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The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov double-diffusion model over a permeable stretched sheet. Features of nonlinear thermal radiation, dual stratification, non-uniform heat generation/absorption, MHD and binary chemical reaction are also evaluated for present flow problem. Walter-B nanomaterial model is employed to describe the significant slip mechanism of Brownian and thermophoresis diffusions. Generalized Fourier’s and Fick’s laws are examined through Cattaneo–Christov double-diffusion model. Modified Arrhenius formula for activation energy is also implemented.

Several techniques are employed for solving nonlinear differential equations. The authors have used a homotopy technique (HAM) for our nonlinear problem to get convergent solutions. The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear coupled ordinary/partial differential equations. The capability of the HAM to naturally display convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations. This analytical method has the following great advantages over other techniques:

• It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

• It guarantees the convergence of series solutions for nonlinear problems.

• It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

It guarantees the convergence of series solutions for nonlinear problems.

It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

Brief mathematical description of HAM technique (Liao, 2012; Mabood et al., 2016) is as follows. For a general nonlinear equation:

where N denotes a nonlinear operator, x the independent variables and u(x) is an unknown function, respectively. By means of generalizing the traditional homotopy method, Liao (1992) creates the so-called zero-order deformation equation:

here q∈[0, 1] is the embedding parameter, H(x) ≠ 0 is an auxiliary function, h(≠ 0) is a nonzero parameter, L is an auxiliary linear operator, u_o(x) is an initial guess of u(x) and u ˆ ( x ; q ) is an unknown function, respectively. It is significant that one has great freedom to choose auxiliary things in HAM. Noticeably, when q=0 and q=1, following holds:

Expanding u ˆ ( x ; q ) in Taylor series with respect to (q), we have:

If the initial guess, the auxiliary linear operator, the auxiliary h and the auxiliary function are selected properly, then the series (4) converges at q=1, then we have:

By defining a vector u → = ( u o ( x ) , u 1 ( x ) , u 2 ( x ) , … , u n ( x ) ) , and differentiating Equation (2) m-times with respect to (q) and then setting q=0, we obtain the mth-order deformation equation:

where:

Applying L⁻¹ on both sides of Equation (6), we get:

In this way, we obtain u_m for m ⩾ 1, at mth-order, we have:

It is evident from obtained results that the nanoparticle concentration field is directly proportional to the chemical reaction with activation energy. Additionally, both temperature and concentration distributions are declining functions of thermal and solutal stratification parameters (P₁) and (P₂), respectively. Moreover, temperature Θ(Ω₁) enhances for greater values of Brownian motion parameter (N_b), non-uniform heat source/sink parameter (B₁) and thermophoresis factor (N_t). Reverse behavior of concentration ϒ(Ω₁) field is remarked in view of (N_b) and (N_t). Graphs and tables are also constructed to analyze the effect of different flow parameters on skin friction coefficient, local Nusselt number, Sherwood numbers, velocity, temperature and concentration fields.

The novelty of the present problem is to inspect the Arrhenius activation energy phenomena for viscoelastic Walter-B nanofluid model with additional features of nonlinear thermal radiation, non-uniform heat generation/absorption, nonlinear mixed convection, thermal and solutal stratification. The novel aspect of binary chemical reaction is analyzed to characterize the impact of activation energy in the presence of Cattaneo–Christov double-diffusion model. The mathematical model of Buongiorno is employed to incorporate Brownian motion and thermophoresis effects due to nanoparticles.

The purpose of this article is to analyze the heat and mass transfer with entropy generation during magnetohydrodynamics (MHD) flow of non-Newtonian Sisko nanofluid over a linearly stretching cylinder under the influence of velocity slip, chemical reaction and thermal radiation. The Brownian motion, thermophoresis and activation energy are assimilated in this nanofluid model. Convective boundary conditions on heat and mass transfer are considered. The physical model may have diverse applications in several areas of technology underlying thermohydrodynamics including supercritical fluid extraction, refrigeration, ink-jet printing and so on.

The dimensional governing equations are nondimensionalized by using appropriate similarity variables. The resulting boundary value problem is converted into initial value problem using the method of superposition and numerically computed by employing well-known fourth-order Runge–Kutta–Fehlberg approach along with shooting technique (RKF4SM). The quantitative impacts of emerging physical parameters on the velocity, temperature, concentration, skin friction coefficient, Nusselt number, Sherwood number, entropy generation rate and Bejan number are presented graphically and in tabular form, and the salient features are comprehensively discussed.

From graphical outcomes, it is concluded that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with rising radiation parameter and thermal Biot number. Nanoparticle concentration is reported in decreasing form with activation energy parameter. Entropy is found to be an increasing function of magnetic field, Brownian motion and material parameters. The entropy is less generated for shear-thinning fluid compared to shear-thickening as well as Newtonian fluids in the system.

Till now no study has been documented to explore the impact of binary chemical reaction with Arrhenius activation energy on entropy generation in an MHD boundary layer flow of non-Newtonian Sisko nanofluid over a linear stretching cylinder with velocity slip and convective boundary conditions.

