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The formulation of nonlinear convective non-Newtonian material is reported in this communication. Aspects of thermal radiation and heat source are taken into account for heat transport analysis. The novel stratifications (thermal and solutal) and convective conditions are considered simultaneously. The boundary-layer concept is implemented to simplify the complex mathematical expressions.

The well-known optimal homotopy scheme develops the computations. Optimal values regarding nonzero auxiliary variables are calculated and examined.

Nonlinear convective flow; Thixotropic non-Newtonian material; Thermal radiation; Heat source; Stratifications and convective conditions; Buongiorno model.

To the best of authors’ knowledge, no such analysis has yet been reported.

The purpose of this study is to explore numerical scrutinization of micropolar and Walters-B non-Newtonian fluids motion under the influence of thermal radiation and chemical reaction.

The two fluids micropolar and Walters-B liquid are considered to start flowing from the slot to the stretching sheet. A magnetic field of constant strength is imposed on their flow transversely. The problems on heat and mass transport are set up with thermal, chemical reaction, heat generation, etc. to form partial differential equations. These equations were simplified into a dimensionless form and solved using spectral homotopy analysis method (SHAM). SHAM uses the basic concept of both Chebyshev pseudospectral method and homotopy analysis method to obtain numerical computations of the problem.

The outcomes for encountered flow parameters for temperature, velocity and concentration are presented with the aid of figures. It is observed that both the velocity and angular velocity of micropolar and Walters-B and thermal boundary layers increase with increase in the thermal radiation parameter. The decrease in velocity and decrease in angular velocity occurred are a result of increase in chemical reaction. It is hoped that the present study will enhance the understanding of boundary layer flow of micropolar and Walters-B non-Newtonian fluid under the influences of thermal radiation, thermal conductivity and chemical reaction as applied in various engineering processes.

All results are presented graphically and all physical quantities are computed and tabulated.

In the present investigation, hydromagnetic boundary layer flow of Walters’-B fluid over a vertical porous surface implanted in a porous material under the action of a strong external applied magnetic field and rotation is presented. In several industrial applications, the external applied magnetic field is strong enough to produce Hall and ion-slip currents. Thus, the influence of Hall and ion-slip currents is also considered in this analysis. The flow through configuration is generated because of time varying motion of the free-stream and buoyancy action.

Regular perturbation scheme is used to obtain the solution of the system of coupled partial differential equations representing the mathematical model of the problem. Numerical computation has been performed to notice the change in flow behavior and the numerical results for velocity field, temperature field, species concentration, skin friction, rate of heat and mass transfer are presented through graphs and tables.

An important fact noticed that the exponential time varying motion of the free-stream induces reverse flow in the direction perpendicular to the main flow. Rising values of the strength of the applied magnetic field give increment in the fluid velocity in the neighbourhood of the vertical surface, this may cause because of the exponential motion of the free-stream. The behaviour of the Darcian drag force is similar as magnetic field on fluid flow.

In literature, very less research works are available on Walters’-B fluid where unsteadiness in the system occurs because of time varying motion of the free-stream. In this paper, the authors have made an attempt to study the action of Hall and ion-slip currents, rotation and external applied magnetic field on hydromagnetic boundary layer flow of Walters’-B fluid over a vertical surface implanted in a porous material.

The main purpose of this paper is to study the effect of heat transfer on the peristaltic flow of a magnetohydrodynamic Walters B fluid through a porous medium in an inclined asymmetric channel.

The approximate analytical solutions of the governing partial differential equations are obtained using the regular perturbation method by taking wave number as a small parameter. The solutions for the pressure difference and friction forces are evaluated using numerical integration.

It is noticed that the pressure gradient and pressure difference are increasing functions of inclination angle and Grashof number. The temperature and heat transfer coefficients both increase with increase in inclination angle, Darcy number, Grashof number and Prandtl number. Increase in Hartmann number and phase difference decreases the size of trapped bolus.

The problem is original, as no work has been reported on the effect of magnetohydrodynamics on the peristaltic flow of a Walters B fluid through a porous medium in an inclined asymmetric channel with heat transfer.

The purpose of this study is to investigate the Dynamics of micropolar – water B Fluids flow simultaneously under the influence of thermal radiation and Soret–Dufour Mechanisms.

The thermal radiation contribution, the chemical change and heat generation take fluidity into account. The flow equations are used to produce a series of dimensionless equations with appropriate nondimensional quantities. By using the spectral homotopy analysis method (SHAM), simplified dimensionless equations have been quantitatively solved. With Chebyshev pseudospectral technique, SHAM integrates the approach of the well-known method of homotopical analysis to the set of altered equations. In terms of velocity, concentration and temperature profiles, the impacts of Prandtl number, chemical reaction and thermal radiation are studied. All findings are visually shown and all physical values are calculated and tabulated.

The results indicate that an increase in the variable viscosity leads to speed and temperature increases. Based on the transport nature of micropolar Walters B fluids, the thermal conductivity has great impact on the Prandtl number and decrease the velocity and temperature. The current research was very well supported by prior literature works. The results in this paper are anticipated to be helpful for biotechnology, food processing and boiling. It is used primarily in refrigerating systems, tensile heating to large-scale heating and oil pipeline reduction.

