Nonlinear Boussinesq Approximation Research Articles

Repercussion of quadratic density variation on nonlinear mixed convective Darcy–Forchhimer Al2O3, Cu\\EG flow over an inclined plate with exponential heat source and Arrhenius equation

Generating and controlling energy at high temperatures is extremely challenging in solar energy applications with hybrid nanofluids (HNFs). This challenge is tackled with nonlinear changes in density with temperature and concentration. Hence, a nonlinear Boussinesq approximation is taken on Darcy – Forchhimer hybrid flow containing aluminium oxide ( A l 2 O 3 ) and copper ( Cu ) nanoparticles with base fluid Ethylene Glycol (EG) over an inclined plate at an angle of ξ = π 6 . The physical model is supported by a space-based exponential heat source (EHS) along with a temperature-based heat source (THS) in the energy equation and Arrhenius equation in diffusion relation with suction and blowing on the wall. The regulating equations are transformed into standard differential equations using the similarity conversions, and these equations are subsequently solved in MAPLE 2022. The thermal field is affected positively by EHS and THS parameters, which fulfil the purpose of including these parameters in the flow model. The rate of heat transport increment for Q E parameter by 1.04% for HNF whereas 1.06% for NF when Su > 0 . Also, Su < 0 heat transfer rate increases by 3.68% for HNF whereas 3.75% for NF. As A l 2 O 3 , Cu ∖EG HNF move from suction to injection, the Nusselt number reduces by more than 50%.

Mixed convective magnetohydrodynamic and thermally radiative flow of reactive couple stress MWCNT–Ag/C2H6O2 hybrid nanofluid in a porous vertical channel: Entropy analysis

This paper is concerned with the analysis of the mixed convective magnetohydrodynamic (MHD) flow of a reactive couple stress multi-walled carbon nanotube −Ag/C2H6O2 hybrid nanofluid in a porous vertical channel subjected to quadratic thermal radiation along with a uniform inclined magnetic field applied to the channel walls. The flow is driven by the pressure gradient force and the buoyancy force, which is modeled based on the nonlinear Boussinesq approximation. The temperature-dependent reaction rate of the reactant molecule is derived using the Arrhenius law. The momentum and energy equations that govern the system are modeled in consideration of slip and convective conditions. The governing equations are non-dimensionalized by applying relevant dimensionless parameters and are solved using the homotopy analysis method (HAM). To analyze the irreversibilities in the system, the entropy generation number and the Bejan number are defined. Different important physical parameters developing in the system are considered for analysis, and their effects are scrutinized on the velocity and temperature profiles along with entropy generation. The emphasis is given to the concentration of nanoparticles along with the parameters arising due to the reactions of the fluid, buoyancy force, inclined magnetic field, thermal radiation, and porous material. The analysis reveals that the velocity and temperature of the fluid lowers with a higher concentration of nanoparticles, radiation parameter, and Hartmann number, whereas develops for the higher slip parameters and inclination of the magnetic field. The entropy generation rate increases with rising slip parameters and depletes for higher nanoparticle concentration, radiation parameter, Hartmann number, and inclination angle. The irreversibility in the system remains dominant due to heat transfer with higher Frank-Kameneskii and activation energy parameters, Hartmann number, and angle of inclination.

Nonlinear free convective with longitudinal slits in the presence of super-hydrophobic and non-hydrophobic microchannels in a suspension of nanoparticles: Multi-Linear Regression Analysis