The purpose of this paper is to study entropy generation in magneto-Jeffrey nanomaterial flow by impermeable moving boundary. Adopted nanomaterial model accounts Brownian and thermophoretic diffusions. Modeling is arranged for thermal radiation, nonlinear convection and viscous dissipation. In addition, the concept of Arrhenius activation energy associated with chemical reaction are introduced for description of mass transportation.

Homotopy algorithms are used to compute the system of ordinary differential equations.

The afore-stated analysis clearly notes that simultaneous aspects of activation energy and entropy generation are not yet investigated. Therefore, the intention here is to consider such effects to formulate and investigate the magneto-Jeffrey nanoliquid flow by impermeable moving surface.

As per the authors’ knowledge, no such work has yet been published in the literature.

The magnetohydrodynamic (MHD) flow problems are important in the field of biomedical applications such as magnetic resonance imaging, inductive heat treatment of tumours, MHD-derived biomedical sensors, micropumps for drug delivery, MHD micromixers, magnetorelaxometry and actuators. Therefore, there is the impact of the magnetic field on the transport of non-Newtonian Carreau fluid in the presence of binary chemical reaction and activation energy over an extendable surface having a variable thickness. The significance of irregular heat source/sink and cross-diffusion effects is also explored.

The leading governing equations are constructed by retaining the effects of binary chemical reaction and activation energy. Suitable similarity transformations are used to transform the governing partial differential equations into ordinary differential equations. Subsequent nonlinear two-point boundary value problem is treated numerically by using the shooting method based on Runge–Kutta–Fehlberg. Graphical results are presented to analyze the behaviour of effective parameters involved in the problem. The numerical values of the mass transfer rate (Sherwood number) and heat transfer rate (Nusselt number) are also calculated. Furthermore, the slope of the linear regression line through the data points is determined in order to quantify the outcome.

It is established that the external magnetic field restricts the flow strongly and serves as a potential control mechanism. It can be concluded that an applied magnetic field will play a major role in applications like micropumps, actuators and biomedical sensors. The heat transfer rate is enhanced due to Arrhenius activation energy mechanism. The boundary layer thickness is suppressed by strengthening the thickness of the sheet, resulting in higher values of Nusselt and Sherwood numbers.

The effects of magnetic field, binary chemical reaction and activation energy on heat and mass transfer of non-Newtonian Carreau liquid over an extendable surface with variable thickness are investigated for the first time.

This paper aims to peruse the influence of second law analysis for electrically conducting fluid of a Casson nanofluid over a wedge. For activation energy, a modified Arrhenius function is used.

The highly non-linear governing equations are developed using similarity transformations and then computed numerically via Keller–Box method.

The influences of emerging parameters on velocity, temperature distribution and concentration of nanoparticle are explained and presented via graphs and tables. Also, the behavior of fluid flow is investigated through the coefficient of skin friction, Nusselt and Sherwood numbers. Results reveal that the velocity profile enhances due to increasing Casson parameter and magnetic parameter, whereas the temperature distribution and concentration of nanoparticle decrease with larger vales of Casson parameter. It is inspected that the concentration boundary layer increases due to activation energy and decreases due to reaction rate and temperature differences.

The authors believe that all the numerical results are original and significant which are used in biomedicine, industrial, electronics and transportation. The results have not been considered elsewhere.

The purpose of this study is to investigate the Cattaneo-Christov double diffusion, multiple slips and Darcy-Forchheimer’s effects on entropy optimized and thermally radiative flow, thermal and mass transport of hybrid nanoliquids past stretched cylinder subject to viscous dissipation and Arrhenius activation energy.

The presented flow problem consists of the flow, heat and mass transportation of hybrid nanofluids. This model is featured with Casson fluid model and Darcy-Forchheimer model. Heat and mass transportations are represented with Cattaneo-Christov double diffusion and viscous dissipation models. Multiple slip (velocity, thermal and solutal) mechanisms are adopted. Arrhenius activation energy is considered. For graphical and numerical data, the bvp4c scheme in MATLAB computational tool along with the shooting method is used.

Amplifying curvature parameter upgrades the fluid velocity while that of porosity parameter and velocity slip parameter whittles down it. Growing mixed convection parameter, curvature parameter, Forchheimer number, thermally stratified parameter intensifies fluid temperature. The rise in curvature parameter and porosity parameter enhances the solutal field distribution. Surface viscous drag gets controlled with the rising of the Casson parameter which justifies the consideration of the Casson model. Entropy generation number and Bejan number upgrades due to growth in diffusion parameter while that enfeeble with a hike in temperature difference parameter.

To the best of the authors’ knowledge, this research study is yet to be available in the existing literature.

The purpose of this paper is to address double stratification and activation energy in flow of tangent hyperbolic fluid. Flow is induced by non-linear stretching sheet of variable thickness. Heat flux by Cattaneo–Christov theory is implemented.

Non-linear system is computed for the convergent solutions. Attention is particularly focused to the velocity, temperature and concentration.

