KHA model comprising MoS4 and CoFe2O3 in engine oil invoking non-similar Darcy-Forchheimer flow with entropy and Cattaneo-Christov heat flux.

Objective: Nanoliquid flows are widely utilized in industrial, petroleum, engineering, and pharmaceutical applications including electric cooling, drug delivery, nuclear reactor cooling, solar collectors, heat exchangers, magnetohydrodynamic power generators, aerospace, porous media, thermal storage systems, and many others. Darcy-Forchheimer magnetized hybrid nanoliquid subjected to a stretchable cylinder was addressed, and the Cattaneo-Christov heat flux analysis was considered. Herein, disulfido (dithioxo) molybdenum (MoS4) and cobalt ferrite (CoFe2O4) were considered as nanoparticles, and engine oil as a conventional liquid. The thermal relationship of heat generation and radiation was discussed, and the influence of the entropy rate was addressed. Methodology: Governing expressions were transformed into dimensionless forms. Simulation by the ND-solve technique was implemented. Conclusions: Features for the entropy rate, liquid flow, and temperature against emerging variables for nanoliquid (MoS4/engine oil) and hybrid nanoliquid (MoS4 + CoFe2O4/engine oil) were explored. The numerical results of the coefficient of skin friction and thermal transport rate for nanoliquid (MoS4/engine oil) and hybrid nanoliquid (MoS4 + CoFe2O4/engine oil) were examined. Reduction in velocity clearly occurred through a magnetic field, whereas the reverse impact held for the entropy rate. The thermal field and entropy rate against the curvature parameter were enhanced. A decrease in liquid flow occurred for higher porosity variables. An enhancement in the entropy rate was witnessed for radiation and porosity parameters. Higher radiation and thermal relaxation time variables resulted in enhancement of the thermal transport rate.

Entropy generation in bioconvection hydromagnetic flow with gyrotactic motile microorganisms.

Here, the magnetohydrodynamic bioconvective flow of a non-Newtonian nanomaterial over a stretched sheet is scrutinized. The characteristics of convective conditions are analyzed. Irreversibility analysis in the presence of gyrotactic micro-organisms is discussed. Energy expression is assisted with thermal radiation, heat generation and ohmic heating. Buongiorno's model is employed to discuss the characteristics of the nanoliquid through thermophoresis and random diffusions. Nonlinear expressions of the given model are transformed through adequate transformations. The obtained expressions have been computed by the Newton built in-shooting technique. Results of influential variables for velocity, concentration, microorganism field, temperature and entropy rate are graphically studied. Clearly, velocity reduction is witnessed for the bioconvection Rayleigh number and magnetic variable. A higher heat generation variable leads to augmentation of temperature. An increase in the magnetic variable results in entropy and temperature enhancement. A higher Peclet number results in microorganism field reduction. Temperature distribution rises for radiation and the thermal Biot number. A higher solutal Biot number intensifies the concentration. The entropy rate for radiation and diffusion variables is enhanced.

Unsteady nanofluid flow over a cone featuring mixed convection and variable viscosity.

This article addresses unsteady nanofluid flow over a cone with MHD and mixed convection effects. Effects of variable viscosity and viscous dissipation are also considered. The resulting system of equations is tackled through the Homotopy Analysis Method (HAM). The impact of different influential variables on skin friction coefficient, heat and mass flux are discovered through numerical tables and graphs. It is noted that the surface drag force in x and y directions increases against the buoyancy force parameter. Also, it is observed that the tangential and azimuthal velocity decrease against the variable viscosity parameter. Furthermore, the temperature of fluid is observed to decay against the unsteady parameter but it increases against the Eckert number.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response.

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

Impacts of entropy generation in radiative peristaltic flow of variable viscosity nanomaterial.

Current analysis highlights the aspects of different nanoparticles in peristalsis with entropy generation. Mathematical equations of considered problem are modelled via conservation laws for mass, momentum and energy. Such equations contain variable viscosity, nonlinear thermal radiation, viscous dissipation, heat generation/absorption and mixed convection aspects. Boundary conditions comprise the second order velocity and first order thermal slip effects. Entropy expression is obtained by utilization thermodynamics. Simplified and dimensionless forms of the considered conservative laws are obtained through lubrication technique. Resulting system of equations subject to the considered boundary conditions is solved numerically via built-in shooting procedure in Mathematica. Such numerical procedure is very suitable to obtain numerical results directly and fastly in the form of graphs. Further all the considered flow quantities are discussed graphically for the significant parameters of interest in detail. Both velocity and temperature are decreasing against large volume fraction parameter. Increasing temperature dependent viscosity effects decrease the entropy and enhance the Bejan number.