Super hydrophobic microchannels have extremely high water repellency, and such a property is reliant on a set of factors, namely the surface construction and the surface energy. The surface energy can be depressed either by exhausting a chemical film that is coated or stuck to the surface or by adjusting the existing surface interaction or by producing micro- and nanotextures. Further, due to the latter reason of inducing super hydrophobic properties, a study of manufacturing processes to produce surface textures becomes critical to the understanding of the area. The latest generative manufacturing techniques, such as 3-D (three-dimensional) printing, laser machining, and so on are new-generation processes that can be used to write over surfaces at different resolutions. Viewing into this, the natural convection of conductive nanofluids in vertical slot micro-channels with super-hydrophobic slips and temperature jumps, the non-linear Boussinesq approximation approach provides an accurate solution. One inner surface of the microchannel surface has been physically modified to exhibit temperature jumps and super-hydrophobic velocity slips. The transverse magnetic field indicates the direction of flow. In two different physical situations, it is possible to get a single answer. Type I involves heating the super-hydrophobic surface without heating the non-slip surface, and Type II involves heating the non-slip surface without heating the super-hydrophobic surface. Velocity slip reduces the Type I Nusselt number and increases the Type II Nusselt number in both situations. The temperature jump factor has the opposite effect. In contrast to the change in linear density with temperature, the non-linear density change with temperature causes an increase in flow and velocity. It is observed that more slip coefficient corresponds to less Nusselt number and more slip velocity, especially at larger magnetic parameter values to increase the heat transfer rate from the microchannel walls. It is recommended to use Al2O3-water nanofluid the nanofluid composed of nanoparticles with higher thermal conductivity. Applications of the subject include anti-wetting micro technology, electrolytic cell maintenance, micro-hydraulic devices, and micro-electronic heat dissipation.

Study of nonlinear quadratic convection on magnetized viscous fluid flow over a non-Darcian circular elastic surface via spectral approach

The present work investigates quadratic convection on magnetized viscous fluid flow on a circular elastic surface susceptible to Rosseland nonlinear thermal radiation and the nonlinear Boussinesq approximation. The flow is traversing through a Darcy-Brinkman-Forchheimer porous material. The energy equation investigates the implications of heat source/sink, Joule heating, and viscous dissipation. Utilizing suitable similarity variables, the hypothesized mathematical modelling is converted into nonlinear systems. Numerical solutions of nonlinear differential equations are computed using the spectral technique, often recognized as the spectral local linearization method (SLLM). The proposed approach SLLM is based on decoupling and linearizing systems of linear equations using a basic linearization process combined with spectral collocation linearization. The computational findings for nondimensional parameters are reported for the velocity and temperature profiles. As a particular case of our investigation, we also perform a comparison with published results.

Entropy generation and thermal analyses of a Cross fluid flow through an inclined microchannel with non‐linear mixed convection

AbstractThe temperature difference of the various applications such as microchannel heat exchangers, microelectronics, solar collectors, automotive systems, micro fuel cells, and microelectromechanical systems (MEMS) is relatively large. The buoyancy force (mixed convection) modeled by the conventional Boussinesq approximation is inadequate since the density of the operating fluids fluctuates non‐linearly with the temperature difference. Therefore, the mixed non‐linear convective transport of the flow of Cross fluid through three different geometric aspects (horizontal, vertical, and inclined) of the microchannel under the non‐linear Boussinesq (NBA) approximation is investigated. Mechanisms of internal heat source, Rosseland radiative heat flux, and frictional heating are incorporated into the thermal analysis. The mathematical construction is proposed using the Cross fluid model for a steady‐state, and subsequent non‐linear differential equations are deciphered by the spectral quasi‐linearization method (SQLM). Graphical sketches were constructed and displayed that explore the stimulus of various key parameters on Bejan number, velocity, temperature, and entropy generation. It is found that the Bejan number and entropy production improved due to the non‐linear density temperature variation. The convective heating boundary conditions augment the entropy production. The pressure gradient accelerates the transport of fluid in a microchannel. Furthermore, among three different geometries, the velocity, entropy production, and temperature are the highest for the vertical microchannel.

