Theoretical Analysis of Radiative Effects on Transient Free Convection Heat Transfer past a Hot Vertical Surface in Porous Media

The purpose of the present investigation deals with the unsteady free convective flow of a viscous incompressible gray, absorbing-emitting but non-scattering, optically-thick fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity. We employ a Darcian viscous flow model for the porous medium. The momentum and thermal boundary layer equations are non-dimensionalized using appropriate transformations and then solved subject to physically realistic boundary conditions using the Laplace transform technique. Thermal radiation effects are simulated via a radiation-conduction parameter, Kr, based on the Rosseland diffusion approximation. The influence of Grashof (free convection) number, radiation-conduction parameter (Kr), inverse permeability parameter (Kp) and dimensionless time (t) are studied graphically. We observe that increasing thermal radiation parameter causes a noticeable increase in the flow velocity, u. Temperature, θ, is significantly increased within the boundary layer with a rise in Kr since the latter represents the relative contribution of thermal radiation heat transfer to thermal conduction heat transfer. Increased radiation therefore augments heat transfer, heats the fluid and increases the thickness of the momentum and thermal boundary layers. Velocity is found to decrease with an increase in Kp (inverse permeability parameter) as are shear stress function ( ∂u/∂y | y=0) magnitudes owing to greater resistance of the porous medium for lower permeabilities, which decelerate the flow. An increase in Kr however boosts the shear stress function magnitudes i.e. serves to accelerate the flow. Temperature gradient, ∂θ/∂y | y=0 is also positively affected by an increase in thermal radiation (Kr) and with time. The present study has applications in geological convection, forest fire propagation, glass heat treatment processes at high temperature, metallurgical processing etc

A Study of Unsteady Rotating Hydromagnetic Free and Forced Convection in a Channel Subject to Forced Oscillation under an Oblique Magnetic Field

A theoretical analysis is presented for transient, fully-developed magnetohydrodynamic free and forced convection flow of a viscous, incompressible, Newtonian fluid in a rotating horizontal parallel-plate channel subjected to a uniform strength, static, oblique magnetic field acting at an angle to the positive direction of the axis of rotation. A constant pressure gradient is imposed along the longitudinal axis of the channel. Magnetic Reynolds number is sufficiently small to negate the effects of magnetic induction. The channel plates are electrically non-conducting. The conservation equations are formulated in an (x,y,z) coordinate system and normalized using appropriate transformations. The resulting non-dimensional coupled ordinary differential equations for primary and secondary velocity components and transformed boundary conditions are found to be reciprocal of the Ekman number ( 2 K =1/Ek), non-dimensional pressure gradient parameter (Px), Hartmann number ( 2 M ), Grashof number (Gr), magnetic field inclination () and oscillation frequency (). Complex variables are employed to solve the two-point boundary value problem. A steady state resonance of the velocity field is identified for 4 4 4 1/ 2 16 2 1 K M Sin . Furthermore the solutions indicate that the condition 1/2 1 4 4 4 cos 16 2 T K M Sin signifies an oscillatory turbulent dynamo mechanism. A critical Grashof number (Grcx) is also evaluated for which primary flow reversal arises at the upper channel plate. A similar criterion for Grashof number (Grcy) is established for the onset of secondary flow reversal at the upper plate. A detailed assessment of the influence of the control parameters on primary and secondary velocity evolution in the channel is also conducted. The model finds applications in MHD (Magneto Hydro Dynamic) energy generators and also magnetic materials processing systems

Free Convection Flow and Heat Transfer of Tangent Hyperbolic past a Vertical Porous Plate with Partial Slip

This article presents the nonlinear free convection boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic non-Newtonian fluid from a vertical porous plate with velocity slip and thermal jump effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), the power law index (n), Velocity slip (Sf), Thermal jump (ST), Prandtl number (Pr) and dimensionless tangential coordinate () on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that velocity, skin friction and heat transfer rate (Nusselt number) is increased with increasing Weissenberg number (We), whereas the temperature is decreased. Increasing power law index (n) enhances velocity and heat transfer rate but decreases temperature and skin friction. An increase in Thermal jump (ST) is observed to decrease velocity, temperature, local skin friction and Nusselt number. Increasing Velocity slip (Sf) is observed to increase velocity and heat transfer rate but decreases temperature and local skin friction. An increasing Prandtl number, (Pr), is found to decrease both velocity and temperature. The study is relevant to chemical materials processing applications

Mathematical Study of Laminar Boundary Layer Flow and Heat Transfer of Tangenthyperbolic Fluid Pasta Vertical Porous Plate with Biot Number Effects

In this article, we investigate the nonlinear steady boundary layer flow and heat transfer of an incompressible Tangent Hyperbolicnon-Newtonian fluid from a vertical porous plate. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), the power law index (n), Prandtl number (Pr), Biot number (), and dimensionless local suction parameter()on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that velocity, Skin friction and Nusselt number (heat transfer rate) are reduced with increasing Weissenberg number (We), whereas, temperature is enhanced. Increasing power law index (n) enhances velocity and Nusselt number (heat transfer rate) but temperature and Skin friction decrease. An increase in the Biot number () is observed to enhance velocity, temperature, local skin friction and Nusselt number. An increasing Prandtl number, Pr, is found to decrease both velocity, temperature and skin friction but elevates heat transfer rate (Nusselt number). The study is relevant to chemical materials processing applications

