Nonlinear Radiative Heat Research Articles

Non-linear radiative heat flux of Williamson nanofluid with gyrotactic microorganisms, activation energy and bioconvection

Gyrotactic microorganisms and nanoparticles with bioconvection play an important mantle in heat exchanger, biosensors, cooling devices, biotechnology, heating, pharmaceutical, drying food and many more. The main objective and novelty of this study is to compute the numerical solutions for the transient bioconvection flow of non-Newtonian Williamson nanofluid over a permeable contracting/expanding cylinder under the effects of Arrhenius activation energy and gyrotactic microorganisms. Additionally, binary chemical reactions and nonlinear radiation aspects are considered. Furthermore, Buongiorno nanofluid model and revised nanofluid model are utilized to investigate heat and mass transportation. Numerical solutions of highly nonlinear ordinary differential system are developed through RK45 scheme. It is interesting to investigate that motile number is an enhancing function of bioconvection Lewis number but reverse trend is noticed for higher estimation of Peclet number and microorganisms difference parameter in both cases of stretching and shrinking cylinder.

Numerical heat performance of TiO2/Glycerin under nanoparticles aggregation and nonlinear radiative heat flux in dilating/squeezing channel

ApplicationsNewly developed fluids termed as “Nanofluids” and their study in dilating/squeezing channel cannot be disregarded. Such flows under various physical constraints are important for purification purposes and other industrial applications. Purposeand Methodology: This work comprises the modeling and heat transmission ability of TiO2/G inside a dilating/squeezing channel. The conventional model upgraded including the aggregation effects of nanoparticles and directed nonlinear thermal radiations. The resultant model examined through numerical scheme for actual understanding the heat transport phenomena inside the channel. Major findingsThe results reveal that high viscosity parameter (R1=0.5,1.0,1.5,2.0), porous absorber walls and strong surface-surface interaction due to aggregation of nanoparticles significantly control the fluid movement. The pores at the surface (A1=0.1,0.3,0.5,0.7) attract the fluid particles and strong frictional forces between them resists the motion and is rapid for aggregated nanofluid. Further, thermal radiations (Rd=1.0,1.5,2.0,2.5) produce considerable heat which can be used to breakdown the aggregation between the nanoparticles.

Entropy generation on MHD Maxwell hybrid nanofluid over a Stretching cylinder with Cattaneo-Christov heat flux: Analytical and numerical simulations

In the present study, we examine the influence of entropy generation on Maxwell hybrid nanofluid over a cylinder in the presence of non-linear thermal radiation and Cattaneo-Christov heat flux. In this model, we considered [Formula: see text] and [Formula: see text] are the nanoparticles which are suspended in the base fluid blood. The basic PDE’s (Partial differential equations) are transformed into ODE’s (Ordinary differential equations) by ensuring the suitable self-similarity transformations. ODEs are resolved using a Runge–Kutta 4th-order along with shooting procedure. Numerical method ( NM) and Homotopy perturbation method ( HPM) solutions for the nonlinear system are obtained so that they compared to each other for the case of cylinder. The HPM is developed for comparison purposes, and more accurate and reliable outcomes are illustrated through graphs. Moreover, the obtained results are compared with the existing literature and are found to be an excellent agreement. It is found that the fluid velocity reduces for the higher values of magnetic parameter. Higher values of the heat generation parameter improve the temperature profiles. Nusselt number decreases when developing Darcy–Forchheimer number and temperature time relaxation parameter. This type of flow problems may be utilized to improve the blood flow in the blood vessel has attracted the attention of physicians and biomedical researchers as it specializes in various treatments such as drug targeting, cell tissue engineering, cancer, hyperthermia and hypothermia.

Blood-based ternary hybrid nanofluid flow-through perforated capillary for the applications of drug delivery

The goal of this paper is to establish a mathematical framework for Casson liquid flow along a perforated capillary of tri-hybrid nanofluid including nonlinear thermal radiation, energy omission/absorption, vicious dispassion and Ohmic heat. The current mathematical approach is designed for blood-based nanofluids considering three distinct nanomaterials such as CuO, TiO2 and Al2O3 . The nonlinear thermal radiations were set to modify the objective of this framework in order to examine the changes in temperature. Therefore, streamlining the dominating transport equations pertinent adaptations are used to transform the derived partial differential equations to ordinary differential equations. Analytically the restored mathematical formulations are handled using a successful technique known as the HAM scheme. The findings show that heat transfer increases with the radiation parameter while velocity decreases the magnetic strength. The findings of the present research are useful in determining the impact of several key design factors on heat transmission and therefore in optimizing the manufacturing processes. This mathematical model is comprised of thermal radiation and EMHD situations via blood circulation, which has a substantial impact on magnetized blood delivery, hyperthermia therapy, magnetizer endoscopy, blood stream knowledge, transport of complicated bio-waste liquids and heat exchange in capillaries.

