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.

The combined e ects of magnetic field, Navier slip and CONVECTIVE heating on the entropy generation in a flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel plates under a constant pressure gradient have been examined. Both the lower and upper plates of the channel are subjected to asymmetric CONVECTIVE heat exchange with the ambient fluid.The governing non-linear governing partial differential equations are solved using the MATLAB PDE solver. The entropy generation number and the Bejan number are also obtained. The influences of the pertinent flow parameters on velocity, temperature, entropy generation and Bejan number are discussed graphically. It is observed that the plate surfaces act as a strong source of entropy generation and heat transfer irreversibility. Also, the entropy generation number decreases for increasing values of the magnetic parameter. The slip parameters are found to control the entropy generation. By using asymmetric COOLING of the plates, it is possible to operate the system with reduced entropy generation rate.

This article examines the combined effects of buoyancy force and asymmetrical CONVECTIVE COOLING on unsteady MHD channel flow and heat transfer characteristics of an incompressible, reactive, variable viscosity and electrically conducting third grade fluid. The chemical kinetics in the flow system is exothermic and the asymmetric CONVECTIVE heat transfers at the channel walls follow the Newton’s law of COOLING. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi-implicit finite difference scheme. Graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system.

The hydromagnetic flow of a Newtonian incompressible and electrically conducting variable-viscosity liquid film along an inclined isothermal or isoflux hydrophobic surface is investigated numerically. It is assumed that the fluid is subjected to a CONVECTIVE COOLING at the free surface in the presence of a transversely imposed magnetic field. We incorporated in the energy equation, the viscous dissipation, Joule heating due to the magnetic field and the local radiative heat flux term for optically thick gray fluid reported by Roseland approximation. The governing non-linear differential equations are obtained and solved numerically using the shooting method coupled with a fourth-order Runge-Kutta method. The effects of some parameters on velocity and temperature profiles, skin friction, Nusselt number entropy generation rate, and the Bejan number profiles are analyzed graphically and discussed.

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.

In this research, the transient analysis of radiative combustible viscous chemical reactive two-step exothermic fluid flow past a permeable medium with various kinetics, i. e., bimolecular, Arrhenius, and sensitized, are investigated. The hydromagnetic liquid is influenced by periodic vicissitudes in the axial pressure gradient and time along the channel axis in the occurrence of walls asymmetric CONVECTIVE COOLING. The convectional heat transport at the wall surfaces with the neighboring space takes after the COOLING law. The non-dimensional principal flow equations are computationally solved by applying convergent and absolutely stable semi-implicit finite difference techniques. The influences of the fluid terms associated with the momentum and energy equations are graphically presented and discussed quantitatively. The results show that the reaction parameter is very sensitive, and it, therefore, needs to be carefully monitored to avoid systems blow up. Also, a rise in the values of the second step term enhances the combustion rate and thereby reduces the release of unburned hydrocarbon that polluted the environment.

This study investigated the effect of reverting microchannels inside a heat sink on increase of COOLING rate as well as the effect of their different configurations on maximum temperature and pressure drop. Based on the convection heat transfer mechanism, selection of the embedded microchannels’ configurations including circular, square and triangular ones, was studied for geometric optimization of the discussed heat sinks. The goal was to minimize the thermal resistance through optimizing the geometries. The volume ratio  was defined as the ratio of the volume taken up by microchannels to the solid volume (portion of the heat sink not occupied by microchannels) and was considered as 0. 05. According to the results, in addition to obtaining a more uniform temperature distribution, reverting channels remarkably reduced the maximum temperature. Moreover, the heat sink with square shape showed less thermal resistance as compared to the other two geometries.