Effect Of Nonlinear Thermal Radiation Research Articles

Analysis of entropy generation in the nonlinear thermal radiative micropolar nanofluid flow towards a stagnation point with catalytic effects

The major goal of this work is to analyze the entropy generation in a micropolar nanofluid’s hydromagnetic stagnation point flow with the involvement of the catalytic and nonlinear thermal radiation effects. The magnetite nanoparticle is added to the water to form the -water nanofluid. A vertical stretchable sheet is assumed to initiate the two-dimensional time-independent flow. The impacts of Joule heating and viscous dissipation are considered in the development of the governing equations of the concerned problem. An appropriate procedure of similarity transformations is implemented in the system of partial differential equations (PDE) to establish the nonlinear setup of ordinary differential equations (ODE). The behavior of various aspects of fluid such as micro-rotation, entropy generation, temperature, velocity, Bejan number, and concentration relative to the pertinent parameters is graphically revealed. The graphical nature of local Nusselt number and skin friction relative to the physical parameters is also exhibited in this analysis. This study concludes that the amplification in the magnetic field develops a minimization in the velocity field. The Bejan number shows the declining behavior corresponding to the larger quantities of the Brinkman number and Reynolds number, but the entropy of the system escalates for these parameters.

Flow over a shrinking sheet containing hybrid nanoparticles with nonlinear thermal radiation and magnetohydrodynamic effects

This study aims to analyze the magnetohydrodynamic (MHD) and nonlinear thermal radiation effects on flow over a shrinking sheet containing hybrid nanoparticles. By adopting appropriate similarity variables, the partial differential equations are converted to the similarity equations of a particular form. Later, these equations are solved through the bvp4c function. The outcomes reveal that the heat transfer reduces as the nonlinear thermal radiation is introduced in the flow field by increasing the temperature ratio parameter. Physically, rising values of these parameters represent higher radiation heat energy is pumped into the flow field and lead to a growth in the fluid temperature. Consequently, it raises the thermal boundary layer and then reduces the heat transfer rate. However, increasing the magnetic parameter raises the friction factor which impulsively improves the heat transfer performance due to the rising strength of the Lorentz force. Besides, satisfactory suction strength is required to generate the solutions for the shrinking sheet. Lastly, the temporal stability analysis reveals the first solution is stable and thus physically reliable in the long run, whereas the second solution is unstable.

Effect of Non-linear Thermal Radiation and Binary Chemical Reaction on the Williamson Nanofluid Flow Past a Linearly Stretching Sheet

Effect of Non-linear Thermal Radiation and Binary Chemical Reaction on the Williamson Nanofluid Flow Past a Linearly Stretching Sheet

Effect of nonlinear thermal radiation and melting heat transfer assessment on magneto-nanofluid through a shrinking surface

ABSTRACT In this study, we have examined the stagnation point flow of MHD chemically reacting nanofluid along a stretching/shrinking sheet. The chemical reaction has vital applications in food preparation, the mechanism of water and oil emulsions, and chemical engineering. Therefore, this analysis is subjected to the effects of Joule heating, viscous dissipation, Brownian motion, chemical reaction, thermophoresis, and melting heat transfer. The governing transformed equations are solved numerically via shooting scheme together with Runge–Kutta–Fehlberg method. The impacts of various nanofluids and relevant regulating parameters such as chemical reaction parameter, magnetic parameter, radiation parameter, melting parameter, and Eckert number on dimensionless velocity, thermal, and concentration profiles as well as skin friction drag coefficient, Nusselt and Sherwood numbers are presented graphically. Although dual branch solutions are obtained in this investigation, only one solution is determined to be stable. It is seen that the coefficient of skin friction and mass transfer rate tend to be decreasing due to melting heat transfer. The results also revealed that higher estimations of magnetic parameter increase the heat transfer rate, but a reverse trend is noticed for surface drag coefficient and mass transfer rate in case of first solution.

Similarity solution for boundary layer flow near a moving vertical porous plate with combined effects of nonlinear thermal radiation and suction/injection having convective surface boundary condition

This piece of work explored the impact of nonlinear thermal radiation on natural convection flow in the vicinity of a constant moving vertical porous plate with suction/injection. The moving vertical porous plate is considered to be either move in the same direction with fluid in the free stream or move in the negative x-direction while the fluid move in the positive x-direction. The partial differential equations (PDEs) associated with the flow properties are simplified to ordinary differential equations (ODEs) using similarity variables. Then, the resulting ODEs and the boundary condition are translated into the IVP through the shooting method. Furthermore, the final IVP and the reduced boundary conditions are solved numerically through the Runge–Kutta method. The influence of the emerging dimensionless quantities is analyzed through tables and line graphs. The numerical results obtained revealed that with suction/injection, the shear stress could be enhanced by propagating the local convective heat transfer parameter Bix, nonlinear thermal radiation R and the local Grashof number Grx for the two cases of plate motion considered. The result also revealed that in the presence of suction/injection, the heat transfer rate decreases with Bix and Grx, whereas enhanced with R augment for the two plate motions considered. Furthermore, for a constant moving vertical porous plate and constant moving freestream velocity, the convective heat transfer parameter at any point x is proportional to the corresponding heat transfer coefficient related to hot fluid. The nonlinear thermal radiation enhances the velocity and temperature profiles.