Dynamics of tangent-hyperbolic nanoliquids configured by stratified extending surface: Effects of transpiration, Robin conditions and dual stratifications

A mathematical study is presented to evaluate double stratification effects on the dual convected flow of a non-Newtonian (tangent-hyperbolic) nanoliquid persuaded by porous stretching surface. Thermal radiation along with transpiration (wall suction/injection) and heat source/sink are included. Buongiorno's model is employed for nanoscale effects and a Rosseland diffusion approximation for nonlinear radiative heat transfer. Appropriate similarity transformations are deployed to alter the dimensional governing nonlinear PDEs (partial differential equations) to a nonlinear differential one with physically viable boundary conditions. The transformed dimensionless BVP (boundary value problem) is computed analytically by a HAM (homotopic analysis method) algorithm and a symbolic software. Validation with earlier studies employing the numerical method (Runge-Kutta-Fehlberg) is included. The evolution in velocity, thermal and solutal (nanoparticle) fields are interpreted through graphical outcomes for the impact of significant sundry parameters. Tabular outcomes are also presented for skin-friction, local Nusselt and Sherwood numbers. A rise in material variable (Weissenberg number), the flow is decelerated while it is accelerated with increasing nonlinear thermal convective parameter, mixed convection parameter and buoyancy ratio values. Temperatures are boosted with increment in radiative, thermophoresis, Brownian motion, thermal Biot number and heat generation parameters whereas they are reduced with increasing thermal stratification parameter. Nanoparticle concentration values are suppressed with higher Schmidt number, Brownian movement and solutal stratification variable however they are boosted with greater values of thermophoresis and concentration Biot number. Local Sherwood number is improved with Schmidt number, concentration stratification parameter and concentration Biot number. Local Nusselt number is strongly increased with greater Prandtl number, thermal stratification number, thermal Biot number and radiative parameter. The study finds applications in thermal nano-polymeric coating flows in materials processing operations.

Thermophoresis deposition of hybrid ferrite nanoparticles on micropolar flow through a shrinking sheet with non-uniform heat source/sink and nonlinear radiation

Nowadays, the researchers have voiced their enthusiasm and interest in hybrid nanofluids due to their practical uses in engineering and industrial applications. Thus, our goal is to investigate the micropolar fluid flow towards a shrinking sheet containing hybrid ferrite nanoparticles with the substantial influence of thermophoresis particle deposition. Moreover, the impact of nonlinear radiation and non-uniform heat source/sink are also considered. The partial differential equations are converted to the similarity equations of a particular form through the similarity variables. Numerical outcomes are computed by applying the built-in program bvp4c in MATLAB. Multiple solutions are developed for a certain range of the suction parameter. The mass and heat transfer, as well as the friction and couple shear stress factors upsurge owing to the rise of the hybrid nanoparticles. The imposition of nonlinear radiation and non-uniform heat source/sink reduces the heat transfer, significantly. Meanwhile, thermophoresis particle deposition lowers the mass transfer. Lastly, the first solution is shown as a reliable and stable solution.

Electrical magnetohydrodynamic flow of kerosene oil based carbon nanotube's Maxwell nanofluid in the presence of non-linear radiation and Cattaneo-Christov heat diffusion: Applications in aerospace industry

This paper investigates the influence of carbon nanotubes to improve heat transmission with Maxwell nanofluids which is suspended in kerosene oil. This mathematical model has been expressed in terms of partial differential equations, which are transformed by using compatible variables into ordinary differential equation's. The result of this model has been attained numerically via RK fourth order with shooting iteration. The results show that with a larger magnetic field, heat transfer increases radiation while decreasing velocity. The combined electrical magnetohydrodynamic effects have the potential to improve fluid flow rates. Moreover, the non-linear radiation case is dominating to the linear case. This theoretical study may be applied in material science, purification technologies, optics and electricity owing to their astonishing possessions, aerospace industry and many more. Especially in aerospace, by way of the aid in plummeting the weight, satellite weight lessening, lightning protection for aircraft and so on.

