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The study numerically investigates the model of hydromagnetic, dissipative micropolar nanofluid flow being influenced by multiple slips and mass flux. Also, the entropy generated within the conduct...

This study features the entropy generation analysis on a steady two-dimensional flow of an incompressible Casson fluid with heat and mass transfer over a heated linearly stretching surface is investigated using a modified Arrhenius activation energy. The appropriate model governing the physical phenomenon is converted into a dimensionless equation with the aid of appropriate transformation and are numerically solved using the spectral collocation method. The present research model is concerned to study the stagnation point slippery flow, heat, and mass transfer analysis of a Casson fluid flow past an elastic surface with the impact of a magnetic field. The study focuses on the influences of Arrhenius activation energy, melting heat transfer, and heat source on heat and mass transfer behavior posed by Casson fluid. The magnitude of skin becomes lesser for larger values of slip parameter while the rate of mass transfer is enhanced via greater values of the destructive chemical reaction. Also, an excellent agreement is shown with previous studies for the limiting case.

Motivated by enrobing processes in manufacturing technology with intelligent coatings, this work analyses the\ud flow of an electroconductive incompressible nanofluid with heat distribution in a boundary layer containing\ud metallic nanoparticles or ferroparticles along an extending cylindrical body with magnetic induction effects. The\ud quasi-linear boundary conditions for the partial derivative formulations connecting to the far stream and cylinder\ud wall are converted to ordinary non-linear derivatives by applying appropriate similarity transformations. The\ud emerging system of derivatives are solved by a stable, efficient spectral relaxation method (SRM). The SRM\ud procedure is benchmarked with special limiting cases in the literature and found to corroborate exceptionally well\ud with other studies in the literature. Here, water is taken as the base liquid containing homogenously suspended\ud non-magnetic (Nimonic 80a, Silicon Dioxide (SiO2) or magnetic nanoparticles Ferric Oxide (Fe3O4), Manganese\ud Franklinite (Mn-ZnFe2O4),). The influence of all key parameters on the velocity and temperature distributions are\ud displayed in graphs and tables with extensive elucidation. The wall local drag force (skin friction) and local\ud temperature gradient (Nusselt number) are also visualized graphically for various parameters. The rate of\ud convergence of the spectral relaxation method (SRM) convergence is compared with that of the successive over\ud relaxation (SOR) method and observed to converge faster. Larger magnetohydrodynamic body force parameter\ud and inverse of Prandtl magnetic number induces flow deceleration whereas it enhances temperatures. Flow\ud acceleration is computed for SiO2non-magnetic nanoparticles and good heat conduction augmentation is produced\ud with nanoparticle magnetic Fe3O4. Rising fractional volume of the solid nanoparticle decelerates the axisymmetric\ud flow for both non-magnetic and magnetic nanoparticles whereas it elevates the magnetic induction and\ud temperature magnitudes.

This study examines the potential of using nanofluids in solar thermal energy systems. Nanofluids are known to exhibit high convection heat transfer coefficients, low specific heat, and density, making them ideal for improving the performance of solar thermal energy systems. However, this computational study investigates the application of Cattaneo-Christov heat flux on cylindrical surfaces using carbon nanotube (CNT) hybrid nanofluids, for use in a solar-powered ship. The work utilizes numerical simulations to analyze the heat transfer and fluid flow characteristics of the hybrid nanofluids. The research examines the use of single-walled and multi-walled carbon nanotubes (SWCNT and MWCNT) in engine oil (EO) as the working fluid. The Galerkin weighted residual method (GWRM) is utilized to solve the ordinary differential equations (ODEs) governing the system. The impact of various parameters, such as Cattaneo-Christov heat flux, solar thermal radiation, nonlinear stretching surface, slippery velocity, and porous media on the velocity equation, energy equation, and entropy generation are investigated and elaborated through detailed plots. The findings show that the MWCNT-SWCNT/EO hybrid nanofluid (HNF) exhibits maximum efficiency of around 2.4%, while the minimum efficiency is at 2.7%. This research provides valuable insights into the design and optimization of solar thermal systems for sustainable transportation.

The heat distribution and branched-chain thermal criticality for a combustible exothermic reaction is examined in this study. The reactive diffusion occurs in a cylinder with pre-exponential variab...

