Joaquín Zueco

NETWORK NUMERICAL ANALYSIS OF OPTICALLY THICK HYDROMAGNETIC SLIP FLOW FROM A POROUS SPINNING DISK WITH RADIATION FLUX, VARIABLE THERMOPHYSICAL PROPERTIES, AND SURFACE INJECTION EFFECTS

The steady, incompressible, laminar Newtonian magnetohydrodynamic slip flow with heat transfer from an impulsively started, spinning porous disk is investigated when strong injection (blowing) and significant thermal radiation heat transfer are present. The properties of the fluid, i.e., density, viscosity, and thermal conductivity, are assumed to vary with temperature. Using appropriate transformations, the axisymmetric flow conservation equations for mass, momentum, and energy in a cylindrical polar coordinate system (r, ϕ, z) are normalized to yield a series of highly nonlinear, coupled ordinary differential equations that are solved under appropriate boundary conditions with the network simulation method (NSM). Comparisons are made with an earlier study for the case of Prandtl number = 0.64 with suction present and found to be in excellent agreement. The effects of the radiation-conduction parameter (Nr), hydromagnetic parameter (Nm), slip factor (γ, which is related to Knudsen number), uniform injection parameter (W > 0), and temperature difference parameter (ϵ) on the axial, radial, and tangential velocity components, Nusselt number, and temperature function are investigated in detail. Applications of the study include turbine blade systems, magnetic field control of chemical engineering processes, and electronic computer disk drive cooling.

UNSTEADY HYDROMAGNETIC NATURAL CONVECTION OF A SHORT-MEMORY VISCOELASTIC FLUID IN A NON-DARCIAN REGIME: NETWORK SIMULATION

A mathematical model for the unsteady magnetohydrodynamic (MHD) laminar natural convection flow of a viscoelastic fluid from an infinite vertical porous plate to an isotropic, homogeneous, non-Darcian porous regime, with time-dependent suction, in the presence of a uniform transverse magnetic field, is studied. The generalized Beard-Walters rheological model is employed, which introduces a mixed third-order derivative into the momentum conservation equation. The transformed conservation equations are solved using the robust, well-tested computational procedure known as network simulation method (NSM). The NSM computations have shown that with an increase in viscoelasticity parameter (S) the flow accelerates considerably with time. Increasing magnetic field (M), however, retards the flow strongly with time. An increase in the Darcy number (Da) serves to augment the velocity (w) profiles, i.e., accelerate the flow in both the conducting (M ≠ 0) and nonconducting (M = 0) cases. Velocities also increase in value over time (τ). A velocity overshoot is identified close to the plate. A rise in the Forchheimer number (Fs), corresponding to an accentuation in the quadratic porous drag effect, induces a strong deceleration in the flow, in particular near the plate surface, for both conducting and nonconducting cases. Increasing buoyancy effects, as simulated via a rise in the thermal Grashof number (Gr), leads to a substantial retardation in the flow; this effect is enhanced with Lorentzian magnetic drag force. An increase in the suction parameter (A) causes a stronger adherence of the hydrodynamic boundary layer to the plate and leads to a reduction in velocities along the entire plate regime. A similar decrease in temperature (θ) is caused with increasing suction parameter (A). The results are of relevance in, for example, magneto-rheological materials processing operations and advanced hybrid magnetohydrodynamic energy systems exploiting non-Newtonian fluids.

Unsteady Magnetohydrodynamic Heat Transfer in a Semi-Infinite Porous Medium with Thermal Radiation Flux: Analytical and Numerical Study

The unsteady, buoyancy-induced, hydromagnetic, thermal convection flow in a semi-infinite porous regime adjacent to an infinite hot vertical plate moving with constant velocity, is studied in the presence of significant thermal radiation. The momentum and energy conservation equations are normalized and then solved using both the Laplace transform technique and Network Numerical Simulation. Excellent agreement is obtained between both analytical and numerical methods. An increase in Hartmann number (𝑀2) strongly decelerates the flow and for very high strength magnetic fields (𝑀2=20), the flow is reversed after a short time interval. The classical velocity overshoot is also detected close to the plate surface for low to intermediate values of 𝑀2 at both small and large times; however this overshoot vanishes for larger strengths of the transverse magnetic field (𝑀2=10). An increase in radiation-conduction parameter (𝐾𝑟) significantly increases temperature throughout the porous regime at both small and larger times, adjacent to the plate, but decreases the shear stress magnitudes at the plate. Temperature gradient is reduced at the plate surface for all times, with a rise in radiation-conduction parameter (𝐾𝑟). Shear stress is reduced considerably with an increase in Darcian drag parameter (𝐾𝑝).