On the Diffusive Limits of Radiative Heat Transfer System I: Well-Prepared Initial and Boundary Conditions

We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling and greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary conditions for the radiative intensity and with periodic, Dirichlet and Robin boundary conditions for the temperature. The global existence of weak solutions for this system is given by using a Galerkin method with a careful treatment of the boundary conditions. Using the compactness method, averaging lemma and Young measure theory, we prove our main result that the weak solution converges to a nonlinear diffusion model in the diffusive limit. Moreover, under more regularity conditions on the limit system, the diffusive limit is also analyzed by using a relative entropy method. In particular, we get a rate of convergence. The initial and boundary conditions are assumed to be well-prepared in the sense that no initial or boundary layer exists.

Entropy generation analysis for mixed convective flow of Casson fluid in a vertical microchannel with the influence of nonlinear radiation by maintaining inconstant viscosity

AbstractThe study of entropy generation in the fluid flow has great importance in the field of engineering. The present analysis is to investigate the entropy production in Casson fluid flow in a vertically placed porous‐filled microchannel. The flow is influenced by the nonlinear radiation and exponential heat source. Viscosity is kept varying throughout the flow. The equations which govern the considered flow are nonlinear and are nondimensionalized by considering the appropriate nondimensional variables. The flow problem is tackled by converting the ordinary differential equation (ODE) by assigning the new variables. The flow problem is tackled by using the effective mechanism which involves the finite difference technique by converting the equations into a set of first‐order ODE. The results attained are discussed using the graphs. It is noted that by maintaining the lesser values for the Casson parameter and mixed convection parameter, entropy production can be reduced. The Bejan number profile has the highest magnitude for the variation of mixed convection parameter and the same is found to be less for the nonlinear radiation parameter.

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.

Intelligent computing for entropy generation in Jeffrey nanofluid through radiated flow

This study explores the Entropy generation in the Flow of Jeffery Nanomaterial Model (EFJNM) past a variable thicked surface by considering joule heating effect, convectively heated surface, nonlinear radiative heat flux, and convective boundary conditions via Artificial Back Propagated Levenberg Marquardt Neural Networks (ABP-LMNNs). The ODEs system is obtained by implementing suitable transformation on PDEs for EFJNM. Applying homotopy analysis method (HAM) to create dataset for ABP-LMNNs by the variation of physical parameters of EFJNM. The reference datasets are then segmented in validation/training/testing process to scrutinize the approximated solution for EFJNM and further to compare it with standard solution. The better performance is further investigated by MSE based curves, regression fitting, absolute error, error histogram analysis. Results reveals that performance in form of MSE is in ranges of 10−9, 10−11, 10−9, 10−9, 10−10, 10−9, 10−10, 10−9, and 10−10 with 494, 285, 496, 219, 71, 167, 194, 121, 179, and 738, respectively, for all scenarios. The impact of variants of EFJNM on velocity, entropy production rate, temperature, and concentration are also analyzed. As the entropy generation increase with the increment in Deborah number and Brinkman number. The velocity increases with the escalation in Deborah number and wall thickness variable whereas decreases with the increase in relaxation to retardation ratio. The absolute errors of effective parameters for velocity are 10−7-10−4, 10−7-10−3, 10−7-10−4, and 10−6-10−3, the absolute errors for temperature are 10−7-10−3, 10−7-10−3, and 10−7-10−4 whereas the absolute errors for concentration are 10−8-10−4, 10−8-10−3, and 10−8-10−4, which show the accuracy of proposed ABP-LMNNs. Abbreviations: ABP-LMNNs, Artificial back propagated Levenberg Marquardt Neural Networks; EFJNM, Entropy generation in the Flow of Jeffery Nanomaterial Model; HAM, Homotopy analysis method

Nonsimilar solution of a boundary layer flow of a Reiner–Philippoff fluid with nonlinear thermal convection

AbstractThe thermodynamics modeling of a Reiner–Philippoff‐type fluid is essential because it is a complex fluid with three distinct probable modifications. This fluid model can be modified to describe a shear‐thinning, Newtonian, or shear‐thickening fluid under varied viscoelastic conditions. This study constructs a mathematical model that describes a boundary layer flow of a Reiner–Philippoff fluid with nonlinear radiative heat flux and temperature‐ and concentration‐induced buoyancy force. The dynamical model follows the usual conservation laws and is reduced through a nonsimilar group of transformations. The resulting equations are solved using a spectral‐based local linearization method, and the accuracy of the numerical results is validated through the grid dependence and convergence tests. Detailed analyses of the effects of specific thermophysical parameters are presented through tables and graphs. The study reveals, among other results, that the buoyancy force, solute and thermal expansion coefficients, and thermal radiation increase the overall wall drag, heat, and mass fluxes. Furthermore, the study shows that amplifying the space and temperature‐dependent heat source parameters allows fluid particles to lose their cohesive force and, consequently, maximize flow and heat transfer.

