This paper is intended for dealing with the peristaltic flow of an electrically conducting Williamson nanofluid in a tapered asymmetric channel through a porous medium with heat and mass transfer. In the current paper, temperature-dependent electrical conductivity formulation was introduced for the first time in peristaltic literature. The flow is pervaded by an oblique uniform magnetic field. The present investigation includes the influences of thermal radiation, Joule heat, viscous dissipation, Hall Current, 1st order chemical reaction, and Dofour and Soret numbers. Current problem is reformulated under the molds of low Reynolds number and long wavelength approximation. Afterwards, semi analytical solutions have been evaluated for the distributions of velocity, temperature, nanoparticle concentrations as well as longitudinal pressure gradient. Solutions can be obtained by using multi-step differential transform method (MS-DTM), a reliable and powerful technique that improve accuracy and overcome drawbacks raised in using the standard differential transform method (DTM). Detailed comparisons have been made at different values of 𝑥 through graphs by Ms-DTM. The graphically results were prepared to visualize the effects of various physical parameters of interest. The semi-analytical results had shown that, as the thermal radiation increases, the nanoparticles diameter and concentration of fluid increase (thermal radiation is a decreasing function in temperature when the temperature decreases the diameter of the nanoparticles increases i.e. the volume of nanoparticle and its concentration increases and become more effective near to tumor tissues). Consequently, it can be used as agents for radiation therapy, generate localized raises in radiation doses and selectively target tumor cells for localized damage (Radiotherapy of oncology).

The present model is devoted for the steady stagnation point flow of a Williamson micropolar nanofluid with magneto-hydrodynamics and thermal radiation effects passed over a horizontal porous stretching sheet. The fluid is considered to be gray, absorbing-emitting but non-scattering medium. The Cogley-Vincent-Gilles formulation is adopted to simulate the radiation component of heat transfer. By applying similarity analysis, the governing partial differential equations are transformed into a set of non-linear ordinary differential equations and they are solved by using the bvp4c package in MATLAB. Numerical computations are carried out for various values of the physical parameters. The effects of momentum, microrotation, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, reduced Nusselt number and reduced Sherwood number of both active and passive controls on the wall mass flux are graphically presented. The present results are compared with previously obtained solutions and they are in good agreement. Results show that the skin friction is increasing functions of the Williamson parameter in both stretching and shrinking surfaces.

The present study investigates the flow and heat transfer characteristics of blood carrying gold nanoparticles in a porous channel with moving/stationary walls in the presence of thermal radiation. Blood is considered as Newtonian fluid which is the base fluid and gold (Au) as nanoparticles. The governing equations are transformed into system of ordinary differential equations by using similarity transformations. The analytical solutions are obtained for the flow variables by employing homotopy analysis method (HAM). The analytical solutions are compared with the numerical solutions which are obtained by shooting technique along with Runge-Kutta scheme. It was noticed that there is a good agreement between analytical and numerical results. The influence of various parameters on velocity, temperature and heat transfer rate of gold-blood nanofluid has been discussed in detail. The temperature of the nanofluid increases with increasing the nanoparticle volume fraction. The heat transfer rate at the top wall increases with increasing nanoparticle volume fraction while it decreases for a given increase in radiation parameter.

An investigation of unsteady MHD double diffusive natural convection flow of a viscous, incompressible, electrically conducting, heat absorbing, radiating and chemically-reactive fluid past an exponentially accelerated moving inclined plate in a fluid-saturated porous medium, when the temperature of the plate and the concentration at the surface of the plate have ramped profiles, is carried out. Exact solutions for the fluid velocity, fluid temperature and the species concentration, under Boussinesq approximation, are obtained in closed form by the Laplace transform technique. The expressions for the shear stress, rate of heat transfer and the rate of mass transfer at the plate are also derived. Numerical evaluations of the fluid velocity, fluid temperature and the species concentration are performed and displayed graphically whereas those of the shear stress, rate of heat transfer and the rate of mass transfer at the plate are presented in tabular form for various values of the pertinent flow parameters.

