In this paper, we consider the hyperbolic Ricci-Bourguignon ow on a compact man-ifold M and show that this ow has a unique solution on short-time with imposing on initial conditions. After then, we , nd evolution equations for Riemannian cur-vature tensor, Ricci curvature tensor and scalar curvature of M under this ow. In the , nal section, we give some examples of this ow on some compact manifolds.

Use of spike on a hemispherical body changes the ow  eld and hence, the aerodynamic drag. Computational studies have been carried out to obtain the ow  eld around a hemispherical body with spikes at a hypersonic Mach number of 6. The e ect of shape of spike tip and length has been studied. Laminar computations have been made adopting structured grid using commercial software FLUENT. It is observed that use of a sharp spike itself reduces the drag signi cantly. However, the use of a hemispherical head spike further reduces the drag. Contribution of di erent components towards drag indicates that the increase in length of a spike does not change the spike contribution. However, the ow  eld on main body is altered, which leads to reduction in drag with change in length. The estimated maximum drag is found to be highest among all reported drag values with any spike shape and length in the literature.

In the present study, the nonlinear model of non-Newtonian blood flow in cosine-shape stenosed elastic artery is numerically examined. The model is carried out for axisymmetric, two-dimensional and fully developed blood flow. The vessel wall is assumed to be have time-dependent radius that is important factor for study of blood flow. The cosine-shape stenosis convert to rigid artery by using a appropriate coordinate transformation and closed form solutions are discovered. The Sisko non-Newtonian fluid model is used for discribing blood rheology. The Navier-stokes equations of momentom containing pulastic pressure gradient. The resulting explicit of the governing nonlinear equations have been obtained numerically with the help of the finite differece scheme and Matlab program. The key dynamic parametrs similar resistance impedance, velocity profiles and the volumetric flow rate are studied. The influence of non-Newtonian rheological properties of unsteady blood flow and stenosis severity are found and computer modeling and simulation shown graphically.

The present study addresses the entropy generation in the ow of Walters-B nanomaterial. Energy equation consists of ohmic heating, radiation, and heat generation. Binary chemical reaction with the modi ed Arrhenius energy was employed in this study. In addition, the consequences of thermophoresis, Brownian motion, and viscous dissipation were taken into account. Convergent solutions were presented using homotopy analysis. Intervals of convergence were explicitly identi ed. The results of physical quantities of interest were analyzed. There was a decrease in the mass transfer rate at a higher value of chemical reaction parameter. Enhanced values of Brinkman number and magnetic parameter caused a decrease in the total entropy rate.

The cleanroom is a controlled space used in various industries such as electronics, and medical and military industries. One of the most important tests to evaluate the performance of the cleanroom is recovery test. Recovery test determines the time period during which a cleanroom returns to its designated cleanliness level after an instant or a period of deliberate or unintentional contamination. In this paper, a thorough investigation of recovery period has been implemented. In the study, air change rate and its pattern were investigated using the Eulerian and Lagrangian approaches as well as LES, DES, and k 􀀀 ! SST turbulent models. Simulation results were evaluated through control volume analysis. Parameters such as the air change rate, the number of particles, and pressure and energy consumption in various radial and tangential angles of di users were studied. Results showed that radial angle had little positive and occasionally negative e ects on recovery period. On the contrary, tangential angle improved decontamination rate; at maximum performance ( = 45 ), it could reduce recovery period by as much as 25%, which in turn reduced energy consumption. In addition, the DES model provided the best and most coinciding answers among all turbulence models.

This study proposed the heat transfer correlation for a surface  tted with rectangular ribs by solving the continuity, momentum, energy, and turbulence equations by the  nite volume approach. Extensive computations were performed to modify both the duct Reynolds number (ReDh; duct ) and the nozzle Reynolds number (ReDh; nz ) in the range of 6, 000{20, 000. The volume fraction ( ) and the Prandtl number (Pr) of the nano uid varied in the range of 0 to 5% and 7. 288 to 9. 92, respectively. The number of protrusions (n) varied from 1 to 4. The data collected from numerical experimentation were regressed nonlinearly using Levenberg and Marquest (L-M) method to obtain an empirical correlation for the Nusselt number. The Nusselt number predicted from the correlation was compared with its value obtained from the computations. Close agreement between the predicted and computed Nusselt numbers was observed. In terms of heat transfer augmentation, the duct Reynolds number, the nozzle Reynolds number, and the volume fraction of nano uid were found to be some of the signi cant in uencing parameters in heat transfer.

This article addresses salient features of gyrotactic microorganisms and activation energy in the ow of nano fluid by rotating disks. An ESHS process is implemented to examine the thermal transport characteristics. Additionally, the nanoparticle mass flux condition is considered and the solutions are numerically computed. Impacts of various physical variables appearing in the solutions of non-linear systems are carefully analyzed. The current work identifies that temperature distribution of nanoliquid enhances via thermophoresis and Brownian diffusion variables. Moreover, activation energy and temperature difference parameters diminish nanoparticle concentration. Comparative study is provided in order to validate the outcomes.