This study examines Oldroyd 6-constant fluid and thermal explosion branch-chain criticality of a reactive flow in a generalized Couette device. With material consumption assumption, the reactive fluid is assumed to be actively exothermic, and the exchange of heat within the system is greater than the ambient heat exchange. Compared to the diffusion coefficient, the nondimensioned momentum and energy balance fields are influenced by a thermal Grashof number, non-Newtonian term, pressure gradient, branch-chain reaction order, and reaction initiation rate. The weighted residual collocation method is used to analytically obtain solutions to the dimensionless temperature and velocity equations as well as the bifurcation slice branch-chain solutions. The results are graphically presented, and it is revealed that a decrease in the fluid material terms will assist in managing the excessive heat generated by reaction initiation rate, and Frank Kamenetskii term. Also, a rise in the reaction branch order and reaction initiation rate can lead to system thermal runaway. Moreover, for industrial processes as obtained from the study, reactive non-Newtonian Oldroyd 6-constant fluid is thermally stable than reactive Newtonian fluid.

This study analyzes the second law of thermodynamic for entropy generation in an irreversible hydromagneto-micropolar flow system with non-homogenous heat generation. The non-symmetric microstructure fluid flow past a stretching sheet with saturated porous non-linear media under magnetic field influence. Ignoring the fluid particle deformation, the microstructure is assumed rigid with the viscous suspended medium. The reduced dimensionless nonlinear formulated model is computationally coded and solved to obtain solutions for the entropy volumetric production, Bejan number and heat transfer magneto-micropolar fluid. The parameter dependent solutions for the flow characteristics and irreversibility processes are plotted and discussed. It is revealed from the study that minimization of entropy generation in a magneto-micropolar flow system is possible by improving the thermodynamic equilibrium with low material variables, viscosity and hysteresis magnetic. Also, it is seen that the terms that encourage internal heat generation reduces the micropolar fluid viscosity in the system.

This paper deals with the melting effect on steady mixed convection flow of a non-Newtonian fluid containing gyrotatic microorganism along a vertical plate embedded in a saturated non-Darcy porous medium. Variable fluid properties are considered in this paper to describe the variation of permeability, porosity, thermal conductivity which is approximated by an exponential function. The changed non-dimensional governing ordinary differential equations via similarity transformation characterize the flow phenomena subjected to melting surface boundary condition are solved numerically by Matlab bvp4c solver. To analyze the consequences of flow influencing parameters to the flow variables are tabulated and visualized graphically. With increasing non-Darcy and mixed convection parameters velocity profiles decays. Temperature escalates for mixed convection parameter and plunges for melting parameter. Concentration slow down for high melting effect and rises for high Lewis number. Bioconvection Lewis number and Peclet number has an increasing impact on the microorganism profiles. Mixed convection parameters show pronouncing impact on Sherwood number, Nusselt number and motile microorganism density profiles but they decrease mostly for pseudo plastic fluid. Comparisons with prior works show splendid agreement between the results.

This paper derives elliptic gradient estimates for positive solutions to a nonlinear parabolic equation defined on a complete weighted Riemannian manifold. Applications of these estimates yield Liouville-type theorem, parabolic Harnack inequalities and bounds on weighted heat kernel on the lower boundedness assumption for Bakry-Émery curvature tensor.

The report contained in this article is based on entropy generation for a reactive Eyring–Powell nanoliquid transfer past a porous vertical Riga device. In the developed model, the impacts of viscous dissipation, thermophoresis alongside nonlinear heat radiation and varying heat conductivity are modelled into the heat equation. The dimensionless transport equations are analytically tackled via Homotopy analysis method while the computational values of chosen parameters are compared with the Galerkin weighted residual method. Graphical information of the various parameters that emerged from the model are obtained and deliberated effectively. The consequences of this study are that the temperature field expands with thermophoresis, Brownian motion and temperature ratio parameters as the modified Hartmann number compels a rise in the velocity profile. The entropy generation rises with an uplift in fluid material term as well as Biot and Eckert numbers whereas Bejan number lessens with Darcy and Eckert parameters.