The level of public awareness of cancer in Hail, Saudi Arabia.

OBJECTIVE: Cancer is a group of diseases characterized by uncontrolled cell division of abnormal cells that can result in death if not treated well. Cancer is considered to be a leading cause of mortalities throughout the globe and an important barrier to increase life span. This study was conducted to assess awareness among graduates studying in university of Hail related to cancer. MATERIALS AND METHODS: This is an online survey-based study conducted using online tool "Google Forms". The inclusion criteria were that the participants should understand Arabic, must have 18 years or above age and currently living or a permanent resident of Hail city. RESULTS: Total 108 valid responses were included in this analysis, 56 were male and 52 were female participants. Around 106 of the participants were Saudi nationals among which 62 were the permanent resident of the Hail city and 46 were migrants which were not the permanent resident but moved into the city for the purpose of education or business. There was significant association between awareness level of individuals regarding cancer associated symptoms including weight loss, fatigue, inflammation and hair loss and common causes of cancers, including family history, radiation exposure, smoking, obesity, aging and fast-food exposure. However, there was no significance between awareness of cancer and other factors, including age, gender, marital status, education, nationality, residence and monthly income. CONCLUSIONS: Overall our study reveals that there is significant knowledge among Hail population but still there is a need to increase  awareness level of general population to manage the disease more efficiently.

Analytical evaluation of Oldroyd-B nanoliquid under thermo-solutal Robin conditions and stratifications.

Chilling systems are important in the improved technological thermal mechanisms which are considered continuously in passive along with active heat-transference improvement procedures. Engineers recommended several approaches to upsurge heat transference of thermal structures. The pulsating flow, corrugated tube, magnetic field aspect and nanoliquids are the heat-transference improvement procedures delved continuously. In present research work, we addressed the heat-transference characteristics of non-Newtonian (Oldroyd-B) liquid towards heated stratified surface. Thermally radiative laminar flow is modeled. In addition, we accounted Buongiorno's nanoliquid model which includes Brownian along with thermophoretic diffusions. Modeling is further based on heat source, magnetohydrodynamics, dual stratification, thermal radiation and convective conditions. Mathematical system is simplified through boundary-layer idea. Similarity variables are reported with the aim to simplify complex mathematical system. Homotopy algorithm yields convergent results of non-dimensional expressions. Our study unveils diminution of thermal along with solutal fields when stratification factors are increased.

Corrigendum to "Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects" [Computer methods and programs in biomedicine 184 (2020) 105,086].

In this published paper, a mathematical modeling has been conducted for the peristaltic transport in flow of hybrid nanofluid between rotating channel in the presence of nonlinear thermal radiation, slip effects and entropy generation. This corrigendum correct the flow geometry, figures captions and plots "Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects" [Computer Methods and Programs in Biomedicine 184 (2020) 105,086] where these mistake are occurred during production process and therefore, some captions are shuffled. The difference in the captions and plots however does not affect the authenticity and mathematical validity of the problem in purpose of this published research article is to investigate the peristaltic transport in flow of hybrid nanofluid between rotating channel subject to nonlinear thermal radiation, slip effects and entropy generation. However, the flow geometry and the captions and plots should be arranged.

Electro-magneto flow of nanomaterial with irreversibility.

Here we discuss the analysis of irreversibility in electrical magnetohydrodynamic convective flow of nanomaterials over a stretchable surface. Energy equation deliberated through Joule heating, dissipation and heat source/sink. Furthermore features chemical reaction is also considered. Total entropy optimization is calculated. Salient features of thermophoresis effect and random motion of particles are studied. Nonlinear couple equations are converted to ordinary system by using the transformation. The obtained system are elucidated through ND solve technique. Salient features of pertinent variables on entropy optimization, velocity, Bejan number, concentration and temperature are discussed. Nusselt number, gradient of concentration and surface drag force are computationally calculated. Velocity and temperature show opposite behaviors via magnetic parameter. Electric and magnetic field parameters on entropy optimization have opposite results.

Modeling and computational analysis of 3D radiative stagnation point flow of Darcy-Forchheimer subject to suction/injection.