Numerical solution of the heat conduction equation with the electro-thermal analogy and the code PSPICE

The central objective of this paper is to provide numerical analysts with a new procedure named the network simulation method (NSM) for solving the heat conduction equation in bodies of regular shape. In principle, NSM rests on the electro-thermal analogy (loosely called the resistance-capacitance analogy or the RC analogy) that exists between the unsteady, unidirectional conduction of heat and the unsteady flow of electric current. Once the electric network model has been set up for the heat conduction equation, the numerical treatment of the analog electric circuit equation can be easily done with the computer code PSPICE. As a conceptual example, the allied numerical solution of the heat conduction equation for a large plate with symmetric surface temperatures has been carried out, demonstrating that the temperature-time histories and the heat flux-time histories can be obtained simultaneously, quickly, and accurately for the entire time domain.

Network simulation solutions for laminar radiating dissipative magneto-gas dynamic heat transfer over a wedge in non-Darcian porous regime

We study the steady-state, magnetohydrodynamic, optically thick, dissipative gas boundary layer flow and heat transfer past a non-isothermal porous wedge embedded in a scattering, homogenous, isotropic Darcy-Forchheimer porous medium, with significant thermal radiation effects in the presence of heat sink/sources and surface transpiration, in an (x,y) coordinate system. The Rosseland diffusion approximation is employed for which radiative flux can propagate only small distances prior to scattering or absorption. Joule electric dissipation, viscous heating and also stress work are incorporated in the boundary layer equations and a temperature-dependent heat source/sink term utilized. Following a transformation to a (@x,@h) coordinate system, the transformed coupled, nonlinear pseudosimilar equations for momentum and energy are solved using a powerful computational method based on thermoelectric analogy, viz the Network Simulation Method. The effects of magnetism (Hartmann number), Darcy number, Forchheimer number, Rosseland radiation-conduction parameter, pressure gradient parameter, Eckert number, transpiration (wall mass transfer) parameter, and heat source/sink parameter on velocity and temperature profiles are depicted graphically. Numerical solutions are compared where possible with earlier non-porous and non-dissipative studies and found to be in excellent agreement. The current study has potential applications in simulating laminar radiative-magnetohydrodynamic heat transfer over astronautical bodies in debris-laden (porous) regimes and also in geothermal physics and magnetic materials processing.

MODELING OF HEAT AND MASS TRANSFER IN A ROTATING VERTICAL POROUS CHANNEL WITH HALL CURRENT

In this study we have obtained an exact solution to the problem of heat and mass transfer in a rotating vertical porous channel taking into account the effects of Hall current. A strong magnetic field of uniform strength is applied along the axis of rotation. The entire system rotates about the axis normal to the plates with a uniform angular velocity. The porous channel is subjected to a constant suction/injection velocity as well as uniform free stream velocity. The nonlinear and coupled governing equations are solved by perturbation technique. The analytical expressions for primary and secondary velocity components, temperature and concentration fields, and shear stresses are obtained. The effects of the magnetic field, rotation of the channel, buoyancy force, Hall current, injection-suction parameter, and the temperature oscillation frequency are described during the course of discussion. The results are presented graphically and discussed.