Convective heat transfer in MHD Cu-TiO2-H2O cross nanofluid flow over three diverse surfaces

Computational analysis on the flow of hybrid nanofluid along three diverse flow surfaces with magnetized force accomplished numerically. A comparative study was performed for [Formula: see text] hybridized nanoliquid streams along cone, wedge, and plate surfaces. The flow governing equations are embedded with various physical factors: nonlinear radiation, magnetic force, and uneven heat rise/fall. The implication of these biological factors on velocity and thermal distributions, wall friction, and the thermal transfer rate are interpreted via plots and tables. For numerical computation, we implemented the R-K method with a shooting scheme by means of the Matlab package. Results reveal that the implication of embedded factors on hybrid nanofluid flow along cone surfaces is more substantial than flow along wedge and plate surfaces. Also, the utilization of copper and titanium oxide nanoparticles elevates the thermal enactment of the base liquid water to a greater extent. Wall temperature factor and thermal Grashof number effectively amplify the nanofluid thermal transport rate.

Nonlinear radiative heat transfer of magnetohydrodynamic non-newtonian fluid flow past a shrinking sheet: Reiner–Philippoff model

This study aims to analyse the effect of MHD and nonlinear thermal radiation on heat transfer of Reiner–Philippoff fluid flow over a shrinking sheet. By adopting appropriate similarity transformations, the partial derivatives of multivariable differential equations are transformed into the similarity equations of a particular form. The resulting mathematical model is elucidated in MATLAB software using the bvp4c technique. The findings reveal the existence of dual solutions for a certain range of physical parameters. Since the dual solutions are established, stability analysis is employed to examine their stabilities. The outcomes show that the first solution is stable whereas the second solution is unstable. Moreover, the heat transfer rate reduces as the nonlinear thermal radiation is introduced in the operating fluid by increasing the temperature ratio parameter. However, increasing the magnetic parameter raises the friction factor which impulsively improves the heat transfer performance. The suction effect has a noticeable influence on the Reiner–Philippoff fluid, where increasing the suction strength enhances the skin friction coefficient and the heat transfer performance.

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.

Implications of the third-grade nanomaterials lubrication problem in terms of radiative heat flux: A Keller box analysis

Steady flow of non-Newtonian nanofluid impinging on a vertical lubricated surface is numerically investigated. The rheological behaviour of the base fluid is characterized by the constitutive equation of third-grade fluid and the power-law fluid model is used for lubricant. Higher-order chemical reaction and nonlinear radiative heat flux are also taken into account. The governing nonlinear partial differential equations are simplified using the Prandtl boundary layer theory and similarity transformations. An efficient and accurate implicit finite difference method is applied to approximate the resulting nonlinear coupled differential equations with complicated boundary conditions for several values of parameters of interest. The velocity, temperature, nanoparticles concentration profiles Nusselt number, and streamlines are illustrated through graphs for full slip and no–slip case as well as assisting and opposing flow cases. The temperature and concentration profiles are also described for linear and non-linear thermal radiation and for different order chemical reactions. The numerical results are compared with the existing literature and found good agreement. It is found that heat and mass transfer rates reduces over the lubricated surface compared with the rough surface.

Dynamic consequences of nonlinear radiative heat flux and heat generation/absorption effects in cross-diffusion flow of generalized micropolar nanofluid

The double diffusion thermal mechanism of viscoelastic nano-materials has been suggested under the dynamic consequence of nonlinear thermal radiation and temperature absorption/production phenomenon. The electrically conducting generalized micropolar nanofluid is considered to predict the non-Newtonian behavior. The consideration of modified micropolar fluid successfully retained the viscous features as well as results for the second grade fluid. The uniform flow is induced with the linear movement of a flat surface. Following the convective boundary constraints, the heat and mass characteristics are reported. The equations that governs to the flow are reduced into ordinary ones. The homotopy analysis method (HAM) is imposed to develop the analytical expressions by using computational software MATHEMATICA 8. The evaluation of parameters is inspected by performing graphical analysis for transport process. The computational numerically illustration of the local Nusselt number, Sherwood number and the motile microorganism density number is performed. The results claimed that nanofluid temperature declined with the vortex viscosity parameter. The solutal nanoparticles concentration decreases with the Dufour Lewis number while a lower change in solutal nanoparticles concentration has been observed for regular Lewis number. Moreover, the local Nusselt and Sherwood number increases with vortex viscosity parameter.