Numerical simulation of 3D swirling flow of Maxwell nanomaterial with a binary chemical mechanism and nonlinear thermal radiation effects

The effect of activation energy on the 3D swirling flow of Maxwell nanomaterial has been addressed. The mathematical formulation is designed via nonlinear radiation and heat absorption/generation. The novel attributes of an irregular movement and thermophoresis are additionally preserved. Mass convective and thermal convective conditions are considered. Suitable transformations have been considered to convert PDEs into ODEs. The NDSolve technique is employed to obtain numerical simulations. Plots are generated to analyze the role of several influential variables on nondimensional nano-concentration and temperature fields. Moreover, rates of mass and heat transport are also analyzed through plots.

Effect of Non-Linear Thermal Radiation and Partial slip on Unsteady MHD Flow of a Nanofluid Past a Permeable Stretching Sheet through a Porous Medium with Suction/Injection, convective Heat Transfer

We discuss the effect of non-linear thermal radiation on the boundary layer flow of a thermophoretic magnetohydrodynamics dissipative nanofluid over an unsteady stretching sheet in a porous medium with space and temperature dependent internal heat source/sink. The governing equations are transformed to ordinary differential equations by using similarity transformation. Numerical solutions of these equations are obtained by using the Shooting Technique. The effects of non-dimensional governing parameters on the velocity, temperature, concentration profiles, friction factor, Nusselt and Sherwood numbers are discussed and presented through graphs and tables. We observed that the Radiation parameter (Rd) to enhance the velocity, temperature profiles, heat and mass transfer rates of the fluid and reduce the concentration profiles. An increase in slip parameter (A11), reduces the velocity, enhances the temperature and nano-concentration., Nu and Sh reduce with increasing Rd & A11 on =0. Accuracy of the results compared with the existing ones. Excellent agreement is found with earlier studies.

Soret & Dufour and Triple Stratification Effect on MHD Flow with Velocity Slip towards a Stretching Cylinder

The phenomenon of convective flow with heat and mass transfer has been studied extensively due to its applications in various fields. The effects of nonlinear thermal radiation (NLTR), slip, thermal-diffusion (Soret) and diffusion-thermo (Dufour) on magenoto-hydrodynamic (MHD) flow towards a stretching cylinder in the presence of triple stratification (TSF) are investigated in this paper. The governing equations are transformed into an ODE by suitable transformations. The homotopy analysis method (HAM) is used to solve the ODE. The revamping of fluid flow, and heat transfer due to the presence of the Soret and Dufour effect, concentration slip and concentration stratification are analyzed. The temperature and local Sherwood number increases as the Dufour number rises, whereas the local Nusselt number decreases. While elevating the Soret number, the Sherwood number diminishes, whereas the concentration profile rises. The thermal boundary layer thickness enhances when thermal radiation increases. The rate of solute transport reduces while the concentration slip increases.

Effect of NP shapes on Fe3O4 – Ag/kerosene and Fe3O4 – Ag/water hybrid nanofluid flow in suction/injection process with nonlinear-thermal-radiation and slip condition; Hamilton and Crosser's model

This study examines the flow and thermal properties of water and kerosene hybrid nanofluids in a horizontal microchannel. The effects of nonlinear thermal radiation, heat source coefficient, convective and slip boundary conditions on nanofluids in a microchannel have been studied. The impact of different nanoparticle shape factors on the temperature of nanofluids has also been analysed. The governing partial differential equations have been transformed in to ordinary differential equations using dimensionless terms. In the next step, the corresponding ordinary differential equations have been cracked using the RKF45 numerical approach, and the particles shape factor on dimensionless velocity and energy fields for hybrid nanofluid then reported. The results revealed that the spherical and lamina shape factors for both water and kerosene hybrid nanofluid differ the most, the water-based hybrid nanofluid has a higher velocity than the kerosene-based hybrid nanofluid, the thermal energy of both water and kerosene-based hybrid nanofluid was higher in the lower channel plate than the upper channel plate, flow rate falls near the lower channel wall and increases towards the upper channel wall as Reynolds number increases. Thermal energy and entropy generation decrease as the temperature parameter rises.

