The plane Poiseuille flow with unequal wall temperatures of an incompressible fluid having temperature dependent VISCOSITY in the presence of transverse magnetic field is studied. The coupled differential equations of momentum and energy are solved numerically by RKF45 (Runge-Kutta-Fehlberg fourth-fifth) method. Numerical results for the dimensionless velocity profiles, the temperature profiles and the heat transfer coefficient are presented and discussed graphically for various parameters. The study provides quantitative information of interest; in general, it is observed that the maximum velocity does not occur in the middle of the channel but moves towards the upper wall as the magnetic field increases. The temperature and heat transfer coefficient increases with the increasing value of magnetic field and EPr.

This study analyzes the unsteady Rivlin-Ericksen fluid and irreversibility of exponentially temperature dependent VARIABLE VISCOSITY of hydromagnetic two-step exothermic chemical reactive flow along the channel axis with walls convective cooling. The non-Newtonian Hele-Shaw flow of Rivlin-Erickson fluid is driven by bimolecular chemical kinetic and unvarying pressure gradient. The reactive fluid is induced by periodic changes in magnetic field and time. The Newtons law of cooling is satisfied by the constant heat coolant convection exchange at the wall surfaces with the neighboring regime. The dimensionless non-Newtonian reactive fluid equations are numerically solved using a convergent and consistence semi-implicit finite difference technique which are confirmed stable. The response of the reactive fluid flow to variational increase in the values of some entrenched fluid parameters in the momentum and energy balance equations are obtained. A satisfying equations for the ratio of irreversibility, entropy generation and Bejan number are solved with the results presented graphically and discussed quantitatively. From the study, it was obtained that the thermal criticality conditions with the right combination of thermo-fluid parameters, the thermal runaway can be prevented. Also, the entropy generation can minimize at low dissipation rate and VISCOSITY.

This paper investigates numerically the effects of VARIABLE VISCOSITY on unsteady generalized Couette flow of a water base nanofluid with convective cooling at the moving surface. The Buongiorno model utilized for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The nonlinear governing equations of continuity, momentum, energy and nanoparticles concentration are tackled numerically using a semi discretization finite difference method together with Runge-Kutta Fehlberg integration scheme. Numerical results for velocity, temperature, and nanoparticles concentration profiles together with skin friction and Nusselt number are obtained graphically and discussed quantitatively.

In this article we endeavour to analyse the flow and heat transfer characteristics in a fourth-grade fluid with VARIABLE VISCOSITY. Two illustrative models of VARIABLE VISCOSITY namely the Reynolds and Vogels are considered. The flow in a stationary cylinder is induced by a constant pressure gradient. Partial slip is taken into account at the wall of the cylinder. Analytic solutions of velocity and temperature are first developed and then discussed in each case.

The present work illustrates the VARIABLE VISCOSITY of dust nanofluid runs over a permeable stretched sheet with thermal radiation. The problem has been modelled mathematically introducing the mixed convective condition and magnetic effect. Additionally analysis of entropy generation and Bejan number provides the fine points of the flow. The of model equations are transformed into non-linear ordinary differential equations which are then transformed into linear form using the spectral quasi-linearization method (SQLM) for direct Taylor series expansions that can be applied to non-linear terms in order to linearize them. The spectral collocation approach is then applied to solve the resulting linearized system of equations. The validity of our model is established using relative entropy generation analysis. A convergence schematic was obtained graphically. Consequence of various parameters on flow features have been delivered via graphs. Some important findings reported in this study that entropy generation analysis have significant impact in controlling the rate of heat transfer in the boundary layer region. The paper acquires realistic numerical explanations for rapidly convergent solutions using the Spectral quasi-linearization method. Convergence of the numerical solutions was monitored using the convergence graph. The initial guess values are automatically satisfied the boundary conditions. The resulting equations are then integrated using the Spectral quasi-linearization methods. The influence of radiation, heat and mass parameters on the flow are made appropriately via graphs. The effects of varying certain physical parameters of interest are examined and presented.

A numerical study of a mixed convection boundary layer flow on a vertical plate in a porous medium with magnetic field, VARIABLE wall temperature and VARIABLE VISCOSITY is made in this paper using the Darcy model. A free stream that varies as a power function of distance along the plate is assumed to flow parallel to the plate. Similarity solutions are obtained for the problem for both assisting flow and opposing flow. In the opposing flow case dual solutions are obtained for certain values of the parameters, and occurrence of boundary layer separation is also observed. Significant differences are observed between the behaviors of the two solutions of the dual solution case. Critical values of the mixed convection parameter are also obtained beyond which there exists no solution for the problem. Some of the observations of the analysis are - the range of values of the mixed convection parameter over which solutions exist for the problem is more in the presence of magnetic field than in its absence and also in the VARIABLE wall temperature case than in the isothermal case. Both local drag coefficient and heat transfer coefficient assume only positive values in the isothermal case while they assume both positive and negative values in the varying wall temperature case. Drag is less in the presence of magnetic field than in its absence and also in the isothermal case than in the varying wall temperature case. Heat transfer coefficient diminishes in the absence of magnetic field than in the presence of magnetic field.

In this study, the analysis of inherent irreversibility of chemical reactive third-grade poiseuille flow of aVARIABLE VISCOSITY with convective cooling is investigated. The dissipative heat in a reactive exothermic chemicalmoves over liquid in an irreversible way and the entropy is produced unceasingly in the system within the fixedwalls. The heat convective exchange with the surrounding temperature at the plate surface follows Newton’ s law ofcooling. 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. Theinfluence of some pertinent parameters on the entropy generation and the Bejan number are illustrated graphicallyand discussed with respect to the parameters.

The present investigation consists of an analytical treatment of a steady boundary layer flow of an Eyring-Powell model fluid due to a stretching cylinder with temperature dependent VARIABLE VISCOSITY. The heat transfer analysis is also taken into account. Using usual similarity transformations the governing equations have been transformed into non-linear ordinary differential equations and are solved by a powerful technique, the homotopy analysis method. Two models of VARIABLE VISCOSITY, namely, Reynolds' and Vogel's are considered. The convergence is carefully checked by plotting h-curves. The emerging parameters intrinsic to the problem are discussed through graphs.

Analysis of intrinsic irreversibility and heat transfer in a buoyancy-driven changeable VISCOSITY liquid along an incline heated wall with convective cooling taking into consideration the heated isothermal and isoflux wall is investigated. By Newton’ s law of cooling, we assumed the free surface exchange heat with environment and fluid VISCOSITY is exponentially dependent on temperature. Appropriate governing model equations for momentum and energy balance with volumetric entropy generation expression are obtained and then transformed using dimensionless VARIABLEs to form set of nonlinear boundary valued problem. Using shooting method with Runge-Kutta-Fehlberg integration scheme, the model is numerically tackled. Pertinent results for the fluid velocity, temperature, skin friction, Nusselt number, entropy generation rate and Bejan number are obtained and discussed.