NUMERICAL ANALYSIS OF HYDROMAGNETIC GRAVITY-DRIVEN THIN FILM MICROPOLAR FLOW ALONG AN INCLINED PLANE

The steady, gravity-driven, incompressible, hydromagnetic, laminar flow of a viscous, electrically conducting, micropolar liquid along an inclined plane subjected to a uniform transverse magnetic field is examined, neglecting surface tension effects. The governing two-dimensional boundary layer equations in an (x, y) coordinate in the absence of pressure gradient are reduced to a pair of ordinary differential equations for linear momentum and angular momentum conservation subject to generalized micro-rotation and velocity boundary conditions at the plane surface. The film thickness is assumed uniform along the plane. The reduced conservation equations are then nondimensionalized and solved numerically with the network simulation method (NSM) and Sparrow-Quack-Boerner local non-similarity method (LNM) for a wide range of the governing dimensionless fluid dynamics parameters. Excellent agreement is obtained between the NSM and LNM solutions. The computations indicate that increasing micropolarity, i.e., Eringen number, elevates micro-rotation magnitudes but reduces linear velocity, i.e., decelerates the flow. The study has significant applications in magnetic field control of materials processing systems.

Unsteady Free Convection and Mass Transfer Flow with Temperature-Dependent Properties, Using the Electronic Network Simulation Program Spice

In this work the network simulation method (NSM) is proposed as a tool for solving the two-dimensional unsteady free convection and mass transfer flow of a viscous dissipative fluid along a semi-infinite vertical plate, taking into account the variation of the viscosity, thermal conductivity, and mass diffusivity with temperature. A spatial discretization, as in finite-difference schemes, is applied to the governing equations, with the time remains as a real continuous variable, and the different analogies (electrical-motion, electrical-thermal, and electrical-mass) developed in this work are applied to solve the problem in an adequate electric simulation program. The effect of variations in viscosity, thermal conductivity, and mass diffusivity with temperature is discussed. The effects of viscous dissipation and the Schmidt number are also studied.

Non-linear transient hydromagnetic partially ionised dissipative Couette flow in a non-Darcian porous medium channel with Hall, ionslip and Joule heating effects

We study the transient magnetohydrodynamic (MHD) viscous laminar flow and heat transfer in a channel containing a Darcy-Forchheimer porous medium, under a constant pressure gradient with Hall current, ionslip, transpiration, viscous and Joule heating. The dimensionless momentum and heat conservation equations are solved using the Network Simulation Method (NSM). The effects of a number of thermophysical parameters on the transport phenomena are studied including Darcy number (Da), Forchheimer quadratic drag number (Fs), Hartmann number (Ha), Hall current parameter (βe), ionslip parameter (βi) and Eckert number (Ec). The model finds applications in geophysics and MHD energy generators.

NUMERICAL MODELING OF MHD CONVECTIVE HEAT AND MASS TRANSFER IN PRESENCE OF FIRST-ORDER CHEMICAL REACTION AND THERMAL RADIATION

An analysis was carried out numerically to study unsteady heat and mass transfer by free convection flow of a viscous, incompressible, electrically conducting Newtonian fluid along a vertical permeable plate under the action of transverse magnetic field taking into account thermal radiation as well as homogeneous chemical reaction of first order. The fluid considered here is an optically thin gray gas, absorbing-emitting radiation, but a non-scattering medium. The porous plate was subjected to a constant suction velocity with variable surface temperature and concentration. The dimensionless governing coupled, nonlinear boundary layer partial differential equations were solved by an efficient, accurate, extensively validated, and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature, and concentration fields were studied for the effects of Hartmann number (M), radiation parameter (R), chemical reaction (K), and Schmidt number (Sc). The local skin friction, Nusselt number, and Sherwood number are also presented and analyzed graphically. It is found that velocity is reduced considerably with a rise in the magnetic body parameter (M), whereas the temperature and concentration are found to be markedly boosted with an increase in the magnetic body parameter (M). An increase in the conduction-radiation parameter (R) is found to escalate the local skin friction (τ), Nusselt number, and concentration, whereas an increase in the conduction-radiation parameter (R) is shown to exert the opposite effect on either velocity or temperature field. Similarly, the local skin friction and the Sherwood number are both considerably increased with an increase in the chemical reaction parameter. Possible applications of the present study include laminar magneto-aerodynamics, materials processing, and MHD propulsion thermo-fluid dynamics.