medium in the presence of viscous dissipation and chemical reaction effects. The governing equations are formulated and a numerical solution is obtained by using an explicit finite-difference scheme. The solutions at each time step have been found to reach the steady state solution properly. The numerical results are presented in tabular and graphical form to show the effects of material parameters of the problem on the solution

Fluid–structure interaction of free convection in a square cavity divided by a flexible membrane and subjected to sinusoidal temperature heating

Purpose: The purpose of the present paper is to model a cavity, which is equally divided vertically by a thin, flexible membrane. The membranes are inevitable components of many engineering devices such as distillation systems and fuel cells. In the present study, a cavity which is equally divided vertically by a thin, flexible membrane is model using the fluid–structure interaction (FSI) associated with a moving grid approach. Design/methodology/approach: The cavity is differentially heated by a sinusoidal time-varying temperature on the left vertical wall, while the right vertical wall is cooled isothermally. There is no thermal diffusion from the upper and lower boundaries. The finite-element Galerkin technique with the aid of an arbitrary Lagrangian–Eulerian procedure is followed in the numerical procedure. The governing equations are transformed into non-dimensional forms to generalize the solution. Findings: The effects of four pertinent parameters are investigated, i.e., Rayleigh number (104 = Ra = 107), elasticity modulus (5 × 1012 = ET = 1016), Prandtl number (0.7 = Pr = 200) and temperature oscillation frequency (2p = f = 240p). The outcomes show that the temperature frequency does not induce a notable effect on the mean values of the Nusselt number and the deformation of the flexible membrane. The convective heat transfer and the stretching of the thin, flexible membrane become higher with a fluid of a higher Prandtl number or with a partition of a lower elasticity modulus. Originality/value: The authors believe that the modeling of natural convection and heat transfer in a cavity with the deformable membrane and oscillating wall heating is a new subject and the results have not been published elsewhere

Transient Mixed Convection Flow of A Second-Grade Visco-Elastic Fluid over a Vertical Surface

The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical isothermal surface have been examined in this paper. The governing equations are formulated and solved numerically using an explicit finite difference technique. The velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers and the local skin friction coefficients are shown graphically for different values of the viscoelsatic parameter. In general, it is found that the velocity decreases inside the boundary layer as the viscoelsatic parameter is increased and consequently, the local Nusselt number decreases. This is due to higher tensile stresses between viscoelsatic fluid layers which has a retardation effects on the motion of these layers and consequently, on the heat transfer rates for the mixed convection heat transfer problem under investigation. A Comparison with available published results on special cases of the problem shows excellent agreement

MHD natural convection in an inclined cavity filled with a fluid saturated porous medium with heat source in the solid phase

A numerical investigation of unsteady magnetohydrodynamic free convection in an inclined square cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field inclined with the same angle of the inclination of the cavity is applied. The governing equations are formulated and solved by a direct explicit finite-difference method subject to appropriate initial and boundary conditions. Two cases were considered, the first case when all the cavity walls are cooled and the second case when the cavity vertical walls are kept adiabatic. A parametric study illustrating the influence of the Hartmann number, Rayliegh number, the inclination angle of the cavity and the dimensionless time parameter on the flow and heat transfer characteristics such as the streamlines, isotherms and the average Nusselt number is performed. The velocity components at mid section of the cavity as well as the temperature profiles are reported graphically. The values of average Nusselt number for various parametric conditions are presented in tabular form

Free Convection Flow of an Electrically-Conducting Micropolar Fluid between Parallel Porous Vertical Plates Using Differential Transform

In the present study, the effect of temperature-dependent heat sources on the fully developed free convection flow of an electrically conducting micropolar fluid between two parallel porous vertical plates in the presence of a strong cross magnetic field is analyzed. The micropolar fluid fills the space inside the porous plates when the rate of suction at one boundary is equal to the rate of injection at the other boundary. The coupled nonlinear governing differential equations are solved using the differential transform method (DTM). Moreover, the Runge-Kutta shooting method (RKSM), which is a numerical method, is used for the validity of DTM method and an excellent agreement is observed between the solutions of DTM and RKSM. Trusting this validity, the effects of Hartmann number, Reynolds number, micropolar parameter, and applied electric field load parameter are discussed on the velocity, microrotation velocity, and temperature. The skin friction, the couple stress, and Nusselt numbers at the plates are shown in graphs. It is observed that the Hartmann number and the micropolar parameter decreases the skin friction and the couple stress at both plates for suction and injection