Theoretical study of inherent irreversibility and thermal runaway of an exothermic reactive Eyring–Powell fluid flow through a saturated porous fixed horizontal channel with thermal radiation and variable electrical conductivity is investigated. The reactive conducting fluid under bimolecular chemical rate law is propelled by pressure gradient. Ignoring the material assumptions, the governing dimensionless equations of the flow model are solved using semi discretization finite difference techniques coupled with weighted residual method. The results in terms of flow rate, temperature, thermal runaway, Bejan number and entropy generation are presented in graphical form. From the results, it is observed that parameter which argument the entropy production rate also enhances the Bejan number. Also, minimization of entropy generation is achieved at low values of thermal radiation, dissipation rate, electric field loading and viscosity variables. Keywords: Inherent irreversibility, Non-Newtonian, Thermal runaway, Reactive fluid, Thermal radiation

In this study, the viscous dissipation of heat transfer of poiseuille fluid flow of two-step exothermic chemical reaction through a porous channel is investigated under different chemical kinetics. The flow is pressure-driven past fixed plates with heat generation. The upper wall surface is exposed to heat exchange with the temperature of the ambient aligning with the Newton’s law of cooling. The modeled coupled partial differential equations are non-dimensional and solved using stable and unconditional semi-implicit convergent finite difference method. The results are represented graphical and discussed accordingly for the velocity and temperature profiles showing the effect of some embodiment parameters entrenched in the system. From the results it was noticed that an increase in Frank-Kamenetskii parameters produces significant rises in the temperature distribution. Keywords: Dissipation, Poiseuille flow, Exothermic reaction, Convective cooling, Finite difference method

The study examines the thermal explosion branched-chain and entropy generation as a result of irreversibility of hydromagnetic reactive couple stress liquid with viscous heating and Navier slips. The reactive fluid flow is enhanced by heat dependent pre-exponential factor and axial pressure gradient in a porous wall. The flow equations for the non-Newtonian couple stress fluid model and heat transfer are solved by employing a semi-analytical collocation weighted residual method (CWRM). The efficiency and validity of the obtained results was verified with the existing results. The results reveal that at low hysteresis magnetic and viscous dissipation the irreversibility process is minimized and thermodynamic equilibrium is improved. The results from this study can assist in understanding the relationship between thermal and thermal explosions branched-chain. Keywords: Thermal criticality, Entropy generation, Viscous heating, Non-Newtonian fluid

Theoretical analysis of thermal stability and inherent irreversibility of reactive hydro-magnetic Powell-Eyring fluid flow in a fixed vertical channel with variable electrical and thermalconductivities is examined. The conducting reactive fluid is influenced by gravity and axial pressuregradient under bimolecular kinetic rate law. Ignoring the material assumptions, the governingdimensionless equations are solved by finite semi-discretization difference scheme along with inte-gration Fehlberg Runge-Kutta method. The results for the momentum and heat equations, Bejannumber, thermal runaway, entropy generation and current density are graphically presented underdifferent thermophysical parameters. The computational results for the shear stress and heat trans-fer at the wall is also presented and discussed quantitatively. It was observed that the parameterwhich enhance the rate of entropy generation also augment Bejan number with large pitch ratio.Hence, entropy generation can be minimized at low dissipation and material variables.O2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, AlexandriaUniversity. This is an open access article under the CC BY-NC-ND license

This paper is concerned with entropy monotonicity formulas and classification of gradient almost soliton for Ricci-harmonic flow. The new entropy formulas introduced here are monotone in general along the flow and constant exactly on shrinker or expander as the case may be. The consequence of this is the nonexistence of periodic solutions except those that are gradient solitons. Furthermore, the paper discusses gradient almost Ricci-harmonic soliton with respect to a fixed metric, not minding the dynamical nature of the flow but treating the defining elliptic equations and relying on analytic techniques. Finally, we are able to classify gradient almost Ricci-harmonic solitons.

A theoretical study of hydromagnetic reaction of Oldroyd 8-constant exothermic liquid and explosion bifurcation slice is examined. The temperature distribution of the reactive molecular diffusion of the non-Newtonian liquid takes place in a plane bounded Couette. Without displacement of currents and material consumption, the viscoelastic fluid is completely exothermic with low thermal equilibrium. The dynamical flow momentum is not stimulated by the species reaction, but by the chain branched order, Arrhenius generalized kinetics, initiation rate and the flow medium upper plate motion. The nonlinear exothermic reaction differential model is completely solved by adopting a consistent and convergent collocation weighted residual analytical procedure. The qualitative results in graphs and tables are presented for the flow dynamic, heat propagation and ignition bifurcation slice. The results revealed that the viscoelastic property of the material is augmented by an increasing magnetic term. Also, exothermic heat diffusion is enhanced by initiation rate and reaction exponential factor. Hence, heat generation terms must be controlled to prevent thermal science and engineering devices from blowup.

