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The current work presents a theoretical framework to analyze the nonlocal thermoelastic model with a general kernel function for memory-based derivatives by incorporating two-time delays. The introduced model aims at studying the thermomechanical response of rotating size-dependent nanobeams. The nonlocal elasticity theory and the generalized heat conduction model with phase delays are utilized to formulate the problem. In the proposed model, the thermal conductivity is expected to vary linearly with temperature and the system is excited by a variable harmonic heat source by considering the time-dependent exponential decaying load. To this end, the semi-analytical solutions for the transverse and axial displacements, thermodynamic temperature and bending moment are examined using the Laplace transform method. The effects of the nonlocal parameter and various loading conditions are also investigated and discussed. Finally, it is demonstrated that how the linear variation of thermal conductivity could affect the performance of the considered system. [ABSTRACT FROM AUTHOR]

The bioconvective flow of non-Newtonian fluid induced by a stretched surface under the aspects of combined magnetic and porous medium effects is the main focus of the current investigation. Unlike traditional aspects, here the viscoelastic behavior has been examined by a combination of both micropolar and second grade fluid. Further thermophoresis, Brownian motion and thermodiffusion aspects, along with variable thermal conductivity, have also been utilized for the boundary process. The solution of the nonlinear fundamental flow problem is figured out via convergent approach via Mathematica software. It is noted that this flow model is based on theoretical flow assumptions instead of any experimental data. The efficiency of the simulated solution has been determined by comparing with previously reported results. The engineering parameters' effects are computationally evaluated for some definite range. [ABSTRACT FROM AUTHOR]

This investigation deals with the effect of variable thermal conductivity in a micropolar thermoelastic medium without energy dissipation with cubic symmetry. The normal mode technique is employed for obtaining components of physical quantities such as displacement, stress, temperature distribution and microrotation. [ABSTRACT FROM AUTHOR]

The classical viscous theory is limited to illustrating the characteristics of several materials like pseudoplastic and dilatant fluids. Sutterby fluid has the features of shear thinning and shear thickening fluids because of its Power law index. Therefore, this study considered an incompressible, time-independent and electrically conducting Sutterby fluid flow across a rotating and stretchable disk. The disk experiences the effect of porous space. The energy equation has variable conductivity, heat source and thermal relaxation time features while mass equation exploits the influence of chemical reaction. The aspects of Buongiorno nanofluid theory are also examined in the Sutterby flow model. The phenomenon of Stefan blowing is analysed through mass transfer rate at the surface of disk. The flow expressions are first transferred into a new system of single independent variable and then treated numerically via Runge–Kutta–Fehlberg (RKF) method combined through shooting process. The behaviour of distinguished physical quantities is discussed graphically on momentum, mass species and thermal fields. The numeric data of drag force, Sherwood number and Nusselt number is calculated against several physical parameters. [ABSTRACT FROM AUTHOR]

This article employs the Cattaneo-Christov double diffusion concept to examine thermal and solute energy transfer processes in Maxwell liquid movement. The irregular two-dimensional movement of a Maxwell liquid with changing heat conductivity across an extended cylinder is investigated, together with thermal radioactivity and velocity slip. We develop partial differential equations for heat and mass transmission in Maxwell liquid using the Cattaneo-Christov pattern instead of Fourier's and Fick's law. Numerical shooting solves ordinary differential equations obtained from controlling partial differential equations via similarity transformations. We noticed that unstable factor should be no more than one for optimal outcomes. Greater Maxwell values minimize the movement field and increase liquid energy transfer. Heat and concentration diffusions in Maxwell liquids decline as thermal and concentration relaxation times approach maximum. In addition, a low thermal conductivity characteristic improves the temperature field. [ABSTRACT FROM AUTHOR]

The pioneer motivations for current flow model are to study the rheological aspects of chemical reactive Williamson nano-material with utilization of gyrotactic microorganisms. The peak theme of activation energy and variable thermal conductivity are also incorporated. Unlike typical investigations, current flow model is formulated with employment of slip consequences with higher order relations. The induced flow is caused by a porous stretched surface additionally impact by magnetic force. The flow equations are transmuted into dimensionless form first for which numerical simulations are performed using famous finite difference approximations. The results are verified for limiting cases by comparing with various investigations and found excellent accuracy. The physical insight of all flow parameters are graphically underlined with interesting physical appliances. Furthermore, the numerical calculation for heat transfer enhancement, change in mass flux and motile density simulations are also evaluated in tabular form. The stream line and contour plots are also prepared. [ABSTRACT FROM AUTHOR]

In this work, we consider the problem of a semiconductor half-space formed of varying thermal conductivity materials with and without Kirchhoff's transforms. Specifically, we deal with one thermal relaxation time within the context of generalized photothermoelastic theory. It is expected that the thermal conductivity of the material will vary with temperature. The finite element method is used to numerically solve this problem. The Laplace transform and the eigenvalues method are used to determine analytical solutions to the linear problem. Various hypotheses are investigated, both with and without the use of Kirchhoff's transformations, to consider the influence of thermal conductivity change. To verify the accuracy of the proposed approach, we provide a comparison of numerical and analytical results by ignoring the new parameters and investigating the behaviors of physical quantities for numerical outcomes. [ABSTRACT FROM AUTHOR]