Sensitivity analysis of nonlinear convective heat transport of a hybrid nanoliquid sandwiched by micropolar liquid using RSM

Petroleum and polymer industries utilize a multilayer flow model for efficient heat transfer. In such applications, the linear Boussinesq approximation is not recommended as the devices used in such experiments would work at moderate or extremely high temperatures. Therefore, the flow and heat transfer in a multilayer vertical channel with a magnetic field and the nonlinear (quadratic) Boussinesq approximation are investigated, with the central region filled with a hybrid nanoliquid and the outer regions filled with an oil-based micropolar liquid. The effects of Joule heating and viscous dissipation are taken into account. The effective viscosity and thermal conductivity are modeled using the experimental data based Esfe model. The modeled equations are coupled and nonlinear, they are solved using the Differential Transform Method (DTM). Results are analyzed for various values of the material parameter, quadratic convection parameter, Brinkman number, mixed convection parameter, Hartmann number, nanoparticle volume fraction (NVF) on Nusselt number, skin friction, velocity, microrotation velocity and temperature distributions. Additionally, multi-objective optimization of Nusselt number and friction factor is performed for three different levels of the quadratic convection parameter , material parameter and the NVF using the Response Surface Methodology (RSM). The material parameter diminishes the velocity whereas enhances the microrotation velocity. Also, the quadratic convection parameter increases the flow field. Sensitivity computations reveal that the Nusselt number is more sensitive to material parameter and NVF whereas the skin friction coefficient is more sensitive to quadratic convection parameter.

MHD Free-Convective Couette flow in a Vertical Porous Microchannel Using Non-Linear Boussinesq Approximation

An analytical solution for free convection flow of an electrically conducting fluid in a vertical micro-porous-channel, in the existence of transversely applied magnetic-field and nonlinear Boussinesq approximation is carried out in this article. The governing equations representing stated objective are obtained and solved analytically using method of undetermiend coefficients and direct integration. Pictorial and tabularlar representions of solutions obtained are carried out, so as to ascertain the role of various governing parameters entering flow formation. During the course of numerical simulation of results, it is found that the volumetric flow rate increases with increase in Couette flow parameter, asymmetric heating parameter and suction/injection parameter but decreases with increase in nonlinear Boussinesq approximation parameter.

Study of multilayer flow of a bi-viscous Bingham fluid sandwiched between hybrid nanofluid in a vertical slab with nonlinear Boussinesq approximation

Bi-viscosity Bingham plastic fluids are used to understand the rheological characteristics of pigment–oil suspensions, polymeric gels, emulsions, heavy oil, etc. In many industrial and engineering problems involving high-temperature situation, a linear density-temperature variation is inadequate to describe the convective heat transport. Therefore, the characteristics of the nonlinear convective flow of a bi-viscous Bingham fluid (BVBF) through three layers in a vertical slab are studied. The two outer layers of the oil-based hybrid nanofluid and the intermediate layer of BVBF are considered. The thermal buoyancy force is governed by the nonlinear Boussinesq approximation. Continuity of heat flux, velocity, shear stress, and temperature are imposed on the interfaces. The governing equations are derived from the Navier–Stokes equation, conservation of energy, and conservation of mass for three layers. The nonlinear multi-point (four-point) boundary value problem is solved using the differential transform method (DTM). Converging DTM solutions are obtained, and they are validated. The entropy equation and Bejan number were also derived and analyzed. It is established that the nonlinear density–temperature variation leads to a significant improvement in the magnitude of the velocity and temperature profiles due to the increased buoyancy force, and as a result, the drag force on the walls gets reduced. The drag force on the slab gets reduced by decreasing the volume fraction of nanoparticles. Furthermore, nonlinear convection and mixed convection give rise to an advanced rate of heat transport on the walls and thereby to an enhanced heat transport situation.

