Radiative Boundary Layer Flow Research Articles

Numerical Solution of Radiative Boundary Layer Flow in Porous Medium Due to Exponentially Shrinking Permeable Sheet Under Fuzzy Environment

In this paper we are considering a fluid flows problem that contains two equation of motions and more than two parameters in the governing equation of motion. Which is namely Radiative Boundary Layer Flow in Porous Medium due to Exponentially Shrinking Permeable Sheet. The parameter are K=ck0/Lθ, Pr=μcp/κ∞, N=4σ1(T∞)3/(3κ1κ∞), and ε denote the permeability parameter, Prandtl number, and radiation parameter and is the thermal conductivity variation parameter, respectively. The governing differential equation can be obtained by using the similarity variable technique, and then the governing equation of motion can be Fuzzified by the help of Zadeh extension theorem. The technique is used for the validation of the uncertainty of the equation of the motion. The effect of the K, Pr, N, and ε are discussed with the fuzzified governing equation of motion under fuzzy environment. It is observed none of the parameters are directly involved in the occurrence of the uncertainty of the solutions. The uncertainty occurs in the problem is due to the assumption and the numerical computation. Finally, the solution is being carried out under fuzzy environment. It is found that the increasing values of permeability parameter, the values of both the numbers Skin friction coefficient as well as Nusselt number are increases.

Radiative Boundary Layer Flow of Casson Fluid Over an Exponentially Permeable Slippery Riga Plate with Viscous Dissipation

This study is aimed to analyze the steady of stagnation point flow and radiative heat transfer of a non-Newtonian fluid which is Casson fluid passing over an exponentially permeable slippery Riga plate in presence of thermal radiation, magnetic field, velocity slip, thermal slip, and viscous dissipation effects. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation then solved numerically by boundary value problem solver (BVP4C) in MATLAB software package. The numerical results are evaluated with previous researches to reach an agreement with the parameters of the current study. This study is discussing the behavior of the velocity and temperature profiles as well as skin friction coefficient and local Nusselt number for various physical parameters such as magnetic field, radiation, suction, thermal slip, velocity slip, Prandtl number, Eckert number and modified Hartmann number. Numerical results are shown graphically for each parameter with different values. It is found that the momentum boundary layer thickness increases with increasing the values of Casson parameter. The temperature decreases when the velocity slip parameter and thermal slip parameter are increased.

NUMERICAL SOLUTION OF MAGNETOHYDRODYNAMIC (MHD) RADIATIVE BOUNDARY LAYER FLOW AND HEAT TRANSFER ALONG A WEDGE IN THE PRESENCE OF SUCTION/INJECTION

An approximate numerical solution for the two dimensional laminar MHD radiative boundary layer flow along a wall of wedge with appropriate suction and injection in the presence of viscous dissipation and porous medium is considered in the present article. The fluid is considered to be viscous and incompressible. By applying appropriate similarity transformation, the governing flow equations have been transformed into corresponding higher order ordinary differential equations. The flow model is shown to be controlled by a number of flow parameters, viz. the radiation parameter, magnetic parameter, the permeability parameter, Prandtl number, Eckert number, the Hartree pressure gradient parameter and suction-injection parameter. The system of governing differential equations is solved numerically by shooting method and numerical calculations are carried out for different values of above mentioned dimensionless parameters. An analysis of the drawn results predicts that the velocity boundary layer and thermal boundary layer are influenced appreciably by the suction-injection, radiation and viscous dissipation at the wall of wedge.

Zero and nonzero normal fluxes of thermal radiative boundary layer flow of nanofluid over a radially stretched surface

The axisymmetric flow of a nanoparticles-saturated-fluid with existence of thermic radiation over a stretched sheet is investigated. The effects of zero (passive control) as well as nonzero fluxes (active control) of nanoparticles on the plate towards distributions of temperature and volumetric fraction of nanoparticles are investigated together comparatively. Through the supposition of boundary layer, the Navier-Stokes equations are simplified hence converted into non-dimensional form by similarity transformation. A shooting technique is engaged to deal with the emerging nonlinear system of ordinary differential equations numerically in MATLAB software. Several distributions of velocity, thermal energy and volumetric fraction of nanoparticles under zero/nonzero normal flux are graphically demonstrated. The impact of the parameters towards the reduced coefficient of skin friction, and are investigated too. The presence of thermic radiation under consideration of both zero and nonzero normal fluxes have significant effects on the intensification of the flow heat transfer. Thermophoresis enhances the heat conductivity performance in the case of zero fluxes of nanoparticles.

Chemical Reaction Effects on an Unsteady MHD Mixed Convective and Radiative Boundary Layer Flow over a Circular Cylinder

A mathematical model is presented for an optically dense fluid past an isothermal circular cylinder with chemical reaction taking place in it. A constant, static, magnetic field is applied transverse to the cylinder surface. The cylinder surface is maintained at a constant temperature. New variables are introduced to transform the complex geometry into a simple shape and the boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, Crank-Nicolson finite difference scheme. Numerical computations are made and the effects of the various material parameters on the velocity, temperature and concentration as well as the surface skin friction and surface heat and mass transfer rates are illustrated graphs and tables. Increasing magnetohydrodynamic body force parameter (M) is found to decelerate the flow but enhance temperatures. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing radiation parameter.