Space radiators are used to reject waste heat from power units, electronic devices, and various equipment in space vehicles. It is important that radiators can achieve the heat desired to be dissipated into space with the least mass. With a view to ensuring this aim, the heat transfer calculations that must be performed must be highly accurate. Therefore, the variation of conductivity with temperature should also be taken into account in the mathematical model. This paper presents heat transfer performance and optimization of a fin array consisting of straight fins put axially on a tube and radiating heat into deep space. The mathematical model yields the governing equation as a highly nonlinear integro-differential equation which is solved by the variation of parameters method (VPM). By applying an appropriate optimization procedure, the conduction–radiation parameter, Nc, providing maximum heat transfer is obtained for a given fixed fin profile emissivity, ε, opening angle among the fins, γ, and thermal conductivity parameter describing the variation of thermal conductivity, β. For the range of suitable problem parameters, optimum values of the dimensionless conduction–radiation parameter Nc, which is a combination of thermal and geometric quantities, are expressed in ε and γ for a given β. The correlation equations are expected to provide remarkable benefits to the designer. [ABSTRACT FROM AUTHOR]

In the present work, the mathematical model for the solar thermal collectors is considered in the form of a nonlinearly stretching sheet. The radiative heat transfer due to solar radiation in magnetohydrodynamic Sisko nanofluid flow over a stretching sheet in the presence of variable thermal conductivity and a heat source is analyzed effectively. The Sisko fluid has been used as a working fluid in the solar collector. The governing boundary value problem is transformed into a system of nonlinear ordinary differential equations using the similarity transformation technique, which is then solved numerically using the finite difference method combined with the quasilinearization technique. The results shown graphically are discussed for the effects of the thermal conductivity parameter, radiation parameter, and heat source parameter on the flow regime. It is observed that increasing values of radiation parameters imply greater thermal conduction and less thermal radiation, as a result of which the nanofluid temperature in the fluid regime will decrease. [ABSTRACT FROM AUTHOR]

This study deals with the analysis of the heat and velocity profile of the fractional-order Oldroyd-B bio-nanofluid within a bounded channel. The study has a wide range of scope in modern fields of basic science such as medicine, the food industry, electrical appliances, nuclear as well as industrial cooling systems, reducing pollutants, fluids used in the brake systems of vehicles, etc. Oldroyd-B fluid is taken as a bio-nanofluid composed of base fluid (blood) and copper as nanoparticles. Using the fractional-order Oldroyd-B parameter, the governing equation is generalized from an integer to a non-integer form. A strong approach, i.e., a finite difference scheme, is applied to discretize the model, because the fractional approach can well address the physical phenomena and memory effect of the flow regime. Therefore, a Caputo fractional differentiation operator is used for the purpose. The transformations for the channel flow are utilized to transfigure the fractional-order partial differential equations (PDEs) into non-dimension PDEs. The graphical outcomes for non-integer ordered Oldroyd-B bio-nanofluid dynamics and temperature profiles are navigated using the numerical technique. These results are obtained under some very important physical conditions applied as a magnetic field effect, variable thermal conductivity, permeable medium, and heat source/sink. The results show that the addition of (copper) nanoparticles to (blood) base fluids enhances the thermal conductivity. For a comparative study, the obtained results are compared with the built-in results using the mathematical software MAPLE 2016. [ABSTRACT FROM AUTHOR]

Design of an optimal extended surface having functionally graded material is significant in cooling performance of hot attached structures in technological applications. The present endeavor is to search for axially variable thermal conductivity formula for a prescribed longitudinal fin shape of rectangular or triangular cross section. Heat transfer is presumed to take place through conductive, convective and radiative effects. The well-known fact is that it is not possible to solve in closed-form the highly nonlinear heat transfer equation under such considerations in general, unless some effects are ignored. Temperature or spatial dependence of material properties of the fin make the problem even harder to treat without numerical simulations. To help designer to avoid such simulations, prescribed temperature distributions in the form of elementary polynomial functions involving some shape parameters are utilized. Under operative geometric and thermal parameters such as the Biot number and the radiation parameter, exact solution formulae for the pertinent thermal conductivity distribution along the functionally graded extended surface are then obtained. The price to pay is only to work out the domain of definition of physical parameters acting on the loaded temperature profile.Designer can benefit from the advantage of the presented elementary solutions while analyzing the efficiency of convecting-radiating longitudinal fins of rectangular, triangular or a more general tapered longitudinal fin class cross sections and control/adjust the physical parameters to the desired temperature/material conditions. With a preloaded temperature profile to the energy equation, the tip temperature can be adjusted so as to enhance the heat transfer rate by increasing/decreasing the governing fin parameters. Such promising inverse problem of extracting axial thermal conductivity distribution from a prescribed temperature solution can also be utilized in other kinds of fin profiles without resorting to the numerical simulations. [ABSTRACT FROM AUTHOR]