Homotopy analysis of magnetohydrodynamic convection flow in manufacture of a viscoelastic fabric for space applications

Aerospace electro-conductive polymer materials are a new family of “smart” materials being deployed in many complex applications. The precision manufacturing of such processes to manipulate properties and enhance performance can exploit magnetohydrodynamic (MHD) control and simultaneous heat transfer (thermal processing). Motivated by these applications, we develop a model for laminar free convective flow of an incompressible and electrically-conducting viscoelastic fluid (Walters’ liquid B) over a continuously moving stretching surface embedded in a porous medium in the presence of strong radiative heat flux, as a simulation of magnetic smart fabric sheet processing. A heat generation/absorption term is included in the model. Darcy’s law is used to simulate porous media bulk drag effects. The stretching is assumed to be a linear function of the coordinate along the direction of stretching. Using similarity transformations, the governing partial differential equations are converted to nonlinear ordinary differential equations. The energy equation is further rendered into confluent hypergeometric form and then solved analytically for the prescribed surface temperature (PST) case and also for the Prescribed Boundary Surface Heat Flux (PHF) case, using Kummer’s function, subject to physically realistic boundary conditions. The momentum and energy equations are also solved using the semi-numerical homotopy analysis method (HAM), which contains the auxiliary parameter , permitting relatively easy adjustment and control of the convergence region of the series solution. This method provides an efficient approximate analytical solution with high accuracy, minimal calculation, and avoidance of physically unrealistic assumptions. HAM solutions are benchmarked with robust numerical shooting quadrature and found to correlate well. The influence of magnetic field on velocity and temperature profiles is studied via the Chandrasekhar number (Q). Furthermore detailed simulations are conducted for the influence of viscoelastic parameter (k1), Eckert number (E), radiation-conduction parameter (NR), Grashof number (Gr) and heat source/sink parameter () on the flow variables. The study finds applications in electro-conductive polymeric materials processing for aerospace fabric covers and other applications with demanding safety and protection requirements in smart materials synthesis

Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions

Energy conversion under conduction, convection, diffusion and radiation has been studied for MHD free convection heat transfer of a steady laminar boundary-layer flow past a moving permeable non-linearly extrusion stretching sheet. The nonlinear Rosseland thermal radiation flux model, velocity slip, thermal and mass convective boundary conditions are considered to obtain a model with fundamental applications to real world energy systems. The Navier slip, thermal and mass convective boundary conditions are taken into account. Similarity differential equations with corresponding boundary conditions for the flow problem, are derived, using a scaling group of transformation. The transformed model is shown to be controlled by magnetic field, conduction-convection, convection-diffusion, suction/injection, radiation-conduction, temperature ratio, Prandtl number, Lewis number, buoyancy ratio and velocity slip parameters. The transformed non-dimensional boundary value problem comprises a system of nonlinear ordinary differential equations and physically realistic boundary conditions, and is solved numerically using the efficient Runge-Kutta-Fehlberg fourth fifth order numerical method, available in Maple17 symbolic software. Validation of results is achieved with previous simulations available in the published literature. The obtained results are displayed both in graphical and tabular form to exhibit the effect of the controlling parameters on the dimensionless velocity, temperature and concentration distributions. The current study has applications in high temperature materials processing utilizing magnetohydrodynamics, improved performance of MHD energy generator wall flows and also magnetic-microscale fluid devices

Effect of temperature-dependent viscosity on entropy generation in transient viscoelastic polymeric fluid flow from an isothermal vertical plate

A numerical investigation of the viscosity variation effect upon entropy generation in time-dependent viscoelastic polymeric fluid flow and natural convection from a semi-infinite vertical plate is described. The Reiner-Rivlin second order differential model is utilized which can predict normal stress differences in dilute polymers. The conservation equations for heat, momentum and mass are normalized with appropriate transformations and the resulting unsteady nonlinear coupled partial differential equations are elucidated with the well-organized unconditionally stable implicit Crank-Nicolson finite difference method subject to suitable initial and boundary conditions. Average values of wall shear stress and Nusselt number, second-grade fluid flow variables conferred for distinct values of physical parameters. Numerical solutions are presented to examine the entropy generation and Bejan number along with their contours. The outcomes show that entropy generation parameter and Bejan number both increase with increasing values of group parameter and Grashof number. The present study finds applications in geothermal engineering, petroleum recovery, oil extraction and thermal insulation, etc

Influence of Stefan blowing on nanofluid flow submerged in microorganisms with leading edge accretion or ablation

The unsteady forced convective boundary layer flow of viscous incompressible fluid containing both nanoparticles and gyrotactic microorganisms, from a flat surface with leading edge accretion (or ablation), is investigated theoretically. Utilizing appropriate similarity transformations for the velocity, temperature, nanoparticle volume fraction and motile microorganism density, the governing conservation equations are rendered into a system of coupled, nonlinear, similarity ordinary differential equations. These equations, subjected to imposed boundary conditions, are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method in the MAPLE symbolic software. Good agreement between our computations and previous solutions is achieved. The effect of selected parameters on flow velocity, temperature, nano-particle volume fraction (concentration) and motile microorganism density function is investigated. Furthermore, tabular solutions are included for skin friction, wall heat transfer rate, nano-particle mass transfer rate and microorganism transfer rate. Applications of the study arise in advanced micro-flow devices to assess nanoparticle toxicity