BACKGROUND: This manuscript elaborates the three-dimensional radiated Darcy-Forchheimer viscous liquid flow subject to permeable stretched surface. The stretched surface is nonlinear and saturated via Darcy-Forchheimer medium. Energy expression is derived through implementation of first of thermodynamics and discussed subject to convective condition and nonlinear heat flux. Mixed convection is also considered. METHOD: The governing systems of nonlinear equations are tackled numerically by Shooting method. RESULTS: Graphical results are depicted and examined with different values of non-dimensional parameters for velocity and energy equations respectively. Drag force and Nusselt number are computationally computed and analyzed through Tables. CONCLUSIONS: It is concluded from the derived outcomes that both component of velocity decay against higher values of local inertia coefficient and inverse Darcy number variables. For suction case both velocities increases while opposite trend is observed for injection case. Temperature profile has an increasing impact for higher values of Radiation, and Biot number while opposite result is seen for injection. Drag force or skin friction declines via larger injection variable. Nusselt number increases for radiation variable.

Entropy optimization in CNTs based nanomaterial flow induced by rotating disks: A study on the accuracy of statistical declaration and probable error.

BACKGROUND: CNTs (Carbon nanotubes) being allotropes of carbon, made of graphene and diameters of single and multi-walls carbon nanotubes are typically 0.8 to 2 nm and 5 to 20 mn, although diameter of MWCNTs can exceed 100 nm. Carbon nanotubes lengths range from less than 100 nm to 0.5 m. Their impressive structural, electronic and mechanical attributes subject to their small size and mass, their high electrical and thermal conductivities, and their strong mechanical potency. CNTs based materials are successfully applied in medicine and pharmacy subject to their huge surface area that is proficient of conjugating or adsorbing with a wide variety of genes, drugs, antibodies, vaccines and biosensors etc. Therefore, we have presented a theoretical study about mathematical modeling of CNTs based viscous material flow between two rotating disks. Both types of nanotubes i.e., SWCNTs and MWCNTs are considered. Xue model is used for the mathematical modeling. Fluid flow is due to rotating disks. Main focus here is given to probable error and statistical declaration. Entropy is calculated for both single and multi-walls nanotubes. METHOD: Nonlinear PDEs are first converted into ODEs and then computed for homotopy convergent solutions. RESULTS AND CONCLUSION: Statistical declaration and probable error for skin friction and Nusselt number are numerically computed and discussed through Tables. From obtained outcomes it is concluded that magnitude of skin friction increases at both disks surface for higher values of Reynolds number, lower stretching parameter and porosity parameter while it decays for both of disks versus larger rotation parameter. Nusselt number or heat transfer rate also enhances at both disks in the presence of radiation and Reynolds number while it decays against Eckert number.

Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects.

BACKGROUND: In last few decades, a new class of working materials which comprises from two solid materials dispersed in a continuous phase liquid was established and deeply scrutinized. These materials are called hybrid nanomaterials. This research article aims to investigate entropy optimization in hybrid nanomaterial flow through a rotating peristaltic channel walls. Flow behavior is analyzed between the channels which is caused by propagation of sinusoidal waves. Viscosity of fluid is considered variable instead of constant characteristics. Fluid saturates through porous attributes of channel walls. Nonliear radiative flux and convective condition are considered. Slip conditions are imposed at the boundary of walls. METHODS: Built-in-Shooting technique is employed to obtain the numerical outcomes for the considered flow problem. RESULTS: Impacts of sundry variables on the entropy, temperature and velocity are scrutinized through different graphs. Numerical result presents that the axial velocity escalates with the inclusion of hybrid nanomaterial. The temperature of fluid enhances through higher estimations of hybrid nanoparticles. CONCLUSIONS: Here the flow behavior is discussed between the channels which are caused by propagation of sinusoidal waves with speed c. Entropy generation rate is minimum for variable viscosity and maximum for hybrid nanoparticles. Hybrid nanoparticles increase the temperature of fluid. Bejan number presents the similar impact for variable viscosity and thermal slip parameters. Temperature field decays through higher values of Brinkman number.

Entropy optimization analysis in MHD nanomaterials (TiO2-GO) flow with homogeneous and heterogeneous reactions.