Micropolar fluid flow in a channel with variable viscosity, variable thermal conductivity and activation energy is examined numerically using the Runge–Kutta Fehlberg method in this article. Two different boundary conditions are postulated in this study namely Prescribed Surface Temperature (PST) and Newtonian Heating (NH). The numerical outcomes are compared to check the precision of the suggested problem. Significant metrics like Reynolds number, Peclet number for heat and mass transfer, Schmidt number, Activation energy and chemical reaction parameter are graphically described. The influence of the parameters like spin gradient viscosity, vortex viscosity, micro-inertia density on the flow fields are discussed and shown. According to the graphic data, the velocity increases as the viscosity parameter increases whereas the temperature decays for larger values of variable thermal conductivity and also, activation energy enhances the concentration profile. The variation in viscosity parameter shows a significant effect on thermal distribution. The viscosity variation parameter enhances the shear stress and the couple stress. The Peclet number for heat transmission displays a changing effect for high and low Biot numbers regardless of the effect of variable thermal conductivity. This analysis tabulates the link between Nusselt number and Sherwood number over a Peclet number for heat and mass transfer. The skin friction coefficient increases with the viscosity parameter ∊ whereas enhancement in the thermal conductivity parameter decreases the Nusselt number. Furthermore, sensitivity analysis is carried here by developing RSM in order to identify the variations in the input values for the parameters Pe h , Pe m and N 1 . The response surface equation is created by using the software package MINITAB-16 by design of experiments. The regression model's quality of fit is assessed by using the Analysis of Variance. [ABSTRACT FROM AUTHOR]

The fully developed MHD mixed convection flow in a micro channel having variable thermal conductivity is considered. The velocity slip and temperature jump at both plates were taken into consideration. The effects of various flow parameters entering into the problem such as Hartmann number, variable thermal conductivity, mixed convection parameter, rarefaction parameter, fluid-wall interaction parameter and wall-ambient temperature difference ratio were discussed with the aid of line graphs. It is revealed that greater values of variable thermal conductivity tend to significantly improve the temperature and velocity gradients respectively. Furthermore, mixed convection parameter, significantly influence the flow pattern. [ABSTRACT FROM AUTHOR]

Phase change materials (PCM) are substances that release and absorb sufficient energy at phase transition to provide useful heat or cooling. Stefan problems including PCM have many applications in science and engineering. Since an exact solution for this type of Stefan problem does not exist, tracking the moving boundary and obtaining accurate temperature distribution are still challenging issues in mathematical aspects. Therefore, in this paper, a new approach based on combining the cubic B-spline and a fourth-order compact finite difference scheme is developed to capture the behavior of the one-dimensional Stefan problem including moving PCM, variable thermal conductivity and periodic boundary condition. The proposed combined method in space and the Crank–Nicolson method in time are applied to the model after the moving domain is transformed into the fixed domain by the boundary immobilization method. The comparative results have seen a good agreement for a particular case. Besides, the stability of the scheme and the effect of the model parameters on the numerical solution are analyzed. The computations reveal that the new combined method is seen to pull up the accuracy of the model solutions and presents an efficient alternative solution to the model. [ABSTRACT FROM AUTHOR]

Dehumidification on a fin surface happens when the thermal interface state maintains an undervalue corresponding to saturation condition, and a temperature boundary layer develops during heat transmission. The local thickness of the temperature boundary layer changes, and consequently, sensible and latent heat transfer coefficients become highly non-uniform. In this study, a new mathematical procedure depending on the Adomian decomposition method (ADM) is established to predict the heat transfer duty from a moistened fin where all heat transfer modes involved are functions of temperature. A cubic algebraic equation for connecting the specific humidity of air and the thermal state level of a fin is closer to the actual relation determined based on the regression analysis, which converts the governing equation into a highly nonlinear character. The present model has no restriction using the fractional power factor of temperature-dependent convection coefficients. The current results highlight that the variable convection coefficients decrease both the fin performance index and heat load rate, and this influence becomes significant at the optimum design condition. Therefore, establishing the optimum state of a fin adopting all the variability events in the practical design system is essential for the correct analysis. As the equipment implementation analysis always requires an extremum study, the proposed research will help to predict the optimum information in the practical design with the highest accurate prediction of results.

The physical phenomena of nanofluid at high temperature motivate us to analyze problems with temperature-reliant fluid properties, like viscosity and thermal conductivity. Since in glass blowing, viscosity and thermal conductivity of the fluid may gets affected in such high temperature. This communication deals with the unsteady flow of nanofluid generated by nonlinear expansion of the surface. Temperature-dependent fluid viscosity and thermal conductivity are considered in the investigation of the problem. The flow of nanofluid is modeled using famous the Buongiorno's two-phase model, which includes the simultaneous effect of Brownian motion and thermophoresis diffusion. Appropriate transformations are adopted to obtain the ODEs from governing PDEs. Then MATLAB ‘bvp4c’ computation is used to solve the problem and to get a clear insight of the influences of various parameters. Graphical comparisons are made to check the accuracy of used numerical method. The study explores that heat transfer rate significantly enhances by the index of nonlinearity, variable viscosity and thermal conductivity parameters. Unsteadiness of the flow can be used as a controlling parameter to reduce the surface drag, heat and nano-mass transfer rate. Variable viscosity parameter leads to enhance the velocity near the surface and reducing the concentration of the nanoparticles. The thermal and concentration boundary layer thickens with thermal conductivity parameters. Nanofluid temperature and concentration of nanoparticles decay with nonlinear expanding index.