All results are presented graphically and all physical quantities are computed and tabulated.

objective of the present investigation is to examine the influence of Hall on the peristaltic mechanism of Johnson-Segalman fluid in a heated channel with elastic walls. The transmission of heat is carried out. Relevant equations are computed for heat transfer coefficient, temperature and velocity. Low Reynolds number assumptions and long wavelength are employed. The interpretation of various parameters is analyzed. The results indicate that the heat transfer coefficient, temperature and velocity are larger for viscous material in comparison with Johnson-Segalman material.

The transmission of heat is carried out. Relevant equations are computed for heat transfer coefficient, temperature and velocity. Low Reynolds number assumptions and long wavelength are employed. The interpretation of various parameters is analyzed. The results indicate that the heat transfer coefficient, temperature and velocity are larger for viscous material in comparison with Johnson-Segalman material.

The formulation of paper is executed as follows. Section 2 comprises problem summary and mathematical design. Solution methodology is discussed, and expressions for temperature, velocity and coefficient of heat transfer are derived in Section 3. Graphical outcomes for the parameters are reported in Section 4. Conclusions are outlined in Section 5.

Peristaltic phenomenon of fluids has a definite role in many physiological, industrial and engineering processes. The mechanical devices for instance finger and roller pumps operate via this process, and it is quite significant for vasomotion of blood vessels, consumption of food via esophagus, chyme flow in gastrointestinal zone, toxic liquid flow in nuclear industry and transport of corrosive fluids.

Literature review witnesses that information about peristalsis of conducting fluid in a heated channel with flexible walls and Hall effect is scarce. So, our goal is to discuss the peristaltic activity of non-Newtonian fluids in flexible channel. Johnson-Segalman fluid is taken into account. This model is used to allow non-affine deformations. Experimentalists relate “spurt” with wall slip. That is why the work presented is original.

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 study is to study the impacts of exponential space-dependent heat source (ESHS) and thermal radiation in Marangoni convective flow of Cross fluid. The passively controlled model is developed to exhibit the nanoparticles’ concentration on the surface.

The resulting problem under consideration is tackled by using the shooting approach.

Temperature field augments with enhancement of the thermophoretic, exponential-based space heat source (ESHS) and radiation parameters, whereas it decays with the increase of the Marangoni ratio parameter.

To the best of the authors’ knowledge, no such analysis has yet been reported.

The purpose of this paper is to present an analytical study on an unsteady magnetohydrodynamic (MHD) boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream taking Hall and ion-slip currents into account. The unsteady MHD flow in the rotating fluid system is generated due to the buoyancy forces arising from temperature and concentration differences in the field of gravity and oscillatory movement of the free-stream.

The resulting partial differential equations governing the fluid motion are solved analytically using the regular perturbation method by assuming a very small viscoelastic parameter. In order to note the influences of various system parameters and to discuss the important flow features, the numerical results for fluid velocity, temperature and species concentration are computed and depicted graphically vs boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form.

An interesting observation is recorded that there occurs a reversal flow in the secondary flow direction due to the movement of the free stream. It is also noted that a decrease in the suction parameter gives a rise in momentum, thermal and concentration boundary layer thicknesses.

Very little research work is reported in the literature on non-Newtonian fluid dynamics where unsteady flow in the system arises due to time-dependent movement of the plate. The motive of the present analytical study is to analyse the influences of Hall and ion-slip currents on unsteady MHD natural convection flow of a rotating viscoelastic fluid (non-Newtonian fluid) over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream.

To amend the efficiency of engineering processes and electronic devices, it is very urgent to assess the irreversibility in the term entropy generation (EG). The efficiency of energy transportation in a system can be improved by minimization of the rate of EG. In this context, the aim of the present study is to estimate irreversible losses of an unsteady magnetohydrodynamic (MHD) flow of a viscous incompressible electrically conducting non-Newtonian molybdenum disulfide-polyethylene glycol Casson nanofluid past a moving vertical plate with slip condition under the influence of Hall current, thermal radiation, internal heat generation/absorption and first-order chemical reaction. Molybdenum disulfide (MoS₂) nanoparticles are dispersed in the base fluid polyethylene glycol (PEG) to make Casson nanofluid. Casson fluid model is considered to characterize the rheology of the non-Newtonian fluid, whereas Rosseland approximation is adopted to simulate the thermal radiative heat flux in the energy equation.

The closed-form solutions are obtained for the model equations by using the Laplace transform method (LTM). Graphs and tables are prepared to examine the impact of pertinent flow parameters on the pertinent flow characteristics. The energy efficiency of the system via the Bejan number is studied extensively.

Analysis reveals that Hall current has diminishing behavior on entropy production of the thermal system. Strengthening of the magnetic field declines the velocity components and prop-ups the rate of EG. Adding nanoparticles into the base fluid reduces the EG, whereas there are an optimum volume fraction of nanoparticles for which the EG is minimized. Further, the rate of decay of EG is prominent in molybdenum disulfide-polyethylene glycol in comparison to PEG.

The results of this study would benefit the industrial sector in achieving the maximum heat transfer at the cost of minimum irreversibilities with an optimal choice of embedded thermophysical parameters. In view of this agenda, this study would be adjuvant in powder technology, polymer dynamics, metallurgical process, manufacturing dynamics of nano-polymers, petroleum industries, chemical industries, magnetic field control of material processing, synthesis of smart polymers, etc.

The novelty of this study is to encompass the analytical solution by using the LTM. Such an exact solution of non-Newtonian fluid flow is rare in the literature. Limited research articles are available in the field of EG analysis during the flow of non-Newtonian nanoliquid subject to a strong magnetic field.