Rosseland Approximation Research Articles

Thermal performance of straight porous fin with variable thermal conductivity under magnetic field and radiation effects

AbstractThe present numerical study reports the thermal performance of the straight porous fin with temperature‐dependent thermal conductivity, radiation, and magnetic field effects. The heat transfer model comprising the Darcy's law for simulating flow with solid‐fluid interactions in porous medium, Rosseland approximation for heat transfer through radiation, Maxwell equations for magnetic field effect and linearly varying temperature dependent thermal conductivity, results into highly nonlinear ordinary differential equation. The governing equation is solved using a finite difference scheme with suitable boundary conditions. The obtained solutions are physically interpreted by considering the impact of different nondimensional parameters on thermal performance, efficiency, and effectiveness of the system through plotted graphs. A detailed result with regard to the Nusselt number at the fin base is calculated. The results obtained are observed to be in excellent agreement with previous studies. From the study, it is observed that there is a significant effect on the thermal performance of the fin in the presence of porous constraints; also, results reveal that the nonlinear thermal conductivity parameter strengthens the thermal performance, efficiency, and effectiveness of the fin. Furthermore, the results of the study reveal that the rate of heat transfer of the fin increases with the increase in the magnetic parameter and radiation parameter.

Characteristics of combined heat and mass transfer on mixed convection flow of Sisko fluid model: A numerical study

In this paper, the combined heat and mass transfer of mixed convection, non-similar Sisko fluid flow in the presence of a magnetic field is studied. The combined effects of thermal radiation and heat generation/absorption are examined for Sisko fluid flow via local non-similar method. For the radiative heat transfer, Rosseland approximation model is used. The governing partial differential equations of the present problem are transformed into a system of nonlinear ordinary differential equations by employing the Sparrow–Quack–Boerner local non-similarity method (LNM). The obtained equations are then numerically investigated by utilizing the bvp4c function in MATLAB. The impact of different supervising parameters on the velocity, temperature, skin friction and rate of heat transfer is performed graphically. It is observed that the velocity is more for a higher rate of the buoyancy force parameter while it is less for opposing buoyancy fluid. The thermal boundary layer thickness for the shear thickening fluids is smaller than the shear thinning fluids.

Finite Element Numerical Investigation into Unsteady MHD Radiating and Reacting Mixed Convection Past an Impulsively Started Oscillating Plate

In this article, numerical investigation is carried out for the unsteady MHD mixed convection flow of radiating and chemically reacting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion. The transport model employed includes the Hall current. A uniform magnetic field is applied transversely to the direction of the fluid flow. The flow consideration is subject to small magnetic Reynolds number. The Rosseland approximation is used to describe the radiation heat flux in the energy equation. The dimensionless governing system of partial differential equations of the flow has been solved numerically by employing the FEM. The influence of pertinent parameters on primary velocity, secondary velocity, temperature and concentration are presented graphically whereas primary skin friction, secondary skin friction, Nusselt number and Sherwood number are presented in tabular form. The findings of the present study are in good agreement with the earlier reported studies.

Finite element numerical investigation into unsteady MHD radiating and reacting mixed convection past an impulsively started oscillating plate

In this article, numerical investigation is carried out for the unsteady MHD mixed convection flow of radiating and chemically reacting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion. The transport model employed includes the Hall current. A uniform magnetic field is applied transversely to the direction of the fluid flow. The flow consideration is subject to small magnetic Reynolds number. The Rosseland approximation is used to describe the radiation heat flux in the energy equation. The dimensionless governing system of partial differential equations of the flow has been solved numerically by employing the finite element method. The influence of pertinent parameters on primary velocity, secondary velocity, temperature and concentration are presented graphically whereas primary skin friction, secondary skin friction, Nusselt number and Sherwood number are presented in tabular form. A comparison of the present method was madewith the exact solution obtained by Rajput and Kanaujia (2016) by considering primary and secondary skin frictions, it was noticed that a very good agreement.
 Keywords: MHD, radiation parameter, chemical reaction parameter, magnetic parameter, Hall current.