The aim of this work is to investigate the influence of Arrhenius activation energy and variable thermal conductivity with EMHD fluid flow over a nonlinearly radiating stretching sheet in a porous medium. The main objective of this research is to study the effects of variable electromagnetohydrodynamic (EMHD) on fluid flow motion. The significance of the combined effects of electric and magnetic fields is useful where one can create a strong Lorentz force for industry applications. The fundamental laws, that is, conservation of mass, momentum, and energy equations, are given in the form of partial differential equations (PDEs). The current fluid flow problem is not similar, which means that the presented solution is local. The introduction of nonsimilarity variables transforms PDEs into a set of coupled ODEs. The resultant ODEs are not only solved computationally by MATLAB built-in solver bvp4c but the solution is also obtained with other numerical schemes that include the shooting method and the finite element method (FEM). In applying FEM, we choose the Galerkin method in which the weight function is equal to the shape function. The aforementioned numerical methods are implemented and programmed in MATLAB. Graphs illustrate the effects of various parameters on the velocity, temperature, concentration, and microorganism profiles. Physical parameters measure the roughness of the sheet (skin friction coefficient), heat transfer rate at the sheet (local Nusselt number), the mass transfer rate of the concentration gradient (local Sherwood number), and transfer rate of microorganisms at the sheet (density of motile microorganism). The skin friction coefficient increases for higher values of (Kp) and magnetic parameters (M). The local Sherwood number decreases for different values of activation energy. An excellent agreement of FEM results with other numerical methods, shooting method, and bvp4c has been achieved. Moreover, for particular cases, the current results have a good agreement with the published work.

This investigation consists of Maxwell's fluid which describes rate type non-Newtonian fluid in best; it has great applications in engineering, technology and industry. Linear stretching sheet generates the flow in fluid. Flow momentum is measured with MHD effect. When Fourier's and Fick's laws are incorporated relaxation time factor then known as Cattaneo-Christov model which are implemented for heat and mass transport. The features of heat source or sink and non-linear type thermal stratification are employed with variable thermal conductivity. The features of chemical reaction and non-linear type solutal stratification are analyzed along with variable mass diffusivity. By the usage of boundary layer phenomenality in this problem, non-linear PDEs are achieved. These equations are transmuted into non-linear and non-homogeneous differential equations ramified with ordinary derivatives after applying similarity transformations. The most exclusive homotopic analysis method is used to get the analytic solutions of nonlinear and non-dimensional governing equations. The significant results of progressive parameters are dominant in this investigation. The arising parameters are examined in detail and results are shown graphically. It is found out that with the increment of time relaxation factor velocity, temperature and concentration profiles reduce. It increases the viscoelastic impacts related to stress relaxation time which makes viscoelastic materials more durable.

A fluid's moving class improves its heat transmission capability, as well as its rigidity, owing to multivariate molecule suspension. In this way, nanofluids are superior to common fluids. In this study, we evaluated the features of ease and heat transfer. Furthermore, we investigated permeable media, heat source, variable heat conductivity, and warm irradiation results. A mathematical technique known as the Galerkin finite element (G-FEM) approach was used to solve the supervising conditions. Third-grade nanofluid (TGNF), which consists of two types of nanoparticles (NPs), single-walled carbon nanotubes (SWCNT), and multi-walled carbon nanotubes (MWCNTs) distributed in a base liquid of carboxymethyl cellulose (CMC) water, was used for this examination. The main conclusion of this study is that MWCNT-CMC nanofluid has a higher heat transfer velocity than SWCNT-CMC nanofluid. The entropy of the framework can be increased by adjusting the thermal conductivity. Additionally, we found that increasing the main volume section decreases the speed but increases the dispersion of atomic energy. In order to separately account for the development properties of inertial forces and shallow heat dispersion forces, Reynolds and Brinkman values can be used to accelerate the entropy rate of the heating framework. [ABSTRACT FROM AUTHOR]

Cross nanofluid possesses an extraordinary quality among the various fluidic models to explore the key characteristics of flowing fluid during very low and very high shear rates and its viscosity models depend upon shear rate. The current study establishes the numerical treatment regarding variable viscosity-based mixed convective inclined magnetized Cross nanofluid with varying thermal conductivities over the moving permeable surface. Along with variable thermal conductivities, we considered thermal radiation, thermophoresis, and the Brownian motion effect. An inclined magnetic field was launched for velocity scrutiny and the heat transfer fact was numerically seen by mixed convective conditions. Similarity variables were actioned on generated PDEs of the physical model and conversion was performed into ODEs. Numerical results showed that the frictional force and Nusselt quantity considerably influence the skinning heat transfer processes over the geometry of a moving permeable surface. Furthermore, less velocity was noticed for the greater suction parameter and the Brownian motion parameter corresponds to lower mass transport. [ABSTRACT FROM AUTHOR]