Sensitivity computation of Von Kármán’s swirling flow of nanoliquid under nonlinear Boussinesq approximation over a rotating disk with Stefan blowing and multiple slip effects

Von Kármán’s rotatory motion of liquids finds its relevance in an extensive range of fields, including filter systems, heat exchangers, heat/mass transfer applications, rotatory machines, computer storage devices, combustion, geophysical applications, etc. The thermal difference in applications such as heat/mass transfer, heat exchangers and rotating machines is substantial, in those cases; the linear Boussinesq approximation is inadequate for modeling the density change due to the solute and the thermal differences. Therefore, in this paper computational study of the Von Kármán's rotatory dynamics of nanoliquid over a disc with thermal and solute buoyancy forces is presented. The nonlinear Boussinesq approximation is valid. The significance of Stefan blowing, multiple slips, Brownian movement of nanoparticles and thermophoresis are also analyzed. The similarity procedure and numerical method are employed to treat the prevailing nonlinear partial differential equations. The rates of heat and mass transport of the swirling flow system are optimized using the Response Surface Methodology. Sensitivity functions are estimated to explore the sensitivity of the rate of heat/mass transfer of system towards key factors. Among the thermophoresis and Brownian motion, the thermophoresis has the maximum control on the thermal field. The maximum heat and mass transfer rates are and , respectively, with the optimal combination of key parameters is , and .

Nonlinear Boussinesq and Rosseland approximations on 3D flow in an interruption of Ternary nanoparticles with various shapes of densities and conductivity properties

&lt;abstract&gt; &lt;p&gt;In current days, hybrid models have become more essential in a wide range of systems, including medical treatment, aerosol particle handling, laboratory instrument design, industry and naval academia, and more. The influence of linear, nonlinear, and quadratic Rosseland approximations on 3D flow behavior was explored in the presence of Fourier fluxes and Boussinesq quadratic thermal oscillations. Ternary hybrid nanoparticles of different shapes and densities were also included. Using the necessary transformation, the resulting partial differential system is transformed into a governing ordinary differential system, and the solution is then furnished with two mixed compositions (Case-Ⅰ and Case-Ⅱ). Combination one looked at aluminum oxide (Platelet), graphene (Cylindrical), and carbon nanotubes (Spherical), whereas mixture two looked at copper (Cylindrical), copper oxide (Spherical), and silver oxide (Platelet). Many changes in two mixture compositions, as well as linear, quadratic, and nonlinear thermal radiation situations of the flow, are discovered. Case-1 ternary combinations have a wider temperature distribution than Case-2 ternary mixtures. Carbon nanotubes (Spherical), graphene (Cylindrical), and aluminum oxide (Platelet) exhibit stronger conductivity than copper oxide (Spherical), copper (Cylindrical), and silver oxide (Platelet) in Case 1. (Platelet). In copper oxide (Spherical), copper (Cylindrical), and silver (Platelet) compositions, the friction factor coefficient is much higher. The combination of liquids is of great importance in various systems such as medical treatment, manufacturing, experimental instrument design, aerosol particle handling and naval academies, etc. Roseland's quadratic and linear approximation of three-dimensional flow characteristics with the existence of Boussinesq quadratic buoyancy and thermal variation. In addition, we combine tertiary solid nanoparticles with different shapes and densities. In many practical applications such as the plastics manufacturing and polymer industry, the temperature difference is remarkably large, causing the density of the working fluid to vary non-linearly with temperature. Therefore, the nonlinear Boussinesq (NBA) approximation cannot be ignored, since it greatly affects the flow and heat transport characteristics of the working fluid. Here, the flow of non-Newtonian elastomers is controlled by the tension of an elastic sheet subjected to NBA and the quadratic form of the Rosseland thermal radiation is studied.&lt;/p&gt; &lt;/abstract&gt;

Impact of nonlinear thermal radiation on nonlinear mixed convection flow near a vertical porous plate with convective boundary condition