Unsteady Magneto-Hydrodynamic Flow Through Saturated Porous Medium with Thermal Non-equilibrium and Radiation Effects

The effect of thermal non-equilibrium on two-dimensional magnetohydrodynamics flow through a sparsely packed porous medium bounded by two vertical plates has been examined using finite difference approximation. The Rosseland approximation for thermal radiation is incorporated as a pertinent parameter in the liquid phase thermal energy equation. The numerical solutions are used to analyze the effects of Brinkman number, viscosity ratio, porous parameter, magnetic parameter, heat transfer coefficient, and thermal radiation parameter on velocity and temperature profiles. Also, the skin-friction coefficient and Nusselt number are determined at the left boundary of the channel, and results are presented via plots. The results show that the Brinkman number, porous parameter, magnetic parameter, and thermal radiation parameter opposes the liquid flow and enhances the temperature distribution, whereas the interphase heat transfer coefficient, the ratio of thermal diffusivities shows the opposite effect.

An Analysis of Thermal Radiation in Porous Media Under Local Thermal Non-equilibrium

The present work investigates the thermal radiation transport inside porous media under local thermal non-equilibrium conditions. Two different geometrical situations, a two-dimensional channel and a cylindrical geometry, are considered in the analysis. Porous media application is generally associated with high-temperature combustion, and radiative heat transfer is dominant. In this paper, by considering a stream of high-temperature flow in geometries filled with porous medium, the effect of thermal radiation on the solid- and fluid-phase temperature fields is calculated and analyzed. Two radiative heat transfer techniques, the discrete ordinate method (DOM) and the finite volume method (FVM), are tested, and the results are compared with a non-radiative model and with a model-based Rosseland approximation. A sensitivity study for the variation in absorption and scattering coefficients and the effect on the solid- and fluid-phase temperature fields is also undertaken. The effect of the extinction coefficient on the Nusselt number is also examined. The temperatures obtained through the Rosseland model show differences up to + 34% and − 26% compared to temperatures calculated with the DOM or FVM radiation calculation methods. The temperature fields obtained through DOM and FVM are very similar, and some significant differences can only be seen in the cases where a very low number of angular directions are used.

Influence of magnetic field and thermal radiation on peristaltic motion with double‐diffusive convection in Jeffery nanofluids

AbstractA theoretical study is conducted to examine the peristaltic pumping with double‐diffusive convection in Jeffery nanofluids through a two‐dimensional infinite asymmetric channel. The flow is examined in a wave casing of orientation that moves pace with the velocity of the wave. The peristaltic wave train on the walls that have different amplitude and phase is chosen to form channel irregularity. Rosseland approximation is noticed in the modeling of the transmission radiation heat transfer and temperatures of the walls are recognized constants. The replica has a great impact in discovering nanofluid dynamic influences on peristaltic motion, in biological vessels as symbolized by transportation of heat in blood flow, food molecules, hormones, novel pharmacodynamics pumps, and engineered gastrointestinal motility enhancement. Peristaltic motion has applications in physiology, such as transport of urine, transport of food bolus through gastrointestinal tract, and transport of blood through small blood vessels. Analytical results have been established for stream function, axial velocity, temperature, and absorption and nanoparticle volume fraction. The effect of the principal hydrodynamic parameters (thermophoresis, Brownian motion, Dufour, and Soret) and Grashof numbers (concentration, thermal, nanoparticle) on peristaltic transport patterns with double‐diffusive convection are deliberated with the support of computational outcomes found. The pictorial investigation is done to investigate the possessions of miscellaneous limitations on flow quantities of curiosity.

Thermal radiation on oscillatory flow past a moving vertical plate in a time varying gravity field

Thermal radiation on oscillatory flow of a viscous incompressible fluid of an optically dense medium past a moving hot vertical plate under the influence of a time varying gravity field by using Rosseland approximation is investigated. Since the flow is characterised by a time varying gravity field, a g-jitter force is associated with microgravity field in space. In a g-jitter driven flow, the empty space above the leading edge of the medium corresponds to a crystal growth in space; the net mass flow rate in the system is zero. In a time varying gravity field, the flow is characterised by the oscillating velocity near the plate surface with reference to a phase angle and to increase the fluid velocity with increase in phase angle due to impulsive onset into motion. The effects of radiation parameter, Prandtl number and Grashof number on the velocity field are analysed. The effect of Nusselt number at the plate is discussed.