In the present numerical study, the combined effect of temperature‐dependent thermal conductivity, linear thermal radiation, and magnetic effect on shear‐thinning tangent hyperbolic fluid past a sensor surface has been studied. After converting the modelled partial differential equations into ordinary differential equations by using similarity transformation, the system of equations is tackled with the aid of the shooting method. The influence of important parameters on the fluid motion and energy distribution is displayed graphically and analyzed in detail. The presented simulations depict that a significant rise in fluid velocity is noticed for an enhancement in the magnetic parameter while an opposite trend is observed for the temperature distribution. Moreover, the skin friction coefficient decreases as the squeezed flow index is increased. [ABSTRACT FROM AUTHOR]

Highlights: What are the main findings? The problem of 2-D Prandtl nanofluid past a moving wedge is investigated in detail; Tri-hybrid nanoparticles are considered here; Heat and mass transmission evaluations are conducted in the presence of endothermic/exothermic chemical reactions; The moving wedge is considered; What is the implication of the main finding? LobattoIIIA scheme is implemented for the numerical solution of modeled PDEs. Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick's second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter α brings about a decrement in fluid velocity and augmentation in thermal conductivity ϵ , thermal radiation R d , thermophoresis parameter N t and endothermic/exothermic reaction Ω , and fitted rate constant n accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature. [ABSTRACT FROM AUTHOR]

Nanotechnology is a fundamental component of modern technology. Researchers have concentrated their efforts in recent years on inventing various algorithms to increase heat transmission rates. Using nanoparticles in host fluids to dramatically improve the thermal properties of ordinary fluids is one way to address this problem. The article deals with the bio-convective Walter's B nanofluid with thermophoresis and Brownian diffusion through a cylindrical disk under artificial neural networks (ANNs). In addition, the thermal conductivity, radiation, and motile density of microorganisms are taken into consideration. The Buongiorno model is utilized to investigate the properties of nanofluids in motile microorganisms. By using appropriate similarity variables, a dimensionless system of a differential system is attained. The non-linear simplified system of equations has been numerically calculated via the Runge–Kutta fourth-order shooting process. The consequences of flow parameters on the velocity field, temperature distribution, species volumetric concentration, and microorganism fields are all addressed. Two distinct artificial neural network models were produced using numerical data, and their prediction performance was thoroughly examined. It is noted that according to the error histograms, the ANN model's training phase has very little error. Furthermore, mean square error values calculated for local Nusselt number, local Sherwood number, and local motile density number, parameters were obtained as 3.58 × 10 − 3 , 1.24 × 10 − 3 , and 3.55 × 10 − 5 , respectively. Both artificial neural network models can predict with high accuracy, according to the findings of the calculated performance parameters. [ABSTRACT FROM AUTHOR]

The thermal conductivity of the porous materials is dependent on the temperature in a range of applications, including nuclear reactors and fossil fuel sources. The LTNE (local thermal nonequilibrium) model is widely used to study the thermal interactions between solid and fluid phases inside the porous media. The majority of the prior LTNE models assumed the constant thermal conductivities of both the fluid and solid phases, but in actual practice, the thermal conductivities depend on the temperature variations. In the current study, the effective thermal conductivities of the fluid and solid phases in the porous channel are considered as the functions of the respective temperatures by implementing the LTNE model. The Biot number is assumed to vary linearly, quadratically and sinusoidally along with the channel height. The thermal conductivity variation parameter (δ) , porosity () , the ratio of fluid and solid phase thermal conductivities (k = k f k s ) and heat generation parameter (β) are considered as the main operating parameters. A system of ordinary differential equations has been derived and solved numerically under the above-mentioned conditions which is the generalization of the constant thermal conductivities of both the phases. The present results are validated with the already published results for the constant thermal conductivity and variable Biot number with the LTNE model. The obtained results show that the maximum heat transfer between the two phases is observed by taking Bi as the linear increasing function of η i.e., Bi (η) = 5 0 (1 + η) and correspondingly, it provides the highest values of Nusselt number. The Nusselt number increases with the decrement in thermal conductivity variation parameter (δ) , heat generation parameter (β) and ratio of fluid to solid phase conductivities (k). A complex relationship has been observed between the porosity and the Nusselt number. [ABSTRACT FROM AUTHOR]

The purpose of this work is to investigate, within the context of extended thermo-diffusion theory, the transient thermo-diffusion responses for a half-space with variable thermal conductivity and diffusivity. The half-bounding space's surface is traction-free and exposed to a time-dependent thermal shock, but the chemical potential is believed to be a known function of time. Because the nonlinear equations are complicated, the finite element technique is applied to solve these equations. Numerical outcomes are produced and graphically illustrated. The effects of varying thermal conductivity and diffusivity on the response are studied using parameter studies. Using the results of this study, researchers hope to understand better how thermo-mechanical fields interact in real materials. By ignoring the new parameter, a comparison of numerical results and analytical cases is produced, and the behavior of physical quantities for numerical solutions is studied to ensure that the proposed technique is accurate. [ABSTRACT FROM AUTHOR]

In this paper, the influence of the transverse magnetic field is unraveled on the development of steady flow regime for an incompressible fluid in the boundary layer limit of a semi-infinite vertical plate. The sensitivity of real fluids to changes in temperature suggests a variable thermal conductivity modeling approach. Using appropriate similarity variables, solutions to the governing nonlinear partial differential equations are obtained by numerical integration. The approach used here is based on using the shooting method together with the Runge-Kutta-Fehlberg integration scheme. Representative velocity and temperature profiles are presented at various values of the governing parameters. The skin-friction coefficient and the rate of heat transfer are also calculated for different parameter values. Pertinent results are displayed graphically and discussed. It is found that the heat transfer rate improves with an upsurge in a magnetic field but lessens with an elevation in the fluid thermal conductivity.

