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An investigation is exhibited to analyze the presence of heat source and sink in doubly stratified MHD incompressible tangent hyperbolic fluid due to stretching of cylinder embedded in porous space under nanoparticles. To develop the mathematical model of tangent hyperbolic nanofluid, movement of Brownian and thermophoretic are accounted. The established equations of continuity, momentum, thermal and solutal boundary layers are reassembled into sets of non-linear expressions. These assembled expressions are executed with the help of Runge-Kutta scheme with MATLAB. The impacts of sundry parameters are illustrated graphically and the engineering interest physical quantities like skin friction, Nusselt and Sherwood number are examined by computing numerical values. It is clear that the power-law index parameter and curvature parameter shows favorable effect on momentum boundary layer thickness whereas Weissennberg number reveals inimical influence. Keywords: MHD, Tangent hyperbolic fluid, Heat source/sink, Nanoparticles

The consequence of thermal radiation in laminar natural convective hydromagnetic flow of viscous incompressible fluid past a vertical cone with mass transfer under the influence of chemical reaction with heat source/sink is presented here. The surface of the cone is focused to a variable wall temperature (VWT) and wall concentration (VWC). The fluid considered here is a gray absorbing and emitting, but non-scattering medium. The boundary layer dimensionless equations governing the flow are solved by an implicit finite-difference scheme of Crank–Nicolson which has speedy convergence and stable. This method converts the dimensionless equations into a system of tri-diagonal equations and which are then solved by using well known Thomas algorithm. Numerical solutions are obtained for momentum, temperature, concentration, local and average shear stress, heat and mass transfer rates for various values of parameters Pr, Sc, λ, Δ, Rd are established with graphical representations. We observed that the liquid velocity decreased for higher values of Prandtl and Schmidt numbers. The temperature is boost up for decreasing values of Schimdt and Prandtl numbers. The enhancement in radiative parameter gives more heat to liquid due to which temperature is enhanced significantly. Keywords: Chemical reaction, Heat generation/absorption, MHD, Radiation, Vertical cone

The present research explores the three-dimensional stretched flow of viscous fluid in the presence of prescribed heat (PHF) and concentration (PCF) fluxes. Mathematical formulation is developed in the presence of chemical reaction, viscous dissipation and Joule heating effects. Fluid is electrically conducting in the presence of an applied magnetic field. Appropriate transformations yield the nonlinear ordinary differential systems. The resulting nonlinear system has been solved. Graphs are plotted to examine the impacts of physical parameters on the temperature and concentration distributions. Skin friction coefficients and local Nusselt and Sherwood numbers are computed and analyzed. Keywords: Three-dimensional flow, MHD, Flux conditions, Viscous dissipation, Joule heating, Exponentially stretching surface

The aim of this article is to highlight the unsteady mixed convective couple stress nanoliquid flow passed through stretching surface. The flow is generated due to periodic oscillations of sheet. An appropriate set of dimensionless variables are used to reduce the independent variables in governing equations arising from mathematical modeling. An analytical solution has been computed by employing the technique of homotopy method. The outcomes of various sundry parameters like couple stress parameter, the ratio of angular velocity to stretching rate, thermophoresis parameter, Hartmann number, Prandtl number, heat source/sink parameter, Schmidt number described graphically and in tabular form. It is observed that the velocity profile increases by increasing mixed convection parameter and concentration buoyancy parameter. The temperature enhances for larger values of Hartmann number and Brownian. The concentration profile increases by increasing thermophoresis parameter. Results show that wall shear stress increases by increasing couple stress parameter and ratio of oscillating frequency to stretching rate. Keywords: Oscillatory surface, Couple stress fluid, Nanoparticles, Heat absorption/generation

Objective of present article is to describe magnetohydrodynamic (MHD) non-linear convective flow of Powell-Erying nanofluid over a stretching surface. Characteristics of Newtonian heat and mass conditions in this attempt is given attention. Heat and mass transfer analysis is examined in the frame of thermal radiation and chemical reaction. Brownian motion and thermophoresis concept is introduced due to presence of nanoparticles. Nonlinear equations of momentum, energy and concentration are transformed into dimensionless expression by invoking suitable variables. The series solutions are obtained through homotopy analysis method (HAM). Impact of embedded variables on the velocity, temperature and nanoparticles concentration is graphically presented. Numerical values of skin friction coefficient, local Nusselt and Sherwood numbers are computed and analyzed. It is concluded that velocity field enhances for fluid variable while reverse situation is noticed regarding Hartman number. Temperature and heat transfer rate behave quite reverse for Prandtl number. It is also noted that the concentration and local Sherwood number have opposite behavior in the frame of Brownian motion. Keywords: Powell-Erying nanofluid, Magnetohydrodynamic (MHD), Nonlinear convection, Thermal radiation, Chemical reaction, Newtonian heat and mass conditions