DARCIAN SLIP FLOW OF ROTATING MAGNETOREACTIVE PEG CONVEYING MoS2 CASSON NANOFLUID WITH RAMPED TEMPERATURE AND CONCENTRATION

An analysis is presented to assess the impact of slip condition and rotation on an unsteady hydromanetic Darcy flow of a viscous incompressible electrically conducting non-Newtonian Casson nanofluid past an infinite oscillating vertical plate with ramped heating and concentration embedded in a homogeneous porous medium in the presence of thermal radiation and homogeneous chemical reaction of first order. The nanofluid is composed of molybdenum disulfide (MoS2) nanoparticles suspended in base fluid polyethylene glycol (PEG). A Casson fluid model presents the non-Newtonian fluid behavior. Rosseland approximation for an optically thick fluid is used to describe the radiative heat flux in the energy equation. The classical Dracy model simulates drag effects in the porous medium. The resulting simultaneous ordinary equations governing the flow are solved analytically in closed form by employing the Laplace transform technique. Graphical presentations are portrayed to examine the physical consequences of intricate physical parameters on the pertinent flow characteristics. The obtained results reveal that the velocity components are strongly diminished by intensifying magnetic parameter or slip parameter. The wall shear stresses are increasing functions of rotation parameter. This study finds applications in magnetic material processing and electrically conducting polymer dynamics.

Effect of nonlinear partial slip and thermal radiation on Oldroyd 8‐constant fluid in a channel with convective boundary condition

AbstractThis investigation deals with the effects of nonlinear slip, nonlinear thermal radiation, and non‐Newtonian flow parameters on heat transfer of an incompressible magnetohydrodynamic steady flow of an Oldroyd 8‐constant fluid through two parallel infinite plates with convective cooling. The Rosseland approximation is adopted to simulate the radiation effects. Heat exchange with the surrounding at the surfaces is assumed to obey Newton's law of cooling. The system of coupled and highly nonlinear ordinary differential equations governing the model is solved numerically using the method of weighted residual. The combined effects of non‐Newtonian flow parameters, velocity slip parameter, magnetic field parameter, Biot numbers, thermal radiation on the fluid velocity, temperature distributions, skin friction, and the Nusselt number are presented graphically and discussed. It is found that the velocity slip has an increasing effect on the fluid velocity and temperature profiles. For larger values of the thermal radiation parameter, the temperature profile and the Nusselt number are noticed to be increased.

Sensitivity analysis of radiative heat transfer in Casson and nano fluids under diffusion-thermo and heat absorption effects

The exact analysis of the magnetohydrodynamic flow of a Newtonian nanofluid past an inclined plate through a porous medium is carried out. The flows of a Newtonian nanofluid and a non-Newtonian Casson fluid are juxtaposed. The heat transport phenomenon is analyzed in the presence of Dufour and heat absorption effects. The Darcy model and Rosseland approximation are employed to simulate the effects of porous media and radiative heat. The exact solutions are obtained by using the Laplace transform method. The effects of different physical parameters on the velocity, temperature and concentration profiles are scrutinized using graphs. Statistical techniques, like the slope of data points, coefficient of correlation, probable error, and multiple linear regression, are employed to analyze the rate of heat transfer and skin friction coefficient. Further, the sensitivity of the skin friction coefficient and Nusselt number are analyzed using the Response Surface Methodology (RSM). The Nusselt number has a positive sensitivity towards thermal radiation, and it is negatively sensitive towards nanoparticle volume fraction and Dufour number.

Joule Heating Effects in Thermally Radiative Swirling Flow of Maxwell Fluid Over a Porous Rotating Disk

The current paper studies the swirling flow caused by rotating disk in an electrically conducting upper-convected Maxwell fluid with the novel thermal diffusion and diffusion-thermo features. The analysis is performed for the porous disk surface which contributes to the uniform suction/blowing effects. The computations are carried out to understand heat and mass transfer in the occurrence of non-linear radiation. Furthermore, the Rosseland approximation model is used to scrutinize the impact of thermal radiations on heat transfer traits of Maxwell fluid. The effects of Joule heating are also captured on fluid thermal behavior. The governing partial differential equations representing the flow motion, energy, and concentration are reduced into ordinary differential equations within the framework of similarity transformations. A well-known bvp4c scheme in Matlab is utilized for the solution of governing non-linear problem. The outcomes divulge that increasing Deborah number creates a decline in radial and angular motion while axial flow decreases in magnitude. Moreover, the strength of thermal radiation parameter and temperature ratio parameter is extremely useful to increase the temperature of the fluid. Further, the increase in Soret number (or decreasing Dufour number) results in an increase in the mass transfer rate.