The current research article explores the bio-convection magnetized Carreau-nanofluid flow utilizing activation energy and magnetic dipole. Magnetic nanomaterials have significant effect on the magnetized behavior of ferrofluids which leads to robust the changes in fluid viscosity and thermophysical characteristics. Darcy-Forchheimer flow model is also present. Thermal conductivity of nanofluid is dependent on the temperature. Brownian motion and thermophoresis aspects are also accounted. The PDEs are reduced to set of ODEs via appropriate functions. Numerical solutions are achieved with the help of the famous bvp4c solver a built-in function in MATLAB. Numerous flow parameters are graphically and numerically presented with physical significance. The proposed findings could be useful for applications of extrusion systems, organic compounds, improved energy generation and improved manufacturing techniques.

This investigation examines the Williamson nanofluid flow over an exponentially stretched surface with variable thickness. Cattaneo-Christov double diffusion (CCDD) heat flux model is applied while examining two cases of heat transfer, i.e., prescribed exponential surface temperature (PEST) and prescribed exponential heat flux (PEHF). A mathematical model of the problem based on momentum, mass, and energy conservation. The governing non-linear partial differential equation (PDEs) are converted into non-linear ordinary differential equations (ODEs) via similarity transformations. The velocity, temperature, and concentration profiles are obtained numerically.Additionally, the impacts of numerous physical parameters of engineering significance are visually depicted through graphs and tables. It is noted that by raising the thermal relaxation parameter γ1, the temperature profile decreases. When the concentration relaxation parameter γ2 rises, then the concentration distribution also decays. When the magnetic parameter M increases, then the velocity profile decreases. For the selected numeric values of the Prandtl number Pr, the temperature profile decreases for both PEST and PEHF cases.

In this paper, the effects of various fluid properties on two-dimensional unsteady biomagnetic fluid flow (blood) and heat transfer over a stretching sheet under the appearance of a magnetic dipole is investigated. The governing boundary layer equations are simplified via suitable transformation which are then solved using the bvp4c function approach in MATLAB software. The results indicate that fluid velocity and temperature are greatly influenced by the ferromagnetic interaction parameter. With increasing ferromagnetic number, fluid velocity drops but temperature increases. It is also found that the coefficient of skin friction and Nusselt number increase with an increase in values of thermal conductivity parameter. For certain parameter values, the results are also compared with previously published studies and they are found to be in acceptable agreement.

Here flow for radiative hybrid-nanomaterial (MgO + M o S 2) satisfying Darcy-Forchheimer relation is addressed. Ethylene glycol C 2 H 6 O 2 is utilized as a base fluid. Magnesium oxide (M g O) and Molybdenum disulfide (M o S 2) are considered as distinct nanoparticles. Thermal expression is examined through heat generation and viscous dissipation. Analysis for Cattaneo-Christov theory is carried out. Condition for melting heat is deliberated. Entropy generation is examined. Variable thermal conductivity of hybrid nanomaterial is taken. Suitable transformations are implemented to obtain nonlinear dimensionless systems. Optimal homotopy analysis method (OHAM) is implemented for computations. Temperature, velocity and entropy generation are scrutinized physically. Nusselt number and skin friction are discussed. Conclusion synthesis salient points. Present work is relevant in metallurgical engineering and polymer processing. The findings conclude that Forchheimer number correspond to decline in velocity. Entropy rate and thermal field have similar trend for heat generation variable. A decrease in velocity against melting variable is noted. Temperature increases for variable thermal conductivity and thermal relaxation parameters. Entropy optimization improved for Brinkman number. Skin friction decays for porosity parameter and Forchheimer number. Skin friction improves for melting variable and Forchheimer number. Entropy augments against higher thermal relaxation time. Higher melting variable lead to an enhancement for Nusselt number. There is an improvement for radiation through Nusselt number and temperature. [ABSTRACT FROM AUTHOR]

Current research underscores entropy investigation in an infiltrating mode of Sutterby nanofluid (SNF) stream past a dramatically expanding flat plate that highlights Parabolic Trough Solar Collector (PTSC). Satisfactory likeness factors are utilized to change halfway differential conditions (PDEs) to nonlinear conventional differential conditions (ODEs) along with relating limit requirements. A productive Keller-box system is locked in to achieve approximated arrangement of decreased conventional differential conditions. In the review, two sorts of nanofluids including Copper-sodium alginate (Cu-SA) and Gold-sodium alginate (Au-SA) are dissected. Results are graphically plotted as well as talked about in actual viewpoints. As indicated by key discoveries, an improvement in Brinkmann, as well as Reynolds number, brings about expanding the general framework entropy. Sutterby nanofluid boundary improves heat rate in PTSC. Additionally, Copper-sodium alginate nanofluid is detected as a superior thermal conductor than Gold-sodium alginate nanofluid. Further to that, the reported breakthroughs are beneficial to updating extremely bright lighting bulbs, heating and cooling machinery, fiber required to generate light, power production, numerous boilers, and other similar technologies. [ABSTRACT FROM AUTHOR]

