• Energy Research

AbstractWe present a generalized model to describe the flow of three non‐Newtonian nanofluids, namely, Jeffrey, Maxwell, and Oldroyd‐B nanofluids. Using this model, we study entropy generation and heat transfer in laminar nanofluid boundary‐layer stagnation‐point flow. The flow is subject to an external magnetic field. The conventional energy equation is modified by the incorporation of nanoparticle Brownian motion and thermophoresis effects. A hydrodynamic slip velocity is used in the initial condition as a component of the stretching velocity. The system of nonlinear equations is solved numerically using three different methods, a spectral relaxation method, spectral quasilinearization method, and the spectral local linearization method, first to determine the most accurate of these methods, and second as a measure to validate the numerical simulations. The residual errors for each method are presented. The numerical results show that the spectral relaxation method is the most accurate of the three methods, and this method is used subsequently to solve the transport equations and thus to determine the empirical impact of the physical parameters on the fluid properties and entropy generation.

PurposeThe focus of the paper is only on the contributions toward the use of entropy generation of non-Newtonian Casson fluid over an exponential stretching sheet. The purpose of this paper is to investigate the entropy generation and homogeneous–heterogeneous reaction. Velocity and thermal slips are considered instead of no-slip conditions at the boundary.Design/methodology/approachBasic equations in form of partial differential equations are converted into a system of ordinary differential equations and then solved using the spectral quasi-linearization method (SQLM).FindingsThe validity of the model is established using error analysis. Variation of the velocity, temperature, concentration profiles and entropy generation against some of the governing parameters are presented graphically. It is to be noted that the increase in entropy generation due to increase in heterogeneous reaction parameter is due to the increase in heat transfer irreversibility. It is further noted that the Bejan number decreases with Brinkman number because increase in Brinkman number reduces the total entropy generation.Originality/valueThis paper acquires realistic numerical explanations for rapidly convergent temperature and concentration profiles using the SQLM. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The resulting equations are then integrated using the SQLM. The influence of emergent flow, heat and mass transfer parameters effects are shown graphically.

Abstract The paper discusses the effects of homogeneous-heterogeneous reactions on stagnation-point flow of a nanofluid over a stretching or shrinking sheet. The model presented describes mass transfer in copper-water and silver-water nanofluids. The governing system of equations is solved numerically, and the study shows that dual solutions exist for certain suction/injection, stretching/shrinking and magnetic parameter values. Comparison of the numerical results is made with previously published results for special cases.

Abstract The effects of a homogeneous-heterogeneous reaction on steady micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium are numerically investigated in this paper. The model developed by Chaudhary and Merkin (Fluid Dyn. Res. 16:311-333, 1995) for a homogeneous-heterogeneous reaction in boundary layer flow with equal diffusivities for reactant and autocatalysis is used and extended in this study. The uniqueness of this problem lies in the fact that the solutions are possible for all values of the stretching parameter λ > 0 , while for λ < 0 (shrinking surface), solutions are possible only for a limited range of values. The effects of physical and fluid parameters such as the stretching parameter, micropolar parameter, permeability parameter, Schmidt number, strength of homogeneous and heterogeneous reaction parameter on the skin friction, velocity and concentration are analyzed, and these results are presented through graphs. The solute concentration at the surface is found to decrease with the strength of the homogeneous reaction, and to increase with heterogeneous reactions, the permeability parameter and stretching or shrinking parameters. The velocity at the surface was found to increase with the micropolar parameter.

Abstract In this paper, we present a theoretical study of the combined effects of activation energy and binary chemical reaction in an unsteady mixed convective flow over a boundary of infinite length. The current study incorporates the influence of the Brownian motion, thermophoresis and viscous dissipation on the velocity of the fluid, temperature of the fluid and concentration of chemical species. The equations are solved numerically to a high degree of accuracy using the spectral quasilinearization method. Brownian motion was noted as the main process by which the mass is transported out of the boundary layer. The effect of thermophoretic parameter seems to be contrary to the expected norm. We expect the thermophoretic force to ‘push’ the mass away from the surface thereby reducing the concentration in the boundary layer, however, concentration of chemical species is seen to increase in the boundary layer with an increase in the thermophoretic parameter. The use of a heated plate of infinite length increased the concentration of chemical species in the boundary layer. The Biot number which increases and exceeds a value of one for large heated solids immersed in fluids increases the concentration of chemical species for its increasing values. Highlights Combined effects of activation energy and binary chemical reaction are proposed. Spectral quasi-linearization method (SQLM) is used for computer simulations. Use Arrhenius activation energy in the chemical species concentration. Validate the accuracy and convergence using residual error analysis.

In this paper, the magnetohydrodynamic (MHD) axisymmetric stagnation-point flow of an unsteady and electrically conducting incompressible viscous fluid in with temperature dependent thermal conductivity, thermal radiation and Navier slip is investigated. The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity. The magnetic field is imposed normally to the sheet. The model equations that describe this fluid flow are solved by using the spectral relaxation method. Here, heat transfer processes are discussed for two different types of wall heating; (a) a prescribed surface temperature and (b) a prescribed surface heat flux. We discuss and evaluate how the various parameters affect the fluid flow, heat transfer and the temperature field with the aid of different graphical presentations and tabulated results.

The present study explores magnetic hyperthermia for a treatment of a breast tumour with a surrounding healthy breast gland region and overlying fat and skin regions. A mathematical model that utilizes the Brinkman–Forchheimer-extended Darcy equations and non-Newtonian (Carreau–Yasuda) constitutive equation is constructed for the intratumoural injection of an aqueous iron–platinum (FePt) nanoparticle suspension, blood perfusion through the tissue regions, and the temperature and nanoparticle distributions during the process of hyperthermia therapy. The equations governing nanofluid flow, heat transfer and the suspended and deposited nanoparticle volume fractions are solved numerically via the finite element technique, and numerical results are computed in the FreeFEM++ software. Using the obtained results, the impact of the Reynolds number, nanoparticle diameter and haematocrit on the efficacy of magnetic hyperthermia therapy is investigated. The results revealed that the tissue penetration of nanoparticles is more pronounced when the red blood cell concentration and nanoparticle diameter are lower. Furthermore, the required duration for effective magnetic hyperthermia and the healthy tissue damage decrease with increasing haematocrit and nanoparticle diameter.