Shape Optimization in Phosphate Production

AbstractPhosphate as an industrial product is an essential ingredient in, e.g., agriculture and food industry. The production process is very energy consuming and takes place in high temperature melting furnaces. The costs of the productions are largely governed by the energy costs of the furnace and there is a high potential to save energy by increasing its energy efficiency. Naturally, the shape of the furnace has a high influence on its efficiency. In order to describe the temperature distribution within a furnace mathematically, a widely used model in the industry is the Rosseland approximation. We use this model and discuss the problem in the context of shape optimization.

Magnetic Field Effects on Chemical Reaction of Power-Law Fluid over an Axisymmetric Stretched Sheet

Numerical investigation of the effects of magnetic field strength, thermal radiation, Joule heating, and viscous heating on a forced convective flow of a non-Newtonian, incompressible power-law fluid in an axisymmetric stretching sheet with variable temperature wall is accomplished. The power-law shear-thinning viscosity-shear rate model for the anisotropic solutions and the Rosseland approximation for the thermal radiation through a highly absorbing medium is considered. The temperature-dependent heat sources, Joule heating, and viscous heating are considered to be the source terms in the energy balance. The non-dimensional boundary-layer equations are solved numerically in terms of similarity variable. A parameter study on the boundary value of chemical reaction and Nusselt number is performed as a function of thermal radiation parameter, Brinkman number, Prandtl number, Hartmann number, power-law index, heat source coefficient, Brownian parameter, thermophoresis parameter, and the chemical reaction parameter. The results show that the chemical reaction parameter has an increasing effect on the chemical reaction boundary while the magnetic, thermophoresis, and Brownian effects decrease the rate of the chemical reaction at the boundary.

Non-linear radiation and chemical reaction effects on slip flow of Williamson nanofluid due to a static/moving wedge: a revised model

In the present study, heat and mass transfer characteristics of unsteady, two-dimensional stagnation-point flow of Williamson nanofluid along a static/moving wedge in the presence of velocity slip and chemical reaction effects are investigated. The Rosseland approximation is adopted for thermal radiation effects and Buongiorno model is used for incorporating the effects of Brownian diffusion and thermophoresis. The wall of wedge is heated by the convection current from hotter fluid and revised model is also considered in this study. The governing boundary-layer equations are altered into a coupled non-linear ordinary differential equations using suitable transformations and then tackled numerically employing Runge–Kutta–Fehberg method with shooting technique. The effects of intricate physical parameters on the dimensionless velocity, temperature, nanoparticle concentration profiles as well as skin friction coefficient and local Nusselt number are explored graphically and discussed in detail. Verification of present code is achieved via benchmarking with previously published results, and generally, very excellent agreement is revealed. Our study reveals that the intensifying values of temperature ratio parameter enhances the nanofluid temperature and thermal boundary-layer thickness. The rate of heat transfer is seen to be higher with the growth of Prandtl number and Biot number. Moreover, the nanoparticle concentration is decreased as the Brownian motion and Schmidt number increasing.

Numerical study on performance improvement of a flat-plate solar collector filled with porous foam

Performance improvement of a flat-plate solar collector is studied numerically using computational fluid dynamics based opensource tool, OpenFOAM. The collector channel is filled with fully saturated porous metal foam, and extended Darcy-Brinkman-Forchheimer model is used to model this porous region. The present code has been tested thoroughly against various numerical and experimental works from the literature, and a reasonable agreement is achieved. The influence of permeability (Darcy number, Da = 10−4 - 10−1), radiation insolation parameter (Rd = 0 - 5), buoyancy parameter (Richardson number, Ri = 0 - 5), and collector channel inclination angle (α = 0° - 45°) on the collector channel outlet temperature i.e., effective heating achieved has been studied. The novelty of the present study lies in the implementation of Rosseland approximation for modelling radiation influence, along with buoyancy consideration by varying channel inclination angles. The computational results suggest that the flow and thermal fields vary when modelling buoyancy and radiation influences combined. The insertion of porous metal foam enhances the thermal performance because of better thermal mixing, along with buoyancy parameter and volumetric radiation parameter. Although the performance does improve with the channel inclination angle, the maximum increment is obtained at intermediate angles, while any further rise in inclination gives a minor performance improvement. A comparison of different boundary conditions along with Rosseland approximation usage is given. A remark on the inclusion of the Forchheimer term in the present flow regime is given. The manuscript provides an impetus for further experimental work on the present case and comments on buoyancy parameter influence on channel performance.