Effect of Nonlinear Thermal Radiation on Flow of Williamson Nanofluid in a Vertical Porous Channel with Heat Source or Sink by Using Adomian Decomposition Method

The study examines the entropy generation in the Williamson nanofluid flowing in a vertical porous channel exposed to nonlinear thermal radiation and heat source or sink. Constant temperature and fixed nanoparticle concentration are maintained at the boundaries of the channel. Governing equations are derived by applying the conservation laws incorporating the brownian motion and thermophoretic force impacts of nanofluids utilizing Buongiorno’s model. These equations are non dimensionalised by choosing suitable dimensionless variables. The governing simultaneous equations are tackled by implementing adomian decomposition technique for velocity, tempearture, dimensionless shear stress heat transfer rate. The findings of the study are analysed through graphs. The major findings of the study are porous parameter reduces velocity because of resistance to the flow and enhances temperature. Thermal radiation parameter reduces both velocity and temperature fields. Williamson parameter enhances the velocity field and reduces the temperature to a very small extent. These results are also corresponds with skin friction and Nusselt number graphs. Entropy generation in the considered flow system can be minimized by increasing Williamson number.

Impact of nonlinear radiation on magnetohydrodynamic flow of hybrid nanofluid with heat source effect

This investigation is performed to deliberate the novel significance of nonlinear thermal radiation effect on magnetohydrodynamic flow of Casson hybrid nanoliquid caused by a curved stretching sheet. The flow and thermal transport nature of three different hybrid nanoliquids in the stimulus of viscous dissipation, nonlinear radiation and magnetic force is discussed numerically. The novelty of this work is to obtain the simultaneous solutions for three different types of hybrid nanoliquids, they are obtained by suspending titanium alloy (Ti6Al4vs.) is composed of titanium, aluminum and vanadium in the ratio of 90:6:4 respectively and aluminium alloy (AA7075) is compossed of Aluminum, Zinc, Magnesium and Copper nanoparticles in the ratio of 90:6:3:1 respectives with added metals Silicon, Ferrous and Magnesium. in three various working liquids viz. methanol, ethylene glycol and engine oil. The flow governing PDE's are transmuted into ODE's with suitable similarity transformation and solved by using Runge-Kutta and Newton's approach. Numerical outcomes of flow and temperature profiles are presented via graphical trends, also skin friction coefficient and rate of thermal transfer are illustrated via tabulated values. Major outcomes reveals that, inclusion of hybrid nanometer sized particles in pedestal liquid lead to an large hike in thermal transfer performance. Importantly, thermal transport rate and temperature profiles of the hybrid nanoliquid rises with improving nonlinear radiation values and these results are significant in nonlinear radiation case as compared with linear radiation case.

A Study of Magnetic/Nonmagnetic Nanoparticles Fluid Flow under the Influence of Nonlinear Thermal Radiation

The present research work scrutinizes numerical heat transfer in convective boundary layer flow having characteristics of magnetic ( Fe 3 O 4 ) and nonmagnetic ( Al 2 O 3 ) nanoparticles synthesized into two different kinds of Newtonian (water) and non-Newtonian (sodium alginate) convectional base fluids of casson nanofluid which integrates the captivating effects of nonlinear thermal radiation and magnetic field embedded in a porous medium. The characterization of electrically transmitted viscous incompressible fluid is taken into account within the Casson fluid model. The mathematical formulation of governing partial differential equations (PDEs) with highly nonlinearity is renovated into ordinary differential equations (ODEs) by utilizing the suitable similarity transform that constitutes nondimensional pertinent parameters. The transformed ODEs are tackled numerically by implementing b v p 4 c in MATLAB. A graphical illustration for the purpose of better numerical computations of flow regime is deliberated for the specified parameters corresponding to different profiles (velocity and temperature). To elaborate the behavior of Nusselt and skin friction factor, a tabular demonstration against the distinct specific parameters is analyzed. It is perceived that the velocity gradient of Newtonian fluids is much higher comparatively to non-newtonian fluids. On the contrary, the thermal gradient of non-Newtonian fluid becomes more condensed than that of Newtonian fluids. Graphical demonstration disclosed that the heat transfer analysis in non-Newtonian (sodium alginate)-based fluid is tremendously influenced comparatively to Newtonian (water)-based fluid, and radiation interacts with the highly denser temperature profile of non-Newtonian fluid in contrast to that of Newtonian fluid. Through such comparative analysis of magnetic or nonmagnetic nanoparticles synthesized into distinct base fluids, a considerable enhancement in thermal and heat transfer analysis is quite significant in many expanding engineering and industrial phenomenons.