BACKGROUND: Nanomaterials have higher inspiration in the growth of pioneering heat transportation fluids and good efforts were made in this field during the recent year. Nowadays numerous scientists and researchers have focused their struggle on nanomaterials study. Nanoliquids have advanced properties which make them efficient in various applications including engine cooling, hybrid-power engine, pharmaceutical processes, refrigerator and vehicle thermal management etc. Therefore such implication in mind the entropy optimization in magnetohydrodynamic nanomaterials (TiO2 - GO) flow between two stretchable rotating disks is discussed here. Energy expression subject to Joule heating, thermal radiation and viscous dissipation is modeled. Entropy optimization rate is based upon thermodynamic second law. Here titanium dioxide (TiO2) and graphene oxide (GO) and water (H2O) are used as nanoliquids. Homogeneous and heterogeneous reactions have been accounted. METHODS: Transformation process reduced nonlinear PDE's to ordinary differential systems. Formulated systems are solved due to implementation of Newton built in shooting method. RESULTS: Salient behavior of influential variables on velocity, entropy optimization, temperature, Bejan number and concentration graphically illustrated for (TiO2 and GO). Surface drag force and gradient of temperature ((Cf1, Cf2) and (Nux1, Nux2)) are numerically computed for various interesting parameters at lower and upper disks respectively. Axial and radial velocities components boost up for larger (Re) but opposite is hold for tangential velocity. Entropy optimization and temperature are increased for higher Brinkman number (Br). CONCLUSIONS: A significant augmentation occurs in radial and axial velocities (f'(ξ) and f(ξ)) versus stretching parameter, while opposite is hold for tangential velocity (g(ξ)). For larger values of Reynold and Brinkman numbers the temperature increases. Temperature and entropy optimization have opposite effect for radiation parameter. Concentration has similar results for Reynold and Schmidt numbers. Entropy optimization and Bejan number for radiation parameter have similar outcome. Bejan number decays for Brinkman number.

Theoretical and numerical investigation of Carreau-Yasuda fluid flow subject to Soret and Dufour effects.

BACKGROUND: Newtonian fluids can be categorized by a single coefficient of viscosity for specific temperature. This viscosity will change with temperature; it doesn't change with strain rate. Just a small group of liquids show such steady consistency. A fluid whose viscosity changes subject to relative flow velocity is called non-Newtonian liquids. Here we have summarized a result for the flow of Carreau-Yasuda fluid over a porous stretchable surface. Mixed convection is considered. Modeling of energy expression is performed subject to Soret and Dufour effects. METHOD: The nonlinear PDE's are changed to ODE's through suitable transformations and then solved for numerical solutions via Built-in shooting method (bvp4c). RESULTS: Variation of important variables is studied on the concentration, temperature and velocity fields. Tabular representation for study of skin friction and heat transfer rate is presented for important variables. Our results show that velocity decreases versus higher estimations of Weissenberg number, porosity parameter, buoyancy ratio and mixed convection parameter. Temperature decays via Weissenberg number and porosity parameter. Increase in concentration is noticed through higher Soret number and porosity parameter. Skin friction and heat transfer rate (Nusselt number) boosts versus larger porosity parameter and Prandtl number respectively while it decays against Weissenberg number and Dufour and Eckert number.

Magneto rotating flow of hybrid nanofluid with entropy generation.

BACKGROUND: Study of nanofluids has been enormously increased for the last couple of years. Regardless of some irregularity in the revealed outcomes and lacking consistency, yet the mechanisms of heat transport have been emerged as highly efficient. In the continuation of nanomaterials research, the investigators and analyst have also attempted to utilize hybrid nanomaterial recently, which is designed by suspending unique nanomaterials (nanoparticles) either in mixture or composite structure. The theory of hybrid nanofluids can be further modified for heat transport and pressure drop attributes by trade-off between disadvantages and advantages of individual suspension, ascribed to great aspect ratio, better thermal system and synergistic impact of nanomaterials. Therefore, we have conducted a theoretical attempt on MHD entropy optimized viscous hybrid nanomaterial flow between two parallel plates. The boundaries of plates are fixed with velocity and thermal slip aspects. Chemical reaction with novel aspect of activation energy is accounted. Furthermore, thermal radiation, heat generation and Joule heating are examined. METHOD: The modeled system is numerically simulated through bvp4c technique. RESULTS: Behaviors of pertinent variables on the velocity, skin friction, temperature, Nusselt number, entropy generation rate and concentration are presented and discussed through different graphs. Temperature field decays against higher values of Eckert number and thermal slip variable. CONCLUSIONS: It is noticed that velocity of material particles increase against larger estimations of rotation parameter. Temperature declines versus larger Prandtl and Eckert numbers. Concentration decays when an enhancement is occurred in the Lewis number. Magnitude of surface drag force upsurges for rising values of Prandtl number and radiation parameter. Furthermore, magnitude of Nusselt number enhances through larger Eckert number, magnetic number and Prandtl number.