This study presents similarity solution for boundary layer flow near a vertical porous plate with combined effects of nonlinear density variation with temperature and nonlinear thermal radiation. To accurately predict the flow phenomenon near the porous plate, the convective boundary condition is considered at the plate surface. The two-dimensional partial differential equations are transformed to ordinary differential equations through the similarity transformation. The resulting ordinary differential equations are solved numerically in Maple software using the Runge–Kutta–Ferhlberg fourth-fifth order (RKF45) algorithm. The influence of the inherit parameters like the nonlinear thermal radiation parameter, suction/injection parameter, nonlinear Boussinesq approximation parameters, local convective heat transfer parameter, local Grashof number, and Prandtl number governing the fluid behaviour is discussed. We found that the rate of heat transfer improves with the injection and nonlinear thermal radiation parameter whereas decreases with suction, local convective heat transfer parameter and local Grashof number when air and mercury are used as the working fluids. Furthermore, with the growth in the values of local Grashof number, convective heat transfer parameter and nonlinear thermal radiation parameter and in the presence of suction/injection, the porous plate surface friction witnessed an observable growth. Suction growth plays a supportive role on the velocity curve near the porous plate but a contrary trend is seen in the free stream. The temperature distribution also decays with suction augment. Injection growth is inversely proportional to the velocity profile near the porous plate but we recorded the opposite phenomenon in the free stream.

Unsteady flow analysis of Maxwell fluid with temperature dependent variable properties and quadratic thermo-solutal convection influence

The current work analyzed the surface effect on the motion of Maxwell fluid with variable transport properties (viscosity, diffusivity, thermal conductivity, and electrical field) in porous, magnetized, radiative, and nonuniform (quadratic) convection processes. In this study, the flow examination modeled the motion of Maxwell fluid under MHD and variable properties influence. The flow field solutions were obtained numerically via the Spectral Collocation Approach (SCM) and justified with Galerkin Weighted Residual Method (GWRM). It was shown that the flat surface dominates the flow fields, a rise in variable viscosity diminished the fluid momentum, variable thermal conductivity and diffusivity enhance the consumption of more fluid particles, the velocity field is promoted to a hike in nonlinear Boussinesq approximation numbers, while sheet variable thickness number is aimed at downsizing the flow distributions. Moreover, the current analysis is applicable in metal spinning, polymer extrusion, machine design, architecture, aluminum aircraft skin, and structural steel beam where the extrudate materials are stretched into a sheet.

Mixed convective transport in inclined porous open arc-shaped enclosures saturated by nanofluids using a second-order Boussinesq approximation

Numerical simulations are performed for the mixed convective transport in an inclined open arc-shaped channel filled by isotropic porous media using nanofluids. The Darcy regime is considered and the non-linear Boussinesq approximation (NBA) is applied for the mixture density. The vorticity-stream function scheme based on the finite volume method in case of the non-orthogonal grids is conducted to solve the dimensionless governing system of equations. The local thermal equilibrium model between the mixture and the porous medium is taken into account and water is considered as a base fluid while the Al2O3 is assumed as nanoparticles. The computations are carried out for various values of the curvature parameter ε ranging from 0.1 to 0.5, the Darcy number Da ranging from 10−2 to 10−5, the Rayleigh number ranging from 104 to 107, the Reynolds number Re ranging from 10 to 5×102, the inclination angle γ ranging from 0 to π2, the nonlinear Boussinesq parameter ξ ranging from 0 to 3 and the nanoparticles volume fraction is varied from 0 % to 4 %. The results reveal that an increase in the nonlinear Boussinesq parameter enhances the average Nusselt number regardless of the values of the inclination angle.

Heat transfer of TiO2 − EG nanoliquid with active and passive control of nanoparticles subject to nonlinear Boussinesq approximation

