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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.

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.

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.

This paper aims to analyze heat and mass transfer of magnetohydrodynamic (MHD) non-Newtonian fluids flow past an inclined thermally stratified porous plate using a numerical approach.

The flow equations are set up with the non-linear free convective term, thermal radiation, nanofluids and Soret–Dufour effects. Thus, the non-linear partial differential equations of the flow analysis were simplified by using similarity transformation to obtain non-linear coupled equations. The set of simplified equations are solved by using the spectral homotopy analysis method (SHAM) and the spectral relaxation method (SRM). SHAM uses the approach of Chebyshev pseudospectral alongside the homotopy analysis. The SRM uses the concept of Gauss-Seidel techniques to the linear system of equations.

Findings revealed that a large value of the non-linear convective parameters for both temperature and concentration increases the velocity profile. A large value of the Williamson term is detected to elevate the velocity plot, whereas the Casson parameter degenerates the velocity profile. The thermal radiation was found to elevate both velocity and temperature as its value increases. The imposed magnetic field was found to slow down the fluid velocity by originating the Lorentz force.

The novelty of this paper is to explore the heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium. The model is formulated in an inclined plate and embedded in a thermally-stratified porous medium which to the best of the knowledge has not been explored before in literature. Two elegance spectral numerical techniques have been used in solving the modeled equations. Both SRM and SHAM were found to be accurate.

The purpose of this paper is to investigate fully developed mixed convection flow in the steady-periodic regime for a Newtonian fluid in a vertical microtube in the presence of velocity slip and temperature jump, which has not been accounted for in the literature.

To achieve this objective, the governing equations for the problem are separated into steady and oscillatory components using separation of variable method; this gives a pair of independent boundary value problems. This is then solved along with its boundary conditions and constraint equations using the method of undetermined coefficient. The exact solutions of momentum and energy equations are obtained under the velocity slip and temperature jump conditions.

The significant result from the study is that increase in rarefaction parameter as well as fluid–wall interaction parameter decreases the oscillation amplitude of the dimensionless velocity. Furthermore, it was found that the product of dimensionless frequency and Prandtl number initiate a strong convection current inside the microtube.

Such type of study may be used on the determination of the thermal and tangential momentum accommodation coefficients and be applicable to the designs and fabrications of microheat exchanger. Moreover, it provides the possibility to get a bench mark for numerical solvers with reference to basic flow configuration.

These solutions generally deserve great attention, since the application of a magnetic field has been found to be effective tool in controlling the convection current. The current work is aimed as an extension of the previous analytical studies to prove some insight into a number of industrial applications, which use similar configurations.

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 Hydromagnetics instability of non-Newtonian Walters'B' viscoelastic rotating fluid in porous medium is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. For stationary convection, the Walters'B' viscoelastic fluid behaves like an ordinary (Newtonian) fluid. The magnetic fluid is found to have a stabilizing effect on the thermal convection of Walters'B' fluid in the absence of rotation whereas the medium permeability has a destabilizing effect on the thermal convection of Walters'B' fluid in the absence of rotation, Rotation always has a stabilizing effect. The magnetic field, the medium permeability and rotation introduce oscillatory modes in the systems, which were non-existent in their absence.

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.

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.