MHD radiative boundary layer flow of nanofluid past a vertical plate with internal heat generation/absorption, viscous and ohmic dissipation effects

A mathematical analysis has been carried out to investigate the effects of internal heat generation/absorption, viscous and ohmic dissipations on steady two-dimensional radiative MHD boundary-layer flow of a viscous, incompressible, electrically conducting nanofluid over a vertical plate. A system of governing nonlinear PDEs is converted into a set of nonlinear ODEs by suitable similarity transformations and then solved analytically using HAM and numerically by the fourth order Runge–Kutta integration scheme with shooting method. The effects of different controlling parameters on the dimensionless velocity, temperature and nanoparticle volume fraction profiles are discussed graphically. The reduced Nusslet number and the local Sherwood number are also discussed graphically. It is found that the presence of viscous dissipation, heat generation and magnetic field accelerates the temperature and decelerates the nanosolid volume fraction profile. Furthermore, comparisons have been made with bench mark solutions for a special case and obtained a very good agreement.

Unsteady MHD Mixed Convection, Radiative Boundary Layer Flow of a Micro Polar Fluid Past a Semi-infinite Vertical Porous Plate with Suction

The present study investigates the thermal radiation effect on unsteady magneto hydro dynamic (MHD), mixed convection flow of a micro polar fluid past an infinite, steadily moving plate with variable suction. The dimensionless equations which govern the flow, such as conservation of mass, linear momentum, angular momentum, and energy, are solved by using a regular perturbation method. The expressions for velocity, micro rotation, and temperature are obtained. With the aid of these, the expressions for Skin-friction and Nusselt number are obtained and the behavior of various physical parameters on the above flow quantities is discussed with the help of the graphs. The existence of the magnetic field and as well as radiation decrease the velocity throughout the boundary layer. The effect of increase in the plate moving velocity and the radiation parameter, manifest in a linearly decreasing surface skin-friction on the porous plate, whereas the surface heat transfer from the porous plate tends to increase, with an increase in Prandtl number.

Hydromagnetic convective–radiative boundary layer flow of nanofluids induced by a non-linear vertical stretching/shrinking sheet with viscous–Ohmic dissipation

This paper deals with the study of magnetohydrodynamic boundary layer flow of an electrically conducting convective nanofluids induced by a non-linear vertical stretching/shrinking sheet with viscous dissipation, thermal radiation, and Ohmic heating. The governing equations are solved numerically using a fifth-order Runge–Kutta–Fehlberg method with shooting technique. Numerical results are presented both in tabular and graphical forms for various values of solid volume fraction ϕ (0.01≤ϕ≤0.2), Hartman number Ha (10−12≤Ha≤10−11), Richardson number Ri (0.5≤Ri≤2.0), heat source/sink parameter λ (0.1≤λ≤0.3), Eckert number Ec (0.0≤Ec≤0.5), stretching/shrinking parameter m (0≤m≤25) and non-dimensional parameter ξ (0≤ξ≤2.5) for illustrating its effects on the velocity and temperature profiles as well as on the skin-friction coefficient and local Nusselt number profiles for three types of metallic or nonmetallic nanoparticles, namely copper (Cu), alumina (Al2O3) and titanium dioxide (TiO2) in the base fluid water (Pr=6.8). The results reveal that by increasing the value of Hartman number leads to decrease in the velocity profiles whereas reverse effect is found in the temperature profiles. Also, it is found that increasing the value of nanoparticle volume fraction results in enhancement of heat transfer rate at the boundary layer. Moreover, dual solutions are found in the velocity and temperature fields for higher values of suction/injection parameter S for shrinking sheet.

Radiative Boundary Layer Flow in Porous Medium due to Exponentially Shrinking Permeable Sheet

This communication pertains to the study of radiative heat transfer in boundary layer flow over an exponentially shrinking permeable sheet placed at the bottom of fluid saturated porous medium. The porous medium has permeability of specified form. The fluid considered here is Newtonian, without phase change, optically dense, absorbing-emitting radiation but a nonscattering medium. The setup is subjected to suction to contain the vorticity in the boundary layer. The radiative heat flux in the energy equation is accounted by Rosseland approximation. The thermal conductivity is presumed to vary with temperature in a linear fashion. The governing partial differential equations are reduced to ordinary differential equations by similarity transformations. The resulting system of nonlinear ordinary differential equations is solved numerically by fourth-order Runge-Kutta scheme together with shooting method. The pertinent findings displayed through figures and tables are discussed.

Stagnation Point Flow of a Radiating Gas of a Large Optical Thickness

This paper deals theoretically with the stagnation point flow of a radiating gas when the global optical thickness is large. The radiative heat transfer is assumed to be of the same order of magnitude as the convective one and the Mach number is assumed to be small A method of solution is used in which the isentropic outer flow, the diffusive (Rosseland type) layer flow and the radiation layer flow are considered successively. Actual analysis has been carried out to the second approximation correct to the order of the inverse square root of the Bouguer number. Effects due to the radiation slip are studied in detail. Numerical results are also obtained for the distributions of the flow velocity and the temperature in the diffusive layer and the radiation layer. They are compared with those of a radiative boundary layer flow on a flat plate.