Nonlinear Rosseland Research Articles

Frictional heating effects on entropy generation with nonlinear Rosseland radiation: Implementation of generalized differential quadrature method

This article examines heat transfer and entropy generation analysis for boundary layer flow, considering the impacts of frictional heating and nonlinear Rosseland thermal radiation. The equations governing momentum and energy in a two-dimensional boundary layer are transformed into self-similar equations via similarity operations. The generalized differential quadrature method (GDQM) is then used to numerically solve the no-dimensional governing equations. Entropy generation and Bejan numbers are computed using the acquired solutions and are then plotted against the emerging flow parameters. An in-depth analysis of temperature distribution, entropy generation, velocity profile, and Bejan number. A high level of agreement was seen when the results from the literature were replicated using GDQM to verify the accuracy of the numerical code. It is found that a self-similar solution exists in the presence of viscous dissipation. The primary contributor to entropy generation at the interface is fluid friction, in contrast to heat transfer. Further, the findings indicate that entropy generation positively correlates with the Prandtl number, heating parameter, radiation parameter, and Eckert number. Notably, the results show that a decrease in operational temperature causes a decrease in entropy production.

¬¬Chemical Reaction and Nonlinear Rosseland Approximation Effects On Double-Diffusive MHD Sisko Nanofluid Flow Over a Nonlinear Stretching Sheet in A Porous Medium with Concentration-Dependent Internal Heat Source

This study investigates the two-dimensional magnetohydrodynamics laminar flow of a Sisko nanofluid over a nonlinear stretching sheet in a porous medium, considering chemical reactions, nonlinear Rosseland approximation, and an internal heat source based on concentration. The governing boundary layer equations and associated boundary conditions are transformed into non-dimensional form using appropriate variables. The resulting non-dimensional equations are solved using the modified Adomian decomposition technique, implemented with the symbolic computing software MATHEMATICA. The influence of various parameters, including Prandtl number, thermophoresis parameter, Brownian motion parameter, chemical reaction parameter, Sisko fluid parameters, heat source parameter, radiation parameter, Darcy number, mass Grashof number, magnetic field, and Grashof number, on the flow fields of velocity, temperature, and nanoparticles volume fractions is depicted through graphical representations. The study reveals that the velocity profile is accelerated by the first value of the Sisko fluid parameter and Darcy number, but it diminishes in the presence of a magnetic field and the second Sisko fluid parameter. The temperature profile decreases with an increment in the Prandtl number, while it improves in proportion to increases in the heat source, thermophoresis, Brownian motion, and radiation parameters respectively. Additionally, an increase in the chemical reaction parameter leads to an increase in the concentration profile of the fluid.

Mixed Convection Flow of a Casson Fluid over a Curved Stretching Surface with Nonlinear Rosseland Thermal Radiation

Mixed Convection Flow of a Casson Fluid over a Curved Stretching Surface with Nonlinear Rosseland Thermal Radiation

Application of Arrhenius kinetics on MHD radiative Von Kármán Casson nanofluid flow occurring in a Darcy-Forchheimer porous medium in the presence of an adjustable heat source

This research paper explores the implications of nonlinear Rosseland thermal radiation and temperature-dependent heat generation on non-Darcian steady MHD convective Casson nanofluid flows over a radially extended rotating disk. Besides, the significance of the activation energy is also taken into account in the present modeling during the chemical reaction process. Based on the boundary layer theory, the associated dimensionless boundary layer equations are derived mathematically in the context of Von Kármán’s proposition. By invoking a trustworthy BVP4C numerical algorithm, the nonlinear differential system defining the resulting boundary value problem is handled successfully with the help of an iterative shooting procedure, whose results are profiled graphically and tabularly versus the varying values of the pertinent flow parameters. Furthermore, the displayed findings show that the radial and azimuthal nanofluid motion slows down significantly with the strengthening in the Casson nanofluid parameter, the Forchheimer number, the porosity parameter, and the magnetic parameter. However, the stretching parameter exhibits a dual dynamical tendency. A thermal enrichment can be provided by intensifying the heat generation parameter, the temperature difference parameter, the thermal radiation parameter, the thermophoresis process, and the Brownian motion of nanoparticles. On the other hand, it is perceived a remarkable boosting up in the concentration profile with the higher estimation in the thermophoresis and activation energy parameters.