On the numerical simulation of stagnation point flow of non-Newtonian fluid (Carreau fluid) with Cattaneo-Christov heat flux.

BACKGROUND: This research article is devoted to evaluating the impact of Cattaneo-Christov heat in MHD stagnation point flow over a stretched and shrinking surface of the cylinder. MHD liquid of Carreau fluid is considered. Flow is generated due to stretching and shrinking aspects. The energy equation is developed in the presence of Cattaneo-Christov heat flux, where thermal relaxation time plays an important role in the heat transport. METHOD: The appropriate transformations are employed to solve a differential system via shooting method (bvp4c). RESULTS: The velocity, skin friction coefficient, temperature and Nusselt number are discussed versus different pertinent flow variable graphically. Over results indicate that the velocity distribution decreases against larger magnetic power law index and Weissenberg number. Temperature field diminishes via Prandtl number and thermal relaxation variable. Engineering quantities are discussed graphically. Magnitude of skin friction or velocity gradient upsurges versus magnetic parameter. Moreover, temperature gradient or Nusselt number shows the increasing impact via Prandtl number. Main observations of the considered flow problem are listed as concluding remarks.

Entropy optimized dissipative CNTs based flow with probable error and statistical declaration.

BACKGROUND: CNTs are categorized subject to their structures i.e., SWCNTs (single wall nanotubes), DWCNTs (double wall nanotubes) and MWCNTs (multi-wall nanotubes). The various structures have distinct characteristics that make the nanotubes suitable for various physical applications. It is due their unique electrical, mechanical and thermal attributes CNTs present thrilling opportunities for mechanical engineering, industrial, scientific research and commercial applications. There is fruitful potential for carbon nanotubes in the composites business and industry. Today, CNTs find utilization in frequent various products, and analyst continue to explore new applications. Currently applications comprise wind turbines, bicycle components, scanning probe microscopes, flat panel displays, marine paints, sensing devices, electronics, batteries with longer lifetime and electrical circuitry etc. Such applications in mind, entropy optimized dissipative CNTs based flow of nanomaterial by a stretched surface. Flow is caused due to stretching phenomenon and studied in 3D coordinates. Both types of CNTs are studied i.e., SWCNTs and MWCNTs. CNTs are considered for nanoparticles and water for continuous phase fluid. Special consideration is given to the analysis of statistical declaration and probable error for skin friction and Nusselt number. Furthermore, entropy rate is calculated. Entropy rate is discussed in the presence of four main irreversibilities i.e., heat transfer, Joule heating, porosity and dissipation. METHOD: Homotopy technique is utilized to develop the convergence series solutions. RESULTS: Impacts of sundry variables subject to both SWCNTs (single) and MWCNTs (multi) are graphically discussed. Statistical analysis and probable error for surface drag force and Nusselt number are numerically calculated subject to various flow variables. Numerical results for such engineering quantities are displayed through tables. In addition, comparative analysis for SWCNTs and MWCNTs are presented for the velocity, concentration and thermal fields. CONCLUSIONS: Results for entropy rate is calculated in the presence of various sundry variable through implementation of second law of thermodynamics. It is examined from the results that velocity decreases for both CNTs via higher magnetic, inertia coefficient and porosity parameters. Secondary velocity i.e., velocity in g-direction boosts up versus rotation parameter while it declines for larger slip parameter for both CNTs. thermal field intensifies for both CNTs via larger heat generation/absorption parameter. Concentration which shows the mass transfer of species increases subject to higher homogeneous parameter and Schmidt number in case of both CNTs. Entropy rate in more for larger magnetic, Reynolds number and slip parameter. Bejan number boosts up for higher Reynold number and slip parameter while it declines for magnetic parameter.

Entropy generation minimization (EGM) in magneto peristalsis with variable properties.

OBJECTIVE AND BACKGROUND: This article featuring the peristaltic transport of viscous material with variable properties (i.e. temperature dependent viscosity and thermal conductivity) through curved configuration. Fluid saturating through porous channel walls of uniform space. Entropy generation consideration here is to analyze irreversibility aspects. Channel boundaries retain the velocity and thermal slip conditions. METHOD: Wave frame of reference is attained with the utilization of long wavelength and small Reynolds number approach. Solution of the simplified coupled system of dimensionless constraints is obtained numerically. Detailed analysis of important quantities of interest has