In the study, the steady, laminar, incompressible, convective flow of a viscous fluid over a moving plate is investigated theoretically by adopting different types of nanoparticles. Radiation, internal heat generation and viscous dissipation effects are considered in the energy modeled equation. The governing flow equations for the momentum and temperature are reduced to dimensionless form via similarity transformations. The solutions to the resultant equations alongside with the transformed boundary conditions are numerically obtained using MATLAB package bvp4c. Validation with earlier studies are done for the non-internal heat generation case for two distinct nanoparticles of type Cu-water and Al-water. Extensive visualization of flow rate and heat distributions for various emerging parameters are examined. Temperature is consistently enhanced with a rising Eckert number of both types of nanofluids, whereas it is strongly reduced with rising values of radiation term. Heat transfer coefficient is consistently increased with a nanoparticle volume fraction of high convective heat in the medium.

The study of nonlinear radiation and mixed convection of the MHD heat and mass transfer of Maxwell nanoliquid flow in porous media with Arrhenius kinetic reaction is examined. The non-Newtonian fluid is characterized by Maxwell model, and the species molecular mixture is inspired by the Arrhenius pre-exponential kinetics. Reaction mixture occurs in a boundless slippery plate subject to a considerable quantity of tension that can prevent material deformity. With appropriate similarity variables, the flow model reduces to quasilinear coupled system of derivatives. A numerical simulation of the flow characteristics is carried out, and the results presented in tables and graphs for various thermodynamic phenomena. The results show that the flow momentum is damped by the material term, but augmented by nonlinear heat convection and radiation. The heat transfer rate is significantly propelled by temperature ratio and viscous heating, while the Lewis number, molecular Brownian motion and the chemical reaction term encourage species mass transfer. As such, the study involving activation energy plays a critical part in the diffusion of binary chemical mixtures of energy and species transport which will assist the chemical engineering and others in their activities to prevent reaction blowup.

Parametric sensitivity of unsteady Maxwell magnetohydromagnetic nanofluid and second thermodynamic law analysis under Arrhenius kinetic is investigated in the presence of viscous heating and radiation. The porous flow channel is subjected to tension with material properties that vary with time without deformation. In the absence of fluid charge polarization, the conducting liquid is influenced by the sheet stretching velocity. The flow coupled derivatives model is reduced to dimensionless form by relevant transformation variables. These are computational solved by shooting numerical technique together with Fehlberg Runge-Kutta procedures. The essential characteristics of the flow and thermodynamic irreversibility are determined. The results are quantitatively and qualitatively compared with other studies and are established to agree well. The graphical results revealed that Lewis number increases the molecular species concentration and the thermodynamic stability for reversibility can be enhanced by the augmentation of magnetic field, thermophoresis, and radiation. Therefore, for thermal and chemical reaction systems, increasing heat propagation should be managed to keep the system from blowing up.

Influence of quail egg on pathologies has increased research interests and series of investigations are currently being done on its influence against these pathologies. The influence of quail egg against 2-butoxyethanol induced hemolysis and disseminated thrombosis was investigated to determine the enzymatic regulations that ensue in the amelioration of deleterious hemolytic and disseminated thrombosis displayed in female Wistar rats. Quail egg was separated into three (3) components (extracts)-quail egg yolk water soluble (QYWS) and fat soluble (QYFS), and albumen extract (QA) and the inorganic and organic compositions were characterized. Depranocytotic assaults was achieved by 250 mg/kg of 2-Butoxyethanol administered for 4 days, the clinical observation revealed a dark purple-red discoloration on the distal tails of the rats and therapeutic applications followed with 1000 mg/kg BWT of QYWS, QYFS and QA, and 15 mg/kg BWT of hydroxyurea. Morphological evaluation, haematological estimations and biochemical evaluations of the influence on the activities of sphingosine kinase-1, RNase, red cell carbonic anhydrase, lactate dehydrogenase, glutathione peroxidase and caspase-3, vis a vis the concentrations of sphingosine-1 phosphate, selenium and zinc (plasma and urine). In vitro anti-inflammatory influence of quail egg components were investigated against hemolysis and key enzymes of inflammation-cycloxygenase, lipoxygenase and β-glucuronidase. The in vitro anti-inflammatory effects of QYWS, QYFS and QA were concentration dependent from 200 to 800 μg/ml against hemolysis and the key enzymes of inflammation. The characterization of inorganic and organic bioactive composition of the yolk and albumen revealed the presence of folic acid, cobalamin, pyridine, riboflavin, ascorbic acid as well as vitamins D and E, selenium, zinc, iron and calcium. These had reflected in the attenuation of the induced hemolytic and disseminated thrombosis by regulations of enzymes linked to the infarction, apoptosis and oxidative stress characterized in sickle cell index.