A numerical analysis was performed to study the effects of combined magnetohydrodynamic and thermal radiation under convective boundary condition over a semi infinite vertical plate embedded in a non-Darcy porous medium. Coupled heat and mass transfer of free convective boundary layer with viscous nanofluid are considered. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis mechanisms, while the Darcy-Forchheimer model is used for the porous medium. The governing partial differential equations are transformed into the ordinary differential equations using the similarity transformations. The accuracy of the method is observed by a comparison with other works reduced to a common case. Many results are tabulated and representative set is displayed graphically to illustrate the influence of the various parameters of interest on different profiles. Extensive numerical investigations show that the flow field, temperature, concentration and nanoparticle volume fraction shapes are significantly influenced by magnetic parameter, regular Lewis number, Brownian motion parameter, thermophoresis parameter, regular buoyancy ratio parameter and Biot number. Heat and mass transfer rates are significantly affected by the level of the applied magnetic field and the convective heat coefficient.

An investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equations for the fluid flow and temperature are reduced to a nonlinear system of ordinary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition it is demonstrated that previously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives reported are not correct.

A numerical study has been carried out to analyze the constant heat flux, internal heat generation, variable viscosity and thermal radiation effects on the flow and heat transfer of a Newtonian fluid over an exponentially stretching porous sheet. Using a similarity transformation, the governing partial differential equations are transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by using an efficient Chebyshev spectral method. The effects of various physical parameters such as viscosity parameter, the suction parameter, the radiation parameter, internal heat generation or absorption parameter and the Prandtl number on velocity and temperature are discussed by using graphical approach. Moreover, numerical results indicate that in the presence of constant heat flux, the skin-friction coefficient as well as Nusselt number is strongly affected by the viscosity parameter, suction parameter, radiation parameter and the internal heat generation parameter.

The unsteady MHD free convection and mass transfer boundary layer flow of an incompressible electrically conducting fluid past an accelerated infinite vertical flat plate embedded in porous medium with ramped wall temperature is considered here. It is assumed that the plate accelerates in its own plane in the presence of thermal radiation incorporating first order chemical reaction. The governing equations are solved analytically using the Laplace transformation technique. The flow phenomenon has been characterized with the help of flow parameters such as permeability parameter, Hartmann number, phenomenon has been characterized with the help of flow parameters such as permeability parameter, Hartmann number, thermal radiation parameter etc. The influences of these parameters on the velocity, temperature field and concentration distribution have been studied and the results are presented graphically and discussed quantitatively. Also, the effects of the various parameters on the skin friction coefficient, the rate of heat and mass transfer at the surface are discussed.

In this paper, mixed convection stagnation point flow of nanofluids over a stretching/shrinking surface is studied numerically in the presence of thermal radiation and viscous dissipation. The governing boundary layer equations are transformed into a system of nonlinear ordinary differential equations, by using a similarity transformation, which are then solved numerically using a fifth-order Runge-Kutta-Fehlberg method with shooting technique. The effects of various physical parameters are analyzed and discussed. Computed results are presented in graphical and tabular forms. It is found that the Richardson number, thermal radiation and internal heat generation/absorption have interesting and significant effects on skin-friction and local Nusselt number for all the three types of nanofluids.

A non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

This paper is concerned with the effect of thermally stratification on the steady, two-dimensional mixed convection flow of a micropolar fluid past a vertical stretching permeable surface saturated in porous medium taking into account the effect of thermal radiation. The governing system of partial differential equations describing the problem are converted into a system of non-linear ordinary differential equations using similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the Chebyshev spectral method. The numerical results for the velocity, the micro-rotation and the temperature are displayed graphically showing the effects of various parameters like the buoyancy parameter, the radiation parameter, the stratification parameter, the permeability parameter and the suction/injection parameter. Moreover, the numerical values of the local skinfriction coefficient, the wall couple stress and the local Nusselt number for these parameters are also tabulated and discussed.

Effects of thermal radiation in mixed convection stagnation point flow over a moving surface subject to convective boundary conditions is addressed. Mathematical modeling is based upon constitutive equations of an incompressible Maxwell fluid. Nonlinear analysis is presented through implementation of homotopy analysis method. Numerical values of Local Nusselt number is computed and analyzed.

In this paper, the effect of thermal radiation, variable viscosity and variable thermal conductivity on the flow and heat transfer of a thin liquid film over an unsteady stretching sheet is analyzed. The continuity, momentum and energy equations, which are coupled nonlinear partial differential equations, are reduced to a set of two non-linear ordinary differential equations, before being solved numerically. Results for the skin-friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. It is found that increasing the viscosity parameter leads to a rise in the velocity near the surface of the sheet and a fall in the temperature. Furthermore, it is shown that the temperature increases due to an increase in the values of the thermal conductivity parameter and the thermal radiation parameter, while it decreases with an increase of the Prandtl number.