Nonlinear thermal radiation and temperature dependent viscosity effects on MHD heat and mass transfer in a thin liquid film over a stretching surface

This paper describes nonlinear thermal radiation effects on MHD heat and mass transfer in a thin liquid film over a permeable unsteady stretching surface taking temperature-dependent fluid viscosity with convective boundary condition. For the non-linearity of the momentum, energy and mass diffusion equations, the problem is solved numerically. At first, Similarity transformations is used to the governing equations to reduce the equations into a set of ordinary differential equations. Then the resulting nonlinear ordinary differential equations are solved using Runge-Kutta-Felberg method with shooting technique. Different physical parameters effects on heat and mass transfer in a thin liquid film are presented graphically. It is found that increase in the unsteadiness parameter leads to increase in the velocity distribution, temperature and concentration gradient. Further, increase in the value of magnetic parameter results in a decrease in the velocity profile and increase in the temperature and concentration gradient. For enhancement of thermal radiation decreases the temperature gradient of the thin film flow. Also, for increase in viscosity variation parameter is to decrease velocity distribution but reverse effects shown in case of temperature and concentration gradient.

Analysis of entropy generation in a power-law nanofluid flow over a stretchable rotatory porous disk

A theoretical entropy generation analysis is conducted by applying the MHD and nonlinear thermal radiation effects contained in porous material for a steady three-dimensional power-law nanofluid flow near the stagnation point region. With the assistance of a thermally radiated non-uniform heat source /sink subject to convective boundary conditions, the heat transformation phenomenon is explored within the boundary layer over the stretchable rotatory disk. Multi-wall carbon nanotubes (MWCNTs) are incorporated in the ethylene glycol (C2H6O2) as a base fluid. The proposed problem of fluid flow is mathematically modeled. The governing nonlinear partial differential equations (PDEs) are lessened to highly mixed nonlinear ordinary differential equations (ODEs) after the utilization of appropriate transformations. The effects of several classes of relevant parameters upon total entropy generation and Bejan number profiles are investigated by numerically addressing the ODEs with the purpose of a well-known Keller Box method. Furthermore, the skin friction coefficients and local Nusselt number are calculated for shear-thinning and shear-thickening behaviors of the power-law fluid. Also, the total entropy generation increases for the Brinkman number and the permeability parameter but decreases for the material parameter, whereas the Bejan number has different behavior from entropy generation.

Entropy optimized dissipative flow of hybrid nanofluid in the presence of non-linear thermal radiation and Joule heating

Present article reads three dimensional flow analysis of incompressible viscous hybrid nanofluid in a rotating frame. Ethylene glycol is used as a base liquid while nanoparticles are of copper and silver. Fluid is bounded between two parallel surfaces in which the lower surface stretches linearly. Fluid is conducting hence uniform magnetic field is applied. Effects of non-linear thermal radiation, Joule heating and viscous dissipation are entertained. Interesting quantities namely surface drag force and Nusselt number are discussed. Rate of entropy generation is examined. Bvp4c numerical scheme is used for the solution of transformed O.D.Es. Results regarding various flow parameters are obtained via bvp4c technique in MATLAB Software version 2019, and displayed through different plots. Our obtained results presents that velocity field decreases with respect to higher values of magnetic parameter, Reynolds number and rotation parameter. It is also observed that the temperature field boots subject to radiation parameter. Results are compared with Ishak et al. (Nonlinear Anal R World Appl 10:2909–2913, 2009) and found very good agreement with them. This agreement shows that the results are 99.99% match with each other.

Effect of nonlinear thermal radiation on unsteady MHD flow of Maxwell nanoliquid over a porous vertical sheet with chemical reaction

AbstractThe aim of the current article is to explore the impact of chemical reactions on magnetohydrodynamic mixed convective flow comprising Maxwell nanomaterial over a vertical porous surface with a convectively heated stretched surface. Heat transfers are also accounted for through thermal radiation. The modeled equations are formulated and transmuted into highly nonlinear partial differential equations into ordinary differential equations through suitable alteration, which is settled numerically through the Runge–Kutta method along with the shooting technique. The influences of various physical emerging parameters are plotted graphically for velocity, temperature, and concentration profiles. Friction factor, Nusselt number, and Sherwood number are plotted and discussed numerically. The outcome shows that the influences of fluid parameter lead to less viscosity and also a reduction in temperature as well as concentrations. The result revelas that enhancing Rd and E are esclated the temperature profile. Moreover, the skin friction and Sherwood number are enhanced against various parameters. Finally, the work of previous literature is compared in limiting cases and achieved an excellent agreement.

