On bio-convection thermal radiation in Darcy – Forchheimer flow of nanofluid with gyrotactic motile microorganism under Wu’s slip over stretching cylinder/plate

Purpose The purpose of this study is to discuss the Darcy–Forchheimer nanoliquid bio-convection flow by stretching cylinder/plate with modified heat and mass fluxes, activation energy and gyrotactic motile microorganism features. Design/methodology/approach The proposed flow model is based on flow rate, temperature of nanomaterials, volume fraction of nanoparticles and gyrotactic motile microorganisms. Heat and mass transport of nanoliquid is captured by the usage of popular Buongiorno relation, which allows us to evaluate novel characteristics of thermophoresis diffusion and Brownian movement. Additionally, Wu’s slip (second-order slip) mechanisms with double stratification are incorporated. For numerical and graphical results, the built-in bvp4c technique in computational software MATLAB along with shooting technique is used. Findings The influence of key elements is illustrated pictorially. Velocity decays for higher magnitude of first- and second-order velocity slips and bioconvection Rayleigh number. The velocity of fluid has an inverse relation with mixed convection parameter and local inertia coefficient. Temperature field enhances with the increase in estimation of thermal stratification Biot number and radiation parameter. A similar situation for concentration field is observed for mixed convection parameter and concentration relaxation parameter. Microorganism concentration profile decreases for higher values of bioconvection Lewis number and Peclet number. A detail discussion is given to see how the graphical aspects justify the physical ones. Originality/value To the best of the authors’ knowledge, original research work is not yet available in existing literature.

Mixed convection flow of nanofluid with Hall and ion-slip effects using spectral relaxation method

In this article, the Hall and ion-slip effects on a mixed convection flow of an electrically conducting nanofluid over a stretching sheet in a permeable medium have been discussed. Using the similarity transformations, the partial differential equations corresponding to the momentum, energy, and concentration equations are transformed to a system of nonlinear ordinary differential equations which are solved numerically using a spectral relaxation method (SRM). The effects of significant parameters on the velocities, temperature, and concentration profiles are analyzed graphically. Moreover, the results of the skin friction coefficients, local Nusselt number, and Sherwood number are determined numerically. The results of the analysis showed that the velocity profile in the flow direction increases with an increase in mixed convection parameter λ, Hall parameter βh, and ion-slip parameter βi, and it decreases with an increase in the magnetic parameter M. Furthermore, temperature and concentration profiles decrease as the mixed convection parameter λ and buoyancy ratio Nr increase. It is also observed that the skin friction coefficients, local Nusselt number, and Sherwood number increase with an increase in the Hall parameter βh, mixed convection parameter λ, and buoyancy ratio Nr.

Viscous Dissipation Effect on a Steady Generalised Couette Flow of Heat-Generating/Absorbing Fluid in a Vertical Channel

This article investigates the viscous dissipation effect on steady generalised Couette flow of heat-generating/absorbing fluid in a vertical channel. Equations of energy and momentum are obtained and solved using the homotopy perturbation method. The influences of the dimensionless flow parameter have been plotted graphically and discussed for varying values of the controlling parameters. During the course of computation, it is found that fluid temperature and velocity increase with an increase in viscous dissipation and also seen that growing mixed convection parameter Gre leads to a corresponding rise in temperature and velocity. It is further discovered that heat absorption leads to increase in the heat transfer on the heated wall. Finally, it is concluded that heat generation contributes to increase the mixed convection, hence, it requires decrease in mixed convection parameter to bring about a reverse flow near the stationary plate.

Mixed convection boundary-layer flow of a viscoelastic fluid due to horizontal elliptic cylinder with constant heat flux

This article presents numerical analysis of mixed convection laminar flow of a second grade viscoelastic fluid due to cylinder of elliptic cross-section with prescribed surface heat flux. Dimensionless non-linear analysis is computed employing Keller-box method. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed graphically to examine their behavior along the surface of cylinder. The flow and heat transfer rates are carefully judged while varying the important resulting parameters (mixed convection parameter, viscoelastic parameter aspect ratio, etc.) through sketched graphs keeping major axis of ellipse along and perpendicular to the horizontal. These two positions of major axis are termed as blunt and slender orientations, respectively. The values of skin friction and Nusselt number increase with rise in mixed convection parameter. On the other hand, these quantities lessen by increasing the value of viscoelastic parameter.

Mixed convection flow due to a moving vertical plate parallel to free stream under the influence of Newtonian heating and thermal radiation

The steady mixed convection flow from a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of thermal radiation as well as Newtonian heating effects. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in conjunction with the quasi-linearization technique. Computations are performed and representative set is displayed graphically to illustrate the influence of the mixed convection parameter ( ), Prandtl number (Pr), the ratio of free stream velocity to the composite reference velocity ( ) and the radiation parameter (R) on the velocity and temperature profiles. The numerical results for the local skinfriction coefficient ( ) and surface temperature ( ) are also presented. The results show that the streamwise co-ordinate  significantly influences the flow and thermal fields which indicate the importance of non-similar solutions. Also, it is observed that the increase of mixed convection parameter causes the increase in the magnitude of velocity profile about 65% for lower Prandtl number fluids (Pr=0.7), while it decreases in the temperature profile about 30%. Present results are compared with previously published work and are found to be in excellent agreement.

Mixed convection boundary layer flow from a vertical truncated cone in a nanofluid

Purpose – The purpose of this paper is to investigate the steady mixed convection boundary layer flow from a vertical frustum of a cone in water-based nanofluids. The problem is formulated to incorporate three kinds of nanoparticles: copper, alumina and titanium oxide. The working fluid is chosen as water with the Prandtl number of 6.2. The mathematical model used for the nanofluid incorporates the particle volume fraction parameter, the effective viscosity and the effective thermal diffusivity. The entire regime of the mixed convection includes the mixed convection parameter, which is positive for the assisting flow (heated surface of the frustum cone) and negative for the opposing flow (cooled surface of the frustum cone), respectively. Design/methodology/approach – The transformed non-linear partial differential equations are solved numerically for some values of the governing parameters. The derivatives with respect to? were discretized using the first order upwind finite differences and the resulting ordinary differential equations with respect to? were solved using bvp4c routine from Matlab. The absolute error tolerance in bvp4c was 1e-9. Findings – The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. The effects of the particle volume fraction parameter \phi, the mixed convection parameter \lambda and the dimensionless coordinate? on the flow and heat transfer characteristics are determined only for the Cu nanoparticles. It is found that dual solutions exist for the case of opposing flows. The range of the mixed convection parameter for which the solution exists increases in the presence of the nanofluids. Originality/value – The paper models the mixed convection from a vertical truncated cone using the boundary layer approximation. Multiple (dual) solutions for the flow reversals are obtained and the range of existence of the solutions was found. Particular cases for ?=0 (full cone), ? >>1 and (free convection limit) \lambda>>1were studied. To the authors best knowledge this problem has not been studied before and the results are new and original.