Influence of radiative heat transfer on the thermal characteristics of nanofluid flow over an inclined step in the presence of an axial magnetic field

This research analyzes the influences of radiation heat transfer and Brownian movement on the thermal characteristics of nanofluid flow over an inclined step in the presence of an axial magnetic field. The Rosseland approximation is applied to simulate the divergence of radiative heat flux in the energy equation. The Al2O3–H2O and CuO–H2O nanofluids are considered as the working fluid. The $${\text{KKL}}$$ correlation is used for modeling the Brownian movement influence on the effective viscosity and thermal conductivity. The impacts of radiation parameter $$\left( {0 \le Rd \le 1} \right)$$, nanoparticles concentration $$\left( {0 \le \phi \le 0.04} \right)$$ and Lorentz force $$\left( {0 \le Ha \le 60} \right)$$ on temperature fields, mean bulk temperature and convective, radiative and total Nusselt numbers are examined with full details. The results show that the impact of CuO nanoparticles on the average of total heat transfer rates is greater that the influence of Al2O3 nanoparticles on them. Besides, the highest values of total heat transfer rates occur in the absence of magnetic field and for the highest values of $$Rd$$ and $$\phi$$ parameters.

Role of Suction/Injection on Natural Convection Flow of Magnetite $$ ({\text{Fe}}_{ 3} {\text{O}}_{ 4} ) $$ Nanoparticles in Vertical Porous Micro-annulus Between Two Concentric Tubes: A Purely Analytical Approach

Natural convection heat transfer analysis was carried out to examine the flow of magnetite–water ferrofluid in an annular zone between a pair of vertical micro-cylindrical tubes under conditions of slip velocity and thermal jump at the porous wall of cylinders. The effects of radial magnetic field and thermal radiation are also considered along with suction/injection at the walls. Linear Rosseland approximation was employed to obtain the expression for thermal radiation. Similarity variables and non-dimensional parameters are introduced to express the resultant flow equations in term of continuity, momentum and energy in a dimensionless fashion. A closed-form solution of the problem was constructed in the form of modified Bessel functions of the first and second kind. The numerical values of the obtained expressions for fluid velocity, temperature profiles, volume flow rate, surface friction and Nusselt number were plotted to examine the significance of different flow parameters. It was found that the fluid velocity was reduced when injection parameter was increased, while it was augmented when the suction parameter was increased. In contrast to this, opposite effects were observed in the temperature distribution. Further, the suction parameter enhances the rate of heat transfer at the inner surface of outer porous cylinder, while the injection parameter has a decreasing effect on the same.

Slip flow and radiative heat transfer behavior of Titanium alloy and ferromagnetic nanoparticles along with suspension of dusty fluid

The main concern of current investigation is to develop a steady mathematical model for flow and heat transfer of dusty hybrid nanofluid over a stretching sheet. The amended in the energy equations has been executed by indorsing the viscous dissipation expressions. Moreover, the radiation effects are also permitted with help of Rosseland's approximation. In addition, Titanium alloy, ferromagnetic nanoparticles and slip effect are taken in to the account. The consideration of appropriate variables leads to self-similarity expressions. These non-dimensional expressions are treated numerical scheme known as RKF 45th-order technique. To see clear insight of engineering parameters, a detailed graphical workout has been performed. Various substantial quantities like effective Skin friction coefficient and Nusselt number are adequately altered with physical parameters and delineated through various tables. It is recognized that, the reduction in heat transfer in observed in rising values of Pr for both phases. Further, Hybrid nanomaterial flow plays more effective role in heat transportation process as compared to regular nanofluid flow.

Numerical illustrations of 3D tangent hyperbolic liquid flow past a bidirectional moving sheet with convective heat transfer at the boundary

AbstractConvective heat transfer plays a central role in the numerous industrial devices because it perturbs the mechanical behavior of a system along with its thermodynamics. Keeping such applications in mind, analysis of heat transportation in three‐dimensional tangent hyperbolic fluid flow is investigated here. Convective heat transportation at the boundaries is considered. Rosseland's approximation has been used for the radiation effects. Closed form analytical solutions for the governing equations are difficult to obtain even after the use of similarity transformations. Therefore, the numerical solutions are presented through the Runge‐Kutta‐Fehlberg forth‐fifth method. Graphical analysis of the numerical results has been carried out. Roles of sundry constraints on flow are studied. It is also noted that the rates of heat transportation and skin‐friction are higher in the presence of convective heat transfer near the boundary.