In this study, the buoyancy-driven two-dimensional flow of a nanoliquid past a vertical plate subject to quadratic Rosseland thermal radiation and quadratic thermal convection (quadratic Boussinesq approximation) is investigated. The working liquid is ethylene glycol containing titania nanoparticles. The consequences of aggregation of nanoparticles are included using the modified Maxwell-Bruggeman and Krieger-Dougherty models for thermal conductivity and viscosity respectively. The analysis is performed under active and passive control of nanoparticles (NPs). To simulate the nanoliquid, the modified Buongiorno model is used which includes effective thermophysical properties and two significant slip mechanisms (nanoparticle random motion and thermophoresis). The phenomenon of physical flow is demonstrated with the help of a partial differential equation (PDE) system that uses conservation laws and the thermophysical properties of nanoparticles. Nonlinear PDEs related to the nanoliquid heat transport are transformed into ordinary two-point BVP (boundary value problem)and the obtained system has been solved numerically. It is found that the nanoparticle aggregation and quadratic thermal radiation aspects enhance the temperature field. Furthermore, the quadratic Boussinesq approximation aspect was found to hasten the heat transport rate at the plate.

Exponential heat source effects on the stagnation‐point heat transport of Williamson nanoliquid with nonlinear Boussinesq approximation

AbstractThe nonlinear two‐point partial differential boundary value problem associated with the nano‐pseudoplastic material flow and heat transport subject to nonlinear Boussinesq approximation is computed and explored statistically. Heat transportation features are analyzed by the consideration of an exponential space‐related heat source and the Buongiorno model of nanofluids. The boundary‐driven expressions of the physical phenomenon are coupled and highly complicated due to the consideration of nonlinear convection terms. Reasonable variables are employed to reform the partial differential equations into a system of ordinary differential expressions and are solved numerically. Furthermore, correlation and regression techniques are employed for the statistical evaluation of the phenomenon. The probable error is implemented to calculate the reliability of the computed correlation factors. The exponential index and Schmidt number are positively correlated with the reduced skin friction coefficient whereas the other parameters are negatively correlated with it. The heat transfer rate is improved predominantly by the nonlinear thermal convection parameter. The temperature is enhanced by the intensification of the exponential‐based heat source factor. The temperature and concentration profiles are boosted by incrementing the Biot number values.

A study of quadratic thermal radiation and quadratic convection on viscoelastic material flow with two different heat source modulations

In many practical applications such as plastic manufacturing and the polymer industries, the temperature difference is substantially large as a result the density of the working fluid alters nonlinearly with temperature. Therefore, the nonlinear Boussinesq (NBA) approximation cannot be ignored, as it has a considerable impact on the flow and heat transport characteristics of the working fluid. Here, the non-Newtonian viscoelastic material flow driven by stretching of elastic sheet subjected to NBA and quadratic form of Rosseland thermal radiation is investigated. Two different heat source modulations, viz., exponential space-dependent heat source, and a temperature-related heat source are analyzed. The viscoelastic material obeys the quadratic Boussinesq approximation. The fluctuation of plate temperature is linear and the transpiration (plate mass suction) is also accounted. The Darcy law is employed for a porous medium. The dimensionless profiles of the velocity, heat transport rate, and temperature are simulated by solving the nonlinear two-point boundary value system by employing the finite difference-based routine. The significance of key parameters involved in the problem is studied on various flow fields via surface and streamline plots. It is found that the quadratic convection mechanism enhanced the Nusselt number; however, the quadratic thermal radiation aspect reduced the Nusselt number. The higher velocities are captured in the case of quadratic thermal convection as compared with its absence. Whereas this trend is quite opposite for the thermal field. The velocity of viscoelastic material positively correlated with the viscoelastic material parameter. Further, the outcome of this investigation helps in determining the key parameters which facilitate the desired heat transport rate.

Significance of nonlinear Boussinesq approximation and non-uniform heat source/sink on nanoliquid flow with convective heat condition: sensitivity analysis

The quadratic convective flow of nanoliquid over an elongating plate subjected to non-uniform heat source/sink, partial slip, and Newton boundary conditions is studied by using the modified Buongiorno model. The correlation for effective thermal conductivity and viscosity of nanoliquid are taken from the experimental work of Corcione. The dimensionless velocity, temperature, rate of heat transport, and mass transport distributions are simulated by solving the nonlinear boundary value problem using the finite difference method. The additional novelty of the present study is an application of response surface methodology to scrutinize the interactive impact of key parameters on the rate of heat transfer. Further, the influence of key parameters is deliberated on various flow fields using the surface and streamline plots. The higher velocities are noticed for the case of nonlinear Boussinesq approximation as compared with the usual Boussinesq approximation. The temperature enhances with a non-uniform heat source/sink aspect. The sensitivity of the heat transfer to the nanoparticle volume fraction remains positive.