It is found that temperature and thermal layer thickness are decreased for larger stratification.

In view of aforementioned communication, the aim of the present study is fourfold: First, to inspect stagnation point flow of tangent hyperbolic liquid by a stretched sheet; second, to discuss effect of non-Fourier heat flux and double stratification; third, to investigate activation energy; and fourth, to examine variable thickness effect.

The purpose of this paper is to examine outcome of activation energy in rotating flow of an Oldroyd-B nano liquid.

Flow is generated due to stretched surface. Binary chemical reaction is studied. Brownian and thermophoresis effects are considered. The system of nonlinear ordinary differential equations is derived. Convergent series solutions are obtained by homotopy analysis method. The resulting expressions for velocities, temperature and concentration are computed for different embedded parameters.

It is found that velocities f′ and g  have decreasing effect when rotation parameter is enhanced. Brownian and thermophoresis are increasing functions of temperature and concentration. The physical quantities are sketched and discussed numerically. Concentration and temperature fields show decreasing behavior via Brownian and thermophoresis parameters.

Authors investigate the Rotating flow of Oldroyd-B nano fluid with chemical reactions. This work is not done yet in literature.

The purpose of this paper is to analyze the combined effects of thermal radiation and activation energy with a chemical reaction on the quadratic convective flow of a micropolar fluid over an inclined plate. Convective thermal boundary condition and suction/injection effects are considered at the surface of an inclined plate.

The convection along with nonlinear Boussinesq approximation (i.e. quadratic convection or nonlinear convection) and usual boundary layer assumptions is employed in the mathematical formulation. Highly coupled nonlinear governing equations are tackled by a combined local non-similarity and successive linearization techniques.

The behavior of various pertinent parameters on the fluid flow characteristics is conferred through graphs and it reveals that the qualitative behaviors of velocity, temperature, skin friction and heat transfer rates of a micropolar fluid are similar for Biot number and radiation parameters. The suction/injection and activation energy parameters increase the concentration of the micropolar fluid within the boundary layer, while the chemical reaction parameter reduces the concentration in the same region. Further, this quadratic convection shows a strong influence on the fluid flow characteristics and then the impact of pertinent parameters is more prominent on the physical quantities, compared therewith results of the linear convection.

This kind of investigation is useful in the mechanism of combustion, aerosol technology, high-temperature polymeric mixtures and solar collectors which are operated at moderate to very high temperatures.

This attempt is a unique contribution to the establishment of both micropolar fluid and activation energy. This kind of study even in the absence of quadratic convection is not yet noted.

Dyeing and printing are important steps in textile manufacturing. After the process completion, these dyes are released in the effluent. These dyes impart an unacceptable appearance but are also toxic to the soil and water bodies. The present research has been carried out to study the rate of photocatalytic degradation of an azo dye, namely, CI Direct Green 26, using titania nanoparticles under ultra violet (UV) irradiation as a function of temperature and time. Azo dyes account for the majority of all dyestuffs are produced and extensively used in the textile, paper, food, leather, cosmetics and pharmaceutical industries. Titania nanoparticles have been found to successfully degrade these dyes in the presence of UV light. The purpose of the present paper was to study the photodegradation of azo dyes using titania nanoparticles at different temperatures and time periods.

Titania nanoparticle concentration of 0.1% (w/v) was dispersed in distilled water by sonication for 1 h in sonication bath. The of rate of degradation of Direct Green 26 dye in the titania nanoparticle dispersion, under UV-A exposure was studied at different temperatures ranging from 25°C to 65 °C for time periods ranging from 1 h to 6 h. Photocatalytic degradation tests were performed in a specially designed UV reactor chamber. Raman spectroscopy of Titania nanoparticles, dye and titania/dye mixture before and after UV exposure was carried out using Confocal Laser Dispersion Raman Microscope (Renishaw, UK) with 785 nm excitation laser.

Titanium dioxide is an efficient photocatalyst for decolourisation of direct dye. The photodegradation of the direct Green dye was found to follow the pseudo first-order reaction. The Arrhenius activation energy was found to be 24.8 kJ/mol with A value of 0.0013 for the photocatalytic degradation of the dye. Raman spectroscopy also confirmed the adsorption of dye on titania nanoparticle and its complete degradation on exposure to UV light.

This research highlights the application of titania nanoparticles for the effective degradation of dye in the effluent from textiles, clothing, paper and any kind of dyeing process. Azo dyes account for the majority of all dyestuffs are produced and extensively used in the textile, paper, food, leather, cosmetics and pharmaceutical industries. Titania nanoparticles have been found to successfully degrade these dyes in the presence of UV light which can be very beneficial for the effluent treatment plants in textile and other industries.

Azo dyes are one of the harmful pollutants released in textile waste water. The degradation and removal of the coloured waste in the textile effluent is an important environmental concern and needs to be investigated. The research is one of the first to investigate and understand the mechanism of the degradation of an azo dye in the presence of titania nanoparticles by Raman spectroscopy.