The study of boundary layer flow under mixed convection has been investigated numerically for various nanofluids over a semi-infinite flat plate which has been placed vertically upward for both buoyancy-induced assisting and buoyancy-induced opposing flow cases. To facilitate numerical calculations, a suitable transformation has been made for the governing partial differential equations (PDEs). Then, similarity method has been applied locally to approximate the nonlinear PDEs into a coupled nonlinear ordinary differential equations (ODEs). Then, quasilinearization method has been taken for linearizing the nonlinear terms which are present in the governing equations. Thereafter, implicit trapezoidal rule has been taken for integration numerically along with principle of superposition. The effect of physical parameters which are involved in the study are analyzed on the flow and heat transfer characteristics. This study reveals the presence of dual solutions in case of opposing flow. Further, this study shows that with increasing $$\phi$$ ϕ and Pr, the range of existence of dual solutions becomes wider. Also, it has been noted that nanofluids enhance the process of heat transfer for buoyancy assisting flow and it delays the separation point in case of opposing flow.

In the present study, simulation of a stirred tank using axial flow impeller has been studied numerically to see the behaviour of flow variables in the entire vessel. It is assumed that the flow is steady state, two dimensional, incompressible and axisymmetric. For simulation, Partially-Averaged Navier-Stokes (PANS) $$k_u-\epsilon _u$$ k u - ϵ u turbulence model has been taken into account. For discretization, control volume method along with upwind and power-law schemes have been taken. The solutions are obtained by using the SIMPLE algorithm. The boundary conditions for impeller are given by using the experimental data. The main objective is to investigate the influence of different filters width $$f_k$$ f k of the PANS $$k_u-\epsilon _u$$ k u - ϵ u model parameter on the characteristic flow variables. The predicted results of the PANS $$k_u-\epsilon _u$$ k u - ϵ u model for different $$f_k$$ f k have been compared with the experimental data at different axial levels of the stirred tank. It has been observed that the power-law scheme gives better agreement with the experimental data. Further, near the impeller region, PANS predicted results are better for smaller $$f_k$$ f k . Also, Reynolds-Averaged Navier-Stokes Shear Stress Transport (SST) $$k-\omega $$ k - ω turbulence model has been tested for comparative study.

No abstract

The present study deals with the numerical simulation of stirred tank in the presence of nanofluids to see the effect of different volume fraction (ϕ) of nanoparticles on the behaviour of flow characteristics and for the calculation of mixing time in the entire tank. The flow is assumed to be steady, axisymmetric, two dimensional and incompressible. For the simulation of flow inside the vessel, partially-averaged Navier–Stokes (PANS) k u  − ϵ u turbulence model is used. Control volume method has been taken to descretize the governing equation along with power-law schemes. Further, semi-implicit method for pressure-linked equations revised (SIMPLER) algorithm and line-by-line tri-diagonal matrix algorithm (TDMA) have been taken to obtain the solution. The objective is to investigate the influence of ϕ on the characteristic flow variables and to calculate mixing time for different ϕ of nanofluids and for different values of f k , PANS model parameter. It is noted that with the increase in ϕ, mixing time has also been increased and it increases very fast for PANS k u  − ϵ u model with the increase in filter width f k .

The effect of viscous dissipation on mixed convection boundary layer flow for Ag‐water nanofluid under steady‐state condition has been studied numerically for both the buoyancy assisting and opposing flows over a vertical semi‐infinite flat plate. A new co‐ordinate system true(ξ,ηtrue) has been introduced to transform the governing partial differential equations (PDEs) to facilitate the numerical calculations. Then, the local similarity method has been used for approximating the transformed PDEs to ordinary differential equations. Further, the quasi‐linearization method has been introduced to linearize the nonlinear equations and then numerical integration has been carried out using implicit trapezoidal rule along with the principle of superposition. For higher Pr, the coupled differential equations behave like stiff differential equations. To overcome the situation, orthonormalization process has been introduced. The effects of solid volume fraction of nanoparticles true(φtrue), the mixed convection parameter true(λtrue), Prandtl number true(Prtrue), and Eckart number true(Ectrue) have been analyzed on the heat transfer and flow characteristics. It has been observed that the dual solutions are obtained for buoyancy opposing flow only and the range of dual solutions have become wider with the increases in φ. Further, nanofluids enhance the heat transfer process as compared to conventional heat transfer fluids true(φ=0true). Moreover, the addition of viscous dissipation causes less heat transfer in the boundary.