Multilayer flow and heat transport of nanoliquids with nonlinear Boussinesq approximation and viscous heating using differential transform method

AbstractMultilayer fluid flow models are significant in various applications, namely, cooling electronic systems, solar thermal systems, and nuclear reactors. The density of a fluid fluctuates nonlinearly due to large temperature difference circumstances in thermal systems. Thus, the linear Boussinesq approximation is no longer relevant. Therefore, this article describes a multilayer flow of nanoliquids in the presence of nonlinear Boussinesq approximation. The hybrid nanoliquid layer is sandwiched between two nanoliquid layers. The single‐phase khanafer‐vafai‐lightstone model is implemented to simulate the nanoliquids. The quadratic density temperature fluctuation and viscous heating are taken into account. The temperature and velocity across the interface are assumed to be continuous. The equations that govern the problem are solved analytically by using the differential transformation method. The results show that the presence of a hybrid nanoliquid layer affects the velocity and heat transfer properties of the nanofluid flow. Hybrid nanofluid can be used to achieve the desired multilayer flow properties of a nanofluid and its heat transfer properties. Further, the quadratic convection aspect increases the velocity distributions.

Nanofluid Flows within Porous Enclosures Using Non-Linear Boussinesq Approximation

In this paper, the Galerkin finite element method (FEM) together with the characteristic-based split (CBS) scheme are applied to study the case of the non-linear Boussinesq approximation within sinusoidal heating inclined enclosures filled with a non-Darcy porous media and nanofluids. The enclosure has an inclination angle and its side-walls have varying sinusoidal temperature distributions. The working fluid is a nanofluid that is consisting of water as a based nanofluid and Al2O3 as nanoparticles. The porous medium is modeled using the Brinkman Forchheimer extended Darcy model. The obtained results are analyzed over wide ranges of the non-linear Boussinesq parameter 0 ≤ ζ ≤ 1, the phase deviation 0° ≤ Φ ≤ 180°, the inclination angle 0° ≤ γ ≤ 90°, the nanoparticles volume fraction 0% ≤ φ ≤ 4%, the amplitude ratio 0 ≤ a ≤1 and the Rayleigh number 104 ≤ Ra ≤ 106. The results revealed that the average Nusselt number is enhanced by 0.73%, 26.46% and 35.42% at , 105 and 106, respectively, when the non-linear Boussinesq parameter is varied from 0 to 1. In addition, rate of heat transfer in the case of a non-uniformly heating is higher than that of a uniformly heating. Non-linear Boussinesq parameter rises the flow speed and heat transfer in an enclosure. Phase deviation makes clear changes on the isotherms and heat transfer rate on the right wall of an enclosure. An inclination angle varies the flow speed and it has a slight effect on heat transfer in an enclosure.

Impact of activation energy on hyperbolic tangent nanofluid with mixed convection rheology and entropy optimization

The present work numerically examines the entropy generation in the transport of hyperbolic tangent nanofluid over a stretchable surface with nonlinear Boussinesq approximation. Impacts of viscous dissipation, Joule heating, strength of uniform magnetic field along with modified Arrhenius expression is accounted. Under the significance of Buongiorno’s model, thermophoresis and Brownian effects are considered. The dimensionless form of mathematical system is obtained by adopting similarity variables. Consequence of flow parameters are explored through graphs. More, drag coefficient, heat transfer rate and Sherwood number are presented with tables and bar charts. Here, we noted that power law index parameter declines the fluid motion and entropy generation increases with diffusion variable.