Nanofluid with nonlinear Rosseland thermal radiation and mixed convection

Two dimensional flow of mixed convection nanofluid on horizontal plate with the effect of nonlinear Rosseland thermal radiation has been investigated. Mathematical model of the problem is based on partial differential equations and optimal homotopy analysis method is applied to sort out solutions. Moreover, comprehensive study of influence of emerging parameters is carried out via graphical interpretation and tables.

Analysis of three-dimensional stagnation point flow over a radiative surface

This article aims to explore the three-dimensional stagnation point flow over a radiative wavy cylindrical shaped body. Two cases, namely, nodal and saddle stagnation point flow are examined. Nonlinear Rosseland approximation is employed to model the radiative heat transfer phenomena. Modelled equations are firstly converted in dimensionless forms after defining dimensionless quantities and then transformed into self-similar equations using appropriate similarity variables. Numerical solution of the nonlinear system is computed using shooting method with Runge–Kutta–Fehlberg algorithm and to verify the authenticity, obtained results are also compared with finite-difference based built-in routine bvp5c in MATLAB software. Heat transfer rate in the absence of thermal radiation is juxtaposed with the cases of linear and nonlinear radiation cases.

Blasius and Sakiadis flow with suction and non-linear Rosseland thermal radiation

Abstract The steady laminar boundary layer flow over a stationary plate (Blasius flow) or in a moving plate (Sakiadis flow) with suction and in the presence of non-linear Rosseland radiation is investigated in this paper. When the suction varies in a special way the problem is similar whereas when the suction is constant the problem is non-similar. The results are obtained with the direct numerical solution of the governing equations. The problem is governed by Prandtl number, temperature parameter, radiation parameter and suction parameter and the influence of these parameters on the results are presented in tables and figures. It was found that two asymptotic states exist both in the similar and non-similar problem. The asymptotic temperature field in the similar problem has been calculated numerically whereas for the asymptotic temperature field in the non-similar problem analytical solutions have been found.

Solar radiation effects on MHD stagnation point flow and heat transfer of a nanofluid over a stretching sheet

The aim of this study is investigation of solar radiation influences on two-dimensional stagnation-point flow of nanofluid over a stretching sheet. The magnetic field is considered and the nonlinear Rosseland approximation is applied for thermal radiation in current work. The governing equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations which are solved numerically by means of the efficient differential quadrature method (DQM). The numerical results show the superb accuracy, good convergence with little computational efforts and the great potential of this method. Also, it is found that the temperature and thermal boundary layer thickness are increasing functions of Biot number. The findings narrate that increasing values of Brownian motion parameter make greater temperature values on the profile and thicker thermal boundary layer.

Impact of Nonlinear Rosseland Approximation on Flow of Newtonian Fluid with Unequal Diffusivities of Chemically Reactive Species

This investigation studies the flow of a Newtonian fluid close to stagnation point past a stretching/shrinking plate embedded in a porous media. Heat transfer analysis with nonlinear thermal radiation (TR) is also carried out. Homogeneous-heterogeneous reactions with unequal diffusivities of reactants take place in the fluid. The controlling partial differential equations (DEs) of the existing model are reduced to dimensionless ordinary DEs through similarity transformations. These subsequent equations are numerically tackled with the guide of the shooting procedure. The velocity, temperature and concentration’s behaviour has been inspected for specific estimations of the including parameters. The viscous fluid (VF) temperature increases with nonlinear TR. The change in the concentration profile due to the diffusion coefficient rate $$ \delta $$ is more prominent in the concentration of specie D compared to specie C. Heterogeneous reaction parameter intensity is very helpful in reducing the concentration of bulk fluid $$ \phi_{1}(\eta) $$ as well as increasing the surface catalyst concentration $$ \phi_{2}(\eta) $$

COMBINED EFFECTS OF VARIABLE VISCOSITY, VISCOUS DISSIPATION AND THERMAL RADIATION ON UNSTEADY NATURAL CONVECTION COUETTE FLOW THROUGH A VERTICAL POROUS CHANNEL

The present article investigates combined effects of variable viscosity, viscous dissipation and thermal radiation on unsteady natural convection Couette flow through vertical porous channel. Non-linear Rosseland heat diffusion is deployed for the solution of the flow equations which as a consequence; together with the effects of variable viscosity, viscous dissipation and thermal radiation have resulted to high non-linear equations for the flow formation. Appropriate similarity variables are used to convert the partial differential equations associated with the fluid formation into dimensionless ordinary differential equations (ODEs) and the emerging ODEs are solved using Adomian decomposition method (ADM) and computer aided algebra package. Influences of the physical parameters involved in the problem are presented, discussed and conclusions are drawn. During the investigation; it was found that the fluid velocity and temperature were found to increase with increase in Eckert number, viscosity variation and thermal radiation.

Non-axisymmetric Homann stagnation-point flow of Walter’s B nanofluid over a cylindrical disk

The study of non-axisymmetric Homann stagnation-point flow of Walter’s B nanofluid along with magnetohydrodynamic (MHD) and non-linear Rosseland thermal radiation over a cylindrical disk in the existence of the time-independent free stream is considered. Moreover, the notable impacts of thermophoresis and Brownian motion are analyzed by Buongiorno’s model. The momentum, energy, and concentration equations are converted into the dimensionless coupled ordinary differential equations via similarity transformations, which are later numerically solved by altering the values of the pertinent parameters. The numerical and asymptotic solutions for the large shear-to-strain rate ratio $$\gamma = {b \over a}$$ for the parameters of the displacement thicknesses and the wall-shear stress are computed by perturbative expansion and analyzed. Furthermore, the technique bvp4c in MATLAB is deployed as an efficient method to analyze the calculations for the non-dimensional velocities, temperature, displacement thickness, and concentration profiles. It is observed that the two-dimensional displacement thickness parameters α and β are reduced due to the viscoelasticity and magnetic field effects. Moreover, when the shear-to-strain rate ratio approaches infinity, α is closer to its asymptotic value, while β and the three-dimensional displacement thickness parameter δ1 show the opposite trend. The outcomes of the viscoelasticity and the magnetic field on the skin friction are also determined. It is concluded that $${\widetilde{f}^"}\left( 0 \right)$$ (0) reaches its asymptotic behavior when the shear-to-strain rate ratio approaches infinity. Meanwhile, $${\widetilde{g}^"}\left( 0 \right)$$ (0) shows different results.

Second law analysis of Blasius flow with nonlinear Rosseland thermal radiation in the presence of viscous dissipation

In the present article, we perform the second law analysis of classical Blasius flow accounting the effects of nonlinear radiation and frictional heating. The two-dimensional boundary layer momentum and energy equations are converted to self-similar equations using similarity transformations. The set of resultant ordinary differential equations are solved numerically. The numerical results obtained from solutions of dimensionless momentum and energy equations are used to calculate the entropy generation number and Bejan number. The velocity profile f'(ξ), temperature distribution θ(ξ), entropy production number Ns and Bejan number Be are plotted against the physical flow parameters and are discussed in detail. Further, for the sake of validation of our numerical code, the obtained results are reproduced using Matlab built-in boundary value solver bvp4c resulting in an excellent agreement. It is observed that entropy generation is increasing function of heating parameter, Prandtl number, Eckert number and radiation parameter. Further, it is observed that entropy generation can be minimized by reducing the operating temperature ΔT=Tw−T∞.

Influence of Variable Transport Properties on Nonlinear Radioactive Jeffrey Fluid Flow Over a Disk: Utilization of Generalized Differential Quadrature Method

In the present research work, two-dimensional boundary layer flow of Jeffrey fluid over a radially stretching disk in the presence nonlinear Rosseland thermal radiation is investigated. The thermal conductivity and viscosity of Jeffrey fluid are considered variable and assumed to be a function of temperature. The self-similar equations are obtained by employing appropriate transformations. These transformed highly nonlinear equations are solved numerically by a powerful technique generalized differential quadrature method. Chebyshev–Gauss–Lobatto spectral method and midpoint method with Richardson extrapolation (RMM) are also adopted to establish the validity and reliability of the numerical solution. The variations of velocity and temperature profiles with the governing parameters such as Prandtl number, variable viscosity and thermal conductivity parameters, heating parameter, radiation parameter, Deborah number and ratio of relaxation to retardation time are presented and discussed graphically. Reduction in momentum boundary layer thickness and velocity of fluid is observed by increasing variable viscosity ratio parameter $$\delta $$ . Velocity of fluid increases, whereas the temperature of fluid decreases with an increase in Deborah number De. The rise in temperature is observed with increasing values of variable thermal conductivity parameter $$\varepsilon $$ , ratio of relaxation to retardation time $$\lambda _1 $$ and heating parameter $$\theta _{r} $$ .

Exploration of activation energy and binary chemical reaction effects on nano Casson fluid flow with thermal and exponential space-based heat source

PurposeThe purpose of this paper is to explore the effects of binary chemical reaction and activation energy on nano Casson liquid flow past a stretched plate with non-linear radiative heat, and also, the effect of a novel exponential space-dependent heat source (ESHS) aspect along with thermal-dependent heat source (THS) effect in the analysis of heat transfer in nanofluid. Comparative analysis is carried out between the flows with linear radiative heat process and non-linear radiative heat process.Design/methodology/approachA similarity transformation technique is utilised to access the ODEs from the governed PDEs. The manipulation of subsequent non-linear equations is carried out by a well-known numerical approach called Runge–Kutta–Fehlberg scheme. Obtained solutions are briefly discussed with the help of graphical and tabular illustrations.FindingsThe effects of various physical parameters on temperature, nanoparticles volume fraction and velocity fields within the boundary layer are discussed for two different flow situations, namely, flow with linear radiative heat and flow with non-linear radiative heat. It is found that an irregular heat source/sink (ESHS and THS) and non-linear solar radiation play a vital role in the enhancement of the temperature distributions.Originality/valueThe problem is relatively original to study the effects of activation energy and binary chemical reaction along with a novel exponential space-based heat source on laminar boundary flow past a stretched plate in the presence of non-linear Rosseland radiative heat.

Nonlinear Rosseland thermal radiation and energy dissipation effects on entropy generation in CNTs suspended nanofluids flow over a thin needle

In this paper, we examine thermal radiation effect of the nonlinear form on the dissipative nanofluids containing carbon nanotubes past a moving horizontal thin needle. We also perform a second law analysis with viscous dissipation. Single-wall carbon nanotube and multiple-wall carbon nanotube drop in H_{2}O base fluid. Introducing suitable dimensionless variables, we reduce the governing equations to self-similar nonlinear differential equations. Matlab in-built boundary value solver bvp4c and shooting method are applied for the solution of the reduced set of self-similar differential equations. The numerical results thus obtained are compared, which agree well with respect to desired accuracy. Various graphs are depicted and illustrate qualitatively the influence of flow controlling parameters such as Eckert number, heating parameter, radiation parameters, nanoparticles solid volume fraction, and size of thin needle on entropy generation, temperature distribution, and Bejan number.

Impact of Non-linear Radiation on MHD Non-aligned Stagnation Point Flow of Micropolar Fluid Over a Convective Surface

Abstract We aimed at examining the magnetohydrodynamic (MHD) radiative non-aligned stagnation point motion of non-Newtonian liquid over a stretched surface. The heat transfer mechanism is investigated in the presence of variable heat sink/source, non-linear Rosseland approximation and Biot number. Appropriate transmutations are exploited to metamorphose the flow equations into ODEs. The acquired non-linear ODEs are highly coupled. These are tackled with the consecutive implication of fourth-order Runge–Kutta and shooting techniques. The variations of flow governing parameters on the dimensionless velocity, micro-rotation and temperature plus the measure of heat transport, couple stress coefficient and friction factor are thoroughly explained using plots and tables. Outcomes stipulate that increasing the values of the stretching ratio parameter causes the thermal field to decline and the velocity field to inflate. Also, an upsurge in the micropolar parameter produces an increase in the rate of heat transport but an opposite outcome is detected with the couple stress coefficient. To the best of our knowledge the non-orthogonal stagnated motion of micropolar liquid with radiation as non-linear and variable heat source/sink has never before been scrutinized.

Second Law Analysis of Dissipative Flow over a Riga Plate with Non-Linear Rosseland Thermal Radiation and Variable Transport Properties.

In this article, we investigated entropy generation and heat transfer analysis in a viscous flow induced by a horizontally moving Riga plate in the presence of strong suction. The viscosity and thermal conductivity of the fluid are taken to be temperature dependent. The frictional heating function and non-linear radiation terms are also incorporated in the entropy generation and energy equation. The partial differential equations which model the flow are converted into dimensionless form by using proper transformations. Further, the dimensionless equations are reduced by imposing the conditions of strong suction. Numerical solutions are obtained using MATLAB boundary value solver bvp4c and used to evaluate the entropy generation number. The influences of physical flow parameters arise in the mathematical modeling are demonstrated through various graphs. The analysis reveals that velocity decays whereas entropy generation increases with rising values of variable viscosity parameter. Furthermore, entropy generation decays with increasing variable thermal conductivity parameter.

Dual stratification effects on double-diffusive convective heat and mass transfer of a sheet-driven micropolar fluid flow

The intent of this study is to analyse the influence of nonlinear thermal radiation, thermophoresis, second order slip and magnetic field on the doubly stratified flow of a non-Newtonian micropolar fluid induced by a stretched sheet along with transport of thermal energy and mass species. The radiative heat flux term is modified using the non-linear Rosseland diffusion approximation. The partial differential equations governing the physics of the problem are recast into a set of coupled non-linear ordinary differential equations by using appropriate similarity transformations and later they are solved numerically using RKF-45 algorithm along with shooting technique. Results of the numerical solution are illustrated graphically for several sets of values of the governing parameters. Comparison of our results with the available results in literature for some special cases reveals close agreements. The results indicate that material parameter boosts the velocity and micro-rotation. The temperature ratio parameters that arise due to non-linear thermal radiation are seen to have opposite effect on temperature. It is seen that for strong thermal stratification reverse flow takes place accompanied by an undershoot in temperature. Excessive mass stratification and weaker molecular diffusivity resulted in a significant undershoot of species concentration.

Entropy generation and heat transfer in boundary layer flow over a thin needle moving in a parallel stream in the presence of nonlinear Rosseland radiation

Analysis of entropy generation and heat transfer in the boundary layer flow over a thin needle moving in a parallel stream is performed in this work. Energy dissipation and nonlinear radiation terms are incorporated in the energy equation. It is assumed that the free stream velocity u∞ is in the direction of positive x−axis (axial direction) and the thin needle moves in the direction of free stream velocity. The problem is self-similar in the presence of viscous dissipation and non-linear Rosseland thermal radiation. The reduced self-similar governing equations are solved numerically using shooting and fourth order Runge-Kutta method. The expressions for dimensionless volumetric entropy generation rate and Bejan number are also obtained by selecting suitable similarity variables. The effects of the Eckert number, heating parameter, radiation parameter, Prandtl number, velocity ratio parameter and dimensionless size of a thin needle are described graphically in detail. The analysis reveals that the entropy generation decreases by decreasing the size of the thin needle. Entropy generation number increases with the increasing values of the Eckert number, Prandtl number and the temperature parameter. Moreover, it is observed that the Bejan number decreases by increasing the thermal radiation parameter. Validation of present analysis is performed by comparing the obtained results with those available in the existing literature and found a very good agreement.

Nonlinear Rosseland thermal radiation and magnetic field effects on flow and heat transfer over a moving surface with variable thickness in a nanofluid

A numerical investigation has been done to study the impact of nonlinear magnetic field, nonlinear thermal radiation, variable thickness, and Brownian motion on flow and heat transfer characteristics (i.e., skin friction and surface heat flux) as a physical application. Moreover, the impact of these forces on the rate of cooling and the mechanical properties (i.e., hardness, ductility, …) of a surface that is cooled using nanofluid as a coolant is explored. The governing boundary layer equations describing the problem are transformed to ordinary differential equations using the similarity transformation method and are then solved numerically using the fourth-order Runge–Kutta method with shooting technique with the assistance of Mathematica program.