This study is carried out to analyze the Rabinowitsch fluid flow through a non-uniform channel between two flexible and symmetric inclined channel under peristaltic motion. Considering long wavelength and low Reynolds number assumptions the governing equations are simplified and thus obtained coupled non-linear governing equations are tackled via analytical method. The Graphs are drawn for the relevant parameters to explore the characteristics of the velocity field, temperature, and streamlines. The temperature profile are the increasing function of cofeeicent of viscosity and Thermal condectivity. [ABSTRACT FROM AUTHOR]

This paper deals with an unsteady magnetohydrodynamic (MHD) two-dimensional (2D) second-grade fluid flow towards a permeable exponentially stretching surface with homogeneous–heterogeneous reactions. The non-uniform heat source/sink, variable thermal conductivity and thermal radiation are considered to analyse the thermal attributes. The velocity slip effect is also taken into consideration at the boundary of the surface. The modelled equations of motions and energy are transformed into non-linear ODEs by suitable transformations. The Matlab Bvp4c approach is employed for the numerical solution of the equations. The impacts of various parameters are scrutinised using graphs. The physical quantities of interests such as Sherwood number, Nusselt number and skin friction are presented in the form of graphs and tables and discussed. The velocity profile diminishes by enhancing the values of the parameter of the porous medium. The temperature field rises with larger values of thermal radiation parameters. Decay in concentration profile is noted when the influence of homogeneous–heterogeneous reactions becomes larger. By increasing the values of the second-grade fluid parameter, the magnetic field parameter and the porous medium, the coefficient of skin friction increases, while it reduces by enhancing the values of the unsteady parameter. [ABSTRACT FROM AUTHOR]

This study comprises the flow of Ti6Al4N nanoparticle alloy allowed to flow within the microchannel kept at a certain angle. Engine oil is the base fluid in which nanodimensional particles are immersed. The flow is caused by the influence of linear and exponential heat sources. The microchannel is a permeable media with the suction/injection at the microchannel extremes. During the flow, the impact of the microstructure of these particles is concerned, thus reporting the rotational interaction amidst the particles. The obtained nonlinear equations are solved using the effective numerical method, namely, finite difference code improved by using the Lobatto IIIA formula and the findings are discussed using the graphs. The results attained claim that linear and exponential space‐dependent heat source parameter has augmented the thermal profile. Also, consideration of the couple stress of the fluid is known to retard the flow. [ABSTRACT FROM AUTHOR]

We consider a stochastic heat equation with variable thermal conductivity, on infinite domain, with both deterministic and stochastic source and with stochastic initial data. The stochastic source appears in the form of multiplicative generalized stochastic process. The generalized stochastic process appearing in the equation could be a generalized smoothed white noise process or any other generalized stochastic process of a certain growth. In our solving procedure we use regularized derivatives and the theory of generalized uniformly continuous semigroups of operators. We establish and prove the result concerning the existence and uniqueness of solution within certain generalized function space. We justify our procedure by proving that, under certain conditions, the operators of non-regularized and the corresponding regularized problems are associated. [ABSTRACT FROM AUTHOR]

This article presents the transport of thermal energy and mass in the mixed convection steady planar Couette flow of power-law nanofluid with variable thermal conductivity through a permeable microchannel. The entropy production deliberation here is to investigate the irreversibility aspects. The momentum equation has been made by the permeability of the porous medium, Hall current effect, thermal, and solutal bouncy force. The mathematical model for the thermal energy has been formulated by Ohmic dissipation, Brownian motion, temperature-dependent thermal conductivity, and thermophoresis. The microchannel boundaries retain the no-slip boundary conditions. The concentration formulation has been made by nanoparticle injection rate and chemical reaction. The momentum, energy, and solutal formulations have been numerically cracked by means of Runge–Kutta–Fehlberg fourth fifth-order numerical procedure. The applied Hall current effect generates the fluid flow in the transverse direction. The flow along both axial and transverse direction enhances with thermal and solutal Grashof number and diminutions with permeability of the porous medium. Optimum magnitude of thermophoresis and Brownian motion amplifies the thermal energy of the shear thinning fluid. Concentration field exhibits the opposite nature with the nanoparticle injection rate parameter and chemical reaction parameter. Hall current parameter enhances the irreversibility of the Newtonian nanofluid. [ABSTRACT FROM AUTHOR]