We apply the supersymmetric quantum mechanics and shape invariance approach to obtain the solutions of the 3-dimensional Schrödinger equation in the presence of a newly proposed potential model called hyperbolic-sinus potential function for any ℓ-state. Rotational-vibrational energy eigenvalues of some diatomic molecules are numerically calculated. Special cases of interest of the hyperbolic-sinus potential function are also studied. Our results indicated that the energy eigenvalue is highly sensitive to the potential parameters.

This study investigates the current density and branch-chain thermal criticality for a non-Newtonian hydromagnetic second-grade fluid flow in a Poiseuille device with varying electrical conductivity. The combustible reactive fluid is fully exothermic without material consumption, and the fluid is induced by electric and magnetic fields in the presence of axial gradient pressure. With suitable variables, the equations are translated to dimensionless form and solved by semi finite discretization difference scheme to provide solutions for the heat and velocity dependent parameters. The thermal ignition and slice bifurcation for the criticality, and the current density results are plotted for various dependent terms. It is obtained from the investigation that terms that increases current density in the flow system need to be augmented to improve the current carrying hydromagnetic fluid in order to improve its industrial usage.

The study examines the thermodynamic second law of a Powell-Eyring chemical reaction nanofluid flow with electric field loading and variable heat dependent electrical conductivity. The non-Newtonian radiative flow liquid is induced by electric and magnetic fields. The Powell-Erying Cauchy non-Newtonian model is employed for the viscoelastic effect. With suitable transformations, the modeled equations are successfully solved numerically. The results are plotted to investigate the influences of some emerging terms on the concentration, temperature, momentum, Bejan number and entropy generation. It is revealed from the study that entropy generation is minimized as the radiation, electric field loading and magnetic parameters are increased. Also, to avoid blowing up in the technology and industrial engines, the electric field loading as a current carrying hydromagnetic fluid needs to be encouraged for effective operations and performance of engineering and industrial machines. Keywords: Irreversibility, Viscous heating, Non-Newtonian, Bejan number, Electric field

This study deals with the theoretical analysis of thermal explosion criticality slice-chain and temperature distribution for a unidirectional flow of hydromagnetic exothermic Oldroyd S-constant reactive fluid. With negligible material consumption and absence of currents displacement, the reactive flow takes place in a bounded plane Couette device. The flow momentum is not caused by the chemical reaction but by the upper motion of the wall in the presence of initiation rate, Bimolecular generalized kinetics and reaction chain-branch order. The solutions to the nonlinear combustible, non-Newtonian fluid is done using a semi-analytical Weighted residual method coupled with collocation integrating scheme. Graphical results for the flow velocity field, temperature distribution and the bifurcation slice diagram for the thermal ignition criticality are presented. It is seen that the solution depends on the magnetic and material terms, but activation energy has no significant effect on the considered reactive fluid.

Optimization techniques have been used in this paper to obtain an optimal investment in a selected portfolio that gives maximum returns with minimal inputs based on the secondary data supplied by a particular firm that is examined. Sensitivity analysis is done to ascertain the robustness of the resulting model towards the changes in input parameters to determine a redundant constraint using linear programming. The challenge of determining the available funds and allocating each component of the portfolio to maximize returns and minimize inputs by portfolio holders and managers who are the major decision-makers in allocating their resources cannot be quantified. This optimization technique is used to obtain an optimal investment portfolio including financial risks of a firm with disposable of $15,000,000.00 invested in crude oil, mortgage securities, cash crop, certificate of deposit, fixed deposit, treasury bills, and construction loans. The model is a single-objective model that maximizes the return on the portfolio as the interests on the original data reduces by 5%; then, the return on investments also reduced by almost 15%, with the quantum of money on treasury bills and construction loans posing a significant reduction for the maximum return. The investment in the other options saw a slight decrease. Also, as the interest rates of the original data increase by 5%, the return on investments also grows by almost 17% while the quantum of money on the treasury bills and construction loans increases, and the quantum of money on the other options experienced a decrease except for mortgage securities which recorded a slight increase.