Comparative study for magnetized flow of nanofluids between two parallel permeable stretching/shrinking surfaces

The current study intended to discuss a comparative study on the three dimensional Casson nanofluid with nonlinear radiative MHD flow and heat transfer aspects between two parallel stretching/shrinking surfaces. The mathematical models for momentum and temperature are established by employing the boundary layer flow of fluids with spinel-type ferrite MnFe2O4 nanoparticles being distributed in Pure Water/ (H2O) as the base fluid. Remarkable models like Maxwell-Garnett and Patel models are inserted in view of thermal conductivity augmentation. The suitable similarity transformations are adopted for converting the governing non-linear partial differential equations into non-dimensional ODE's and obtaining the relevant parameters for discussion. The major outers of the present study are axial velocity {F′(η)} peters out with amplifying β subject to stretched and shrunk surfaces in relation to both Maxwell-Garnett and Patel models. Growing θw and n exhibits opposite effect on heat transfer rate.

Thermal enhancement in the mixed convective flow of unsteady Carreau nanofluid with slip conditions: A numerical study

Nanofluids are formed by incorporating very small sized particles consist of metals, oxides, carbides, or carbon nanotubes into base fluids like water, oil, ethylene glycol etc. Due to number of applications and amazing heat flow features of nanofluids, we are motivated to devote this article to explore the heat transform characteristics in transient flow of Carreau nanofluid over an inclined stretching cylinder. We have modeled the nonlinear mixed convection flow of Carreau nanoparticles in term of Lorentz force. Heat transfer mechanism in the flow is examined in view of nonlinear thermal radiation and non-uniform heat source/sink influences. Additionally, the effects of joule heating are also taken into account for examining the heat transport mechanism in the flow. Moreover, the effects of chemical reaction are also employed in concentration equation for investigation of mass transport phenomenon in the flow of nanofluid. To see the influence of involved physical parameters bvp4c numerical technique is employed. The numerical outcomes of physical parameters are assessed and depicted with logical discussion in the results and discussion section. The section of concluding remarks is designed to highlight the core findings of this study. It is revealed that the flow curves of nanofluid significantly grow up for escalating scales of nonlinear thermal convection constant. Moreover, an escalation is detected in the transport of thermal energy for growing scales of Eckert number and thermal radiation constant. Also, it is assessed that the flow velocity deteriorates by with an escalation in the magnitude of buoyancy force ratio parameter.

On the magnetized 3D flow of hybrid nanofluids utilizing nonlinear radiative heat transfer

This article analyzes the heat transfer, non-linear thermal radiation, the Cattaneo-Christov heat flux model and velocity slip effects in hybrid nanofluid flow over a 3D moving sheet. The hybrid type nanoparticles like Ag-Cu and MoS2 and GO are suspended in working liquid. Hybrid nanoliquid is homogeneous-mixture with novel physical and chemical structures making it a promising option for improving thermal efficiency. Hybrid nanoliquids have high ability to absorb and preserve the hydrogen because of their very huge unique surface-area and distinctive and unusual nature of an each nanostructure. Nanostructure carbon atoms like graphite, graphene and few metals like molybdenum and magnesium have recently been found to store hydrogen due to their larger storage-capacity and the higher dehydrogenation and hydrogenation speeds. The system of the mathematical relation in PDEs form is converted to system of ODEs by employing suitable variables. The bvp4c tool available in computational software MATLAB is used for solving the dimensionless ordinary differential system. Furthermore, the flow expectations for each physical flow parameter like are discussed. The physical consequence of flow parameters against subjective flow fields are graphically highlighted with physical justifications. The vitality of prominent parameters against velocity field and temperature distribution is illustrated through graphs. The velocity field diminishes with a larger velocity slip parameter. The velocity field is enhanced by the higher estimations of the Grashof number. The consequence of temperature ratio parameter on thermal field is delineated. By enhancing the thermal relaxation parameter, the thermal field reduces.