The flow via needle has prominent applications in the modern world such as nano-wires, microstructure electric gadgets, microsensors, surgical instruments and biological treatments. The present investigation focuses on boundary layer heat, flow, and mass transfer of MHD tangent hyperbolic fluid (conveying tiny particles) via a thin needle under the impacts of activation energy, non-constant thermal conductivity, heat source, and nonlinear thermal radiation. In the description of the Buongiorno model, the significant features of Brownian motion and thermophoresis have been included. Adopting appropriate transformations to the given problem specified by the set of partial differential equations yields the dimensionless form of ordinary differential equations After that, these obtained ODEs are solved numerically via MATLAB bvp4c. A comparative result with previous findings is conducted. Physical parameters’ impact on flow rate, heat, and concentration is exhibited and explained in depth. The main findings of this study are that flow patterns reduce as the magnetic parameter and the Weissenberg number grow. Higher values of Brownian motion, heat source/sink, nonlinear radiation, and thermophoretic parameter improve the thermal profile. Moreover, the rate of heat transfer for the variable property case is significantly improved. Concentration profiles reduce as the thermophoresis parameter and chemical reaction parameter grow but improve as the activation energy and Brownian motion parameter rise. The percentage increase in Sherwood number is 35.07 and 5.44 when the thermophoresis takes input in the range 0 ≤ Nt ≤ 0.2 and activation energy parameters 0 ≤ E ≤ 0.2. The Weissenberg number and power-law index parameters are all designed to boost the Sherwood number.

In this paper, the heat transfer equation is coupled to Navier–Stokes equations for a steady vertical channel. The objective of the present study is to investigate the electrically conducting viscous fluid with isothermal wall conductions with variable properties. The combined effects of temperature dependent thermal conductivity and temperature dependent viscosity are examined. The analysis is presented in dimensionless form and the resultant equations are obtained both analytically (Perturbation method) and numerically by fourth order R–K​ Fehlberg with shooting technique. The dimensionless parameters that influence the temperature field and the transverse velocity field are variable thermal conductivity parameter −0.5≤bk≤0.5, variable viscosity parameter −0.5≤bv≤0.5, applied electric field parameter E=−1,0,1, Hartman number 1≤M≤3, buoyancy parameter 0≤N≤1.5and wall temperature ratio parameter −2≤m≤2.

Heat is absorbed from radiations of the sun by a solar collector, concentrated, and then transmitted to an active nanofluid. The flow of Casson nanofluid is utilized in Parabolic Trough Solar Collector (PTSC) in the present analysis over an infinite and porous sheet. Ordinary differential equations are derived in nonlinear form and solved using suitable similarity transformation reducing into boundary conditions. Keller box method was employed to solve the system of ODEs. Results for nanofluids of Copper-engine oil (Cu-EO), as well as Iron (II, III) oxide-engine oil (Fe3O4-EO), were examined and detailed. With the help of the induced magnetic factor, the rate of heat transfer decreased while the parameter of skin resistance increased prominently. While using Cu/Fe3O4-EO as base fluid, the rate of heat transfer is an important factor. Total enhancement in the thermal efficiency of Cu-EO on Fe3O4-EO has a minimum value of 2.7% while the maximum value is 18.5%.

The thermal analysis of the annular fin is performed by applying the differential transformation method. The thermal conductivity of the annular fin has been considered as a function of temperature. The effects of non-dimensional parameters, namely thermal conductivity and thermo-geometric fin parameters on the fin efficiency and temperature distribution are determined. Obtained results from the differential transformation method are also compared with the exact analytical results and the results of the finite difference method in the constant thermal conductivity condition. It has been concluded that the differential transformation method provides accurate results in the solution of non-linear problems. [ABSTRACT FROM AUTHOR]

Researchers have commonly known non-Newtonian materials for their extensive technical and industrial uses including coal slurries, clay mixture, food dispensing, paper manufacturing, nutritional preparation, wiring coatings, polymers, cosmetics, oil recovery, rubber, crystal growth and plastic sheeting. The goal of presented research is to analyze bioconvectional second-grade nanoliquid flow with implications of thermal conductivity and motile microorganism across three-dimensional sheet. A transmuted construction is formed in the ordinary differential method by the use of suitable similarity functions. Governing relations of present flow problem are presented graphically and solved numerically by utilizing built-in MATLAB computational tool with the help of the famed numerical shooting method bvp4c (Lobatto IIIa Formula). The influences of physical parameters like activation energy parameter, bioconvection Lewis number, Lewis number, Peclet number, thermophoresis number, mixed convective number, buoyancy ratio number and Brownian motion number via the velocity profile, temperature concentration, volumetric concentration and motile concentration are discussed in detail. The current research has major applications in medical, contemporary aerospace technologies and importance to energy systems. The results designate that x-component of skin friction is enhanced for larger values of bioconvection Rayleigh number by 25%. The y-component of skin friction is enhanced for larger values of mixed convection parameter by 10%. Furthermore, local Nusselt number is upgraded for growing values of thermal Biot parameter by 57%. [ABSTRACT FROM AUTHOR]

The porous fin of radial profile is considered in the current analysis along with the radiation and thermal-dependent internal heat generation condition. In addition, two different cases have been examined based on the linear dependency and exponential dependency of thermal conductivity on temperature. The Darcy's law is used to study the porous nature of fin. The modeled governing equation is a second-order nonlinear ordinary differential equation and is solved via Runge–Kutta–Fehlberg fourth–fifth-order method. The important terms are grouped as dimensionless parameters and discussed their influence on the heat transfer rate and thermal stresses of the fin. The thermal stresses like radial stress and tangential stress are addressed comprehensively and interpreted graphically. Also, the fin efficiency is defined and discussed graphically. It is found that the tangential stress shows higher compression near fin base region and larger tensile stress near tip radius. [ABSTRACT FROM AUTHOR]