The simultaneous interaction of viscous dissipative and thermal radiation in MHD two dimensional flows of ferro-liquid over a nonlinear moving surface is analyzed here. The slip on velocity and convective boundary condition on temperature are imposed on stretching surface. We used water as conventional base liquid which have magnetite (Fe3O4) and alumina (Al2O3) as nanoparticles. The governing mathematical expressions are converted into non-dimensional form via nonlinear type similarity variables. The resulting mathematical model is numerically solved with the help of MATLAB solver bvp4c. The roles of non-dimensional constraints on velocity and temperature are elaborated through plots. The numerical data of skin-friction coefficient and Nusselt number is presented and visualized. The validity of computed results is analyzed through comparative benchmark. Keywords: Ferro fluid, Velocity slip condition, Convective boundary condition, Viscous dissipation, Radiation

This paper communicates the analysis of MHD three-dimensional flow of Jeffrey nanoliquid over a stretchable surface. Flow due to a bidirectional surface is considered. Heat and mass transfer subject to volume fraction of nanoparticles, heat generation and nonlinear solar radiation are examined. Newtonian heat and mass transportation conditions are employed at surface. Concept of boundary layer is utilized to developed the mathematical problem. The boundary value problem is dictated by ten physical parameters: Deborah number, Hartman number, ratio of stretching rates, thermophoretic parameter, Brownian motion parameter, Prandtl number, temperature ratio parameter, conjugate heat and mass parameters and Lewis number. Convergent solutions are obtained using homotopic procedure. Convergence zone for obtained results is explicitly identified. The obtained solutions are interpreted physically. Keywords: Hydromagnetic flow, Viscoelastic nanofluid, Thermophoretic and Brownian moment, Nonlinear thermal radiation, Heat generation

A numerical investigation of unsteady stagnation point flow of bioconvective nanofluid due to an exponential deforming surface is made in this research. The effects of Brownian diffusion, thermophoresis, slip velocity and thermal jump are incorporated in the nanofluid model. By utilizing similarity transformations, the highly nonlinear partial differential equations governing present nano-bioconvective boundary layer phenomenon are reduced into ordinary differential system. The resultant expressions are solved for numerical solution by employing a well-known implicit finite difference approach termed as Keller-box method (KBM). The influence of involved parameters (unsteadiness, bioconvection Schmidt number, velocity slip, thermal jump, thermophoresis, Schmidt number, Brownian motion, bioconvection Peclet number) on the distributions of velocity, temperature, nanoparticle and motile microorganisms concentrations, the coefficient of local skin-friction, rate of heat transport, Sherwood number and local density motile microorganisms are exhibited through graphs and tables. Keywords: Unsteadiness, Bio-convection, Slip regime, Stagnation point flow, Numerical modeling

Nonlinear convective flow of magneto-Carreau-Casson liquids past a deformable surface under the aspects of heterogeneous and homogeneous reactions is investigated. The present phenomenon also included the interaction of nonlinear radiation, Ohmic and Joule dissipations. At moderate to high temperature, the nonlinear convection and radiation are significant. The governed nonlinear system is illustrated numerically via Runge-Kutta based shooting scheme in the domain [0,∞). Role of significant parameters on flow fields as well as on the fiction factor, heat and mass transportation rates are determined and discussed in depth. Comparison is done for distinct flow fields of Carreau and Casson fluids. It is evaluated that the velocities of Casson liquid are higher in comparison to Carreau fluid model. However, liquid temperature for Casson fluid model is weaker in comparison to Carreau fluid. Keywords: Carreau fluid, Casson fluid, Nonlinear thermal radiation: Nonlinear convection, Homogeneous–heterogeneous reaction

This paper investigates the effects of heat and mass transfer in the mixed convection flow of an Oldroyd-B fluid over a stretching surface with convective boundary conditions. Emphasis is given to the analysis of Soret and Dufour effects. Relevant problems are first formulated and then computed by homotopy analysis method (HAM). Soret and Dufour effects are considered. Velocity, temperature and concentration fields are given. In addition, the local Nusselt and Sherwood numbers are examined through numerical values. Keywords: Soret and Dufour effects, Mixed convection flow, Oldroyd-B fluid, Convective boundary condition

Mathematical analysis of magnetohydrodynamic (MHD) three-dimensional nonlinear convective flow of Maxwell nanofluid towards a stretching surface is made in this article. Characteristics of heat transfer are examined under thermal radiation, heat generation/absorption and prescribed heat flux condition. Nanofluid model includes Brownian motion and thermophoresis. Dimensional nonlinear expressions of momentum, energy and concentration are converted into dimensionless systems by invoking suitable similarity variables. A well-known homotopic technique is implemented for dimensionless expressions. Impact of different quantities on velocities, temperature and concentration are scrutinized graphically and discussed in detail. The expressions of Nusselt and Sherwood numbers are calculated and addressed comprehensively. It is also seen that thermal radiation parameter enhances the temperature field and heat transfer rate. Keywords: Maxwell nanofluid, Magnetohydrodynamic (MHD), Thermal radiation, Nonlinear convection, Flux conditions, Heat generation/absorption