Numerical Solutions of Free Convective Flow from a Vertical Cone with Mass Transfer under the Influence of Chemical Reaction and Heat Generation/Absorption in the Presence of UWT/UWC

The purpose of this paper is to present a mathematical model for the combined effects of chemical reaction and heat generation/absorption on unsteady laminar free convective flow with heat and mass transfer over an incompressible viscous fluid past a vertical permeable cone with uniform wall temperature and concentration (UWT/UWC).The dimensionless governing boundary layer equations of the flow that are transient, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicholson type. The velocity, temperature, and concentration profiles have been studied for various parameters viz., chemical reaction parameter , the heat generation and absorption parameter , Schmidt number Sc , Prandtl number Pr , buoyancy ratio parameter N . The local as well as average skin friction, Nusselt number, Sherwood number, are discussed and analyzed graphically. The present results are compared with available results in open literature and are found to be in excellent agreemen

Network electro-thermal simulation of non-isothermal magnetohydrodynamic heat transfer from a transpiring cone with buoyancy and pressure work

The steady, axisymmetric laminar natural convection boundary layer flow from a non-isothermal vertical circular porous cone under a transverse magnetic field, with the cone vertex located at the base, is considered. The pressure work effect is included in the analysis. The governing boundary layer equations are formulated in an (x,y) coordinate system (parallel and normal to the cone slant surface), and the magnetic field effects are simulated with a hydromagnetic body force term in the momentum equation. A dimensionless transformation is performed rendering the momentum and also heat conservation equations. The thermal convection flow is shown to be controlled by six thermophysical parameters- local Hartmann number, local Grashof number, pressure work parameter, temperature power law exponent, Prandtl number and the transpiration parameter. The transformed parabolic partial differential equations are solved numerically using the Network Simulation Method (NSM) based on the electrical-thermodynamic analogy. Excellent correlation of the zero Hartmann number case is achieved with earlier electrically non-conducting solutions. Local shear stress function (skin friction) is found to be strongly decreased with an increase in Prandtl number (Pr), with negative values (corresponding to flow reversal) identified for highest Pr with further distance along the streamwise direction. A rise in local Hartmann number, is observed to depress skin friction. Increasing temperature power law index, corresponding to steeper temperature gradient at the wall, strongly reduces skin friction at the cone surface. A positive rise in pressure work parameter decreases skin friction whereas a negative increase elevates the skin friction for some distance along the cone surface from the apex. Local heat transfer gradient is markedly boosted with a rise in Prandtl number but decreased principally at the cone surface with increasing local Hartmann number. Increasing temperature power law index conversely increases the local heat transfer gradient, at the cone surface. A positive rise in pressure work parameter increases local heat transfer gradient while negative causes it to decrease. A rise in local Grashof number boosts local skin friction and velocity into the boundary layer; local heat transfer gradient is also increased with a rise in local Grashof number whereas the temperature in the boundary layer is noticeably reduced. Applications of the work arise in spacecraft magnetogas dynamics, chemical cooling systems and industrial magnetic materials processing

Natural convection in a square cavity with uniformly heated and/or insulated walls using marker-and-cell method

In this study, a numerical investigation has been performed using the computational Harlow-Welch MAC (Marker and Cell) finite difference method to analyse the unsteady state two-dimensional natural convection in lid-driven square cavity with left wall maintained at constant heat flux and remaining walls kept thermally insulated. The significant parameters in the present study are Reynolds number (Re), thermal Grashof number (Gr) and Prandtl number (Pr) and Peclét number (Pe =PrRe). The structure of thermal convection patterns is analysed via streamline, vorticity, pressure and temperature contour plots. The influence of the thermophysical parameters on these distributions is described in detail. Validation of solutions with earlier studies is included. Mesh independence is also conducted. It is observed that an increase in Prandtl number intensifies the primary circulation whereas it reduces the heat transfer rate. Increasing thermal Grashof number also decreases heat transfer rates. Furthermore the isotherms are significantly compressed towards the left (constant flux) wall with a variation in Grashof number while Peclét number is fixed. The study is relevant to solar collector heat transfer simulations and also crystal growth technologies