In this study, the analysis of inherent irreversibility of chemical reactive third-grade poiseuille flow of a variable viscosity with convective cooling is investigated. The dissipative heat in a reactive exothermic chemical moves over liquid in an irreversible way and the entropy is produced unceasingly in the system within the fixed walls. The heat convective exchange with the surrounding temperature at the plate surface follows Newton’s law of cooling. The solutions of the dimensionless nonlinear equations are obtained using weighted residual method (WRM). The solutions are used to obtain the Bejan number and the entropy generation rate for the system. The influence of some pertinent parameters on the entropy generation and the Bejan number are illustrated graphically and discussed with respect to the parameters.

The numerical investigation of a Casson–Williamson reactive nanofluid species in a moving vertical medium is the subject of this study. The complete exothermic reaction of viscoplastic nanofluid material in a cylindrical system is considered using a generalized Arrhenius kinetic. Casson and Williamson fluids are combined to give the fluid its viscoelastic property. In collaboration with the bivariate overlapping multi-domain technique, the spectral quasi-linearization scheme is used to find solutions to dimensionless mathematical nonlinear formulated flow equations. The findings are displayed in tabular and graphical form, demonstrating the sensitivity of the thermofluid parameters. The study indicates that the flow motion is not caused by the activation energy or the material reaction. It was obtained that the magnetic field increased the viscosity of the material and the thermal conductivity of the nanoparticles. Also, Lewis number enhanced the fluid viscoplastic property. Thermal and chemical engineering, as well as nanotechnology development, will benefit from the findings of this investigation.

This paper examines the transport of nonlinear radiative Casson nanoliquid past a vertical electromagnetic actuator with temperature-dependent transport properties and entropy analysis. The model incorporates the Grinberg-term containing the influence of Lorentz force impinged by the actuator and the impact of the thermo-migration and Brownian motion of nanoparticles. The main equations are translated into non-dimensional forms via appropriate dimensionless variables and then solved using Chebyshev collocation method and verified by Galerkin type of weighted residual method and existing studies found in literature. From the study, the reactions of the embedded physical quantities of interest on the fields of velocity, temperature, nanoparticles concentration and entropy generation number are communicated graphically and deliberated upon. The implications of the results are that the modified Hartmann number aids the fluid flow as the Richardson number boosts the hydrodynamic boundary layer thickness whereas the converse occurs with Casson fluid material parameter. Also, the entropy generation is enhanced in the existence of viscous dissipation and suction while it declines with thermophoretic influence. Conclusively, it is found that the rate of entropy generation can be reduced by augmenting the magnitudes of the thermophoresis and Brownian motion parameters.

The analysis of hydromagnetic inherent irreversibility of reactive third-grade poiseuille flow and incompressible fluid heat properties of a variable viscosity with convective cooling in fixed plates is investigated. The heat dissipation of reactive exothermic chemical in a uniform magnetic field moves past fluid in a porous medium in an irreversible mode and the entropy is created continually in the system within the channel stimulated by bimolecular chemical kinetic. The heat convective transfer at the walls surfaces with the immediate surrounding follows Newton’s law of cooling. The dimensionless nonlinear equations are solved by the method of weighted residual (WRM). The results are used to obtain the Bejan number of the system and the entropy generation rate. The effects of the selected relevant parameters on the flow, entropy generation and Bejan number are demonstrated graphically and conferred with reverence to the parameters

Computational simulations of hydromagnetic dissipative heat transfer of variable electric conductivity of micropolar fluid flow and non - uniform heat absorption or generation with joule heating have been studied in this work. The flow past an inclined surfa ce with an unvarying heat flux. The transformed dimensionless equations of the governing model are solved by Runge - Kutta algorithm coupled with shooting scheme to depict the dimensionless temperature, microrotation and velocity distributions at the border layer. The substantial bodily quantities of the flow are conferred. The results depict that the significance of the coefficient of the skin friction and the Nusselt number increases for uneven electric conductivity and non - homogeneous heat sink or source at the plate

In this work, we have studied analytically the heat and mass transfer of unsteady MHD natural convective flow past a motioning plate with binary chemical reaction. The flow surface spontaneously moves with unvaried velocity in the flow direction or opposite under the influence of magnetic field. We studied both frequency-dependent effects and “long-time” effects that would require non-practically long channels to be observed in steady flow. We also explored mathematically the important aspects of reactive fluid flow, especially the residence time flow behaviour, scale-up and scale-down procedures. From the present study, it is seen amongst others that temperature is enhanced as the fluid angular velocity rises which leads to maximum temperature in the body of the liquid. It is discovered that mean velocity decrease with a rise in the species reaction and reaction order. The graphical results representing the governing flow parameters effect were presented and discussed. The flow conditions at the wall were also investigated, presented and described.