Effect of non-linear thermal radiation on the stagnation point flow of double diffusive free convection due to movingvertical plate

PurposeThis paper aims to find the influence of convective heat transfer, buoyancy proportions, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number on velocity, temperature and concentration profiles.Design/methodology/approachThis paper explores the heat and mass transfer of a stagnation point stream of free convective Casson fluid over a moving vertical plate with nonlinear thermal radiation and convective boundary restrictions. The governing PDEs of stream, heat and concentration profiles were reformed into an arrangement of nonlinear ODEs by using similarity transformation. This framework was then tackled numerically by applying forth-order RK shooting strategy.FindingsDistribution of flow, velocity and temperature profiles for different values of governing parameters are analyzed.Originality/valueThe original results are depicted in terms of plots.

Numerical simulation for bioconvectional flow of burger nanofluid with effects of activation energy and exponential heat source/sink over an inclined wall under the swimming microorganisms

Nanofluids has broad applications such as emulsions, nuclear fuel slurries, molten plastics, extrusion of polymeric fluids, food stuffs, personal care products, shampoos, pharmaceutical industries, soaps, condensed milk, molten plastics. A nanofluid is a combination of a normal liquid component and tiny-solid particles, in which the nanomaterials are immersed in the liquid. The dispersion of solid particles into yet another host fluid will extremely increase the heat capacity of the nanoliquid, and an increase of heat efficiency can play a significant role in boosting the rate of heat transfer of the host liquid. The current article discloses the impact of Arrhenius activation energy in the bioconvective flow of Burger nanofluid by an inclined wall. The heat transfer mechanism of Burger nanofluid is analyzed through the nonlinear thermal radiation effect. The Brownian dispersion and thermophoresis diffusions effects are also scrutinized. A system of partial differential equations are converted into ordinary differential equation ODEs by using similarity transformation. The multi order ordinary differential equations are reduced to first order differential equations by applying well known shooting algorithm then numerical results of ordinary equations are computed with the help of bvp4c built-in function Matlab. Trends with significant parameters via the flow of fluid, thermal, and solutal fields of species and the area of microorganisms are controlled. The numerical results for the current analysis are seen in the tables. The temperature distribution increases by rising the temperature ratio parameter while diminishes for a higher magnitude of Prandtl number. Furthermore temperature-dependent heat source parameter increases the temperature of fluid. Concentration of nanoparticles is an decreasing function of Lewis number. The microorganisms profile decay by an augmentation in the approximation of both parameter Peclet number and bioconvection Lewis number.

Nonlinear thermal radiation and activation energy features in axisymmetric rotational stagnation point flow of hybrid nanofluid

The present study particularizes the effects of nonlinear thermal radiation and the novel accepts of activation energy in the axisymmetric rotational stagnation point flow of hybrid fluid. Thermophysical properties of water and CWCNT/MWCNT are used for base fluid and nanoparticles respectively. The modeled partial differential equations are reduces to system of ordinary differential equations. The resulting equations are integrated numerically and the impact of involved parameters on velocity, temperature and nanoparticle concentration presented graphically. The tabular values for local Nusselt numbers in case of linear and nonlinear thermal radiation and the Sherwood number with and without activation energy are documented. It is observed that concentration of nanoparticles reduces with activation energy and increasing the solid volume fraction of SWCNT as well as MWCNT nanoparticles. Moreover the axial velocity increases while secondary velocity decreases by increasing the rotation parameter.

MHD and nonlinear thermal radiation effects on hybrid nanofluid past a wedge with heat source and entropy generation

PurposeThis study aims to investigate the irreversibility associated with the Fe3O4–Co/kerosene hybrid-nanofluid past a wedge with nonlinear radiation and heat source.Design/methodology/approachThis study reports the numerical analysis of the hybrid nanofluid model under the implications of the heat source and magnetic field over a static and moving wedge with slips. The second law of thermodynamics is applied with nonlinear thermal radiation. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved through the Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerges from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios.FindingsThe significant outcomes of the current investigation are that the velocity field uplifts for higher velocity slip and magnetic strength. Further, the heat transfer rate is reduced with the incremental values of the Eckert number, while it uplifts with thermal slip and radiation parameters. An increase in Brinkmann’s number uplifts the entropy generation rate, while that peters out the Bejan number. The results of this study are of importance involving in the assessment of the effect of some important design parameters on heat transfer and, consequently, on the optimization of industrial processes.Originality/valueThis study is original work that reports the hybrid nanofluid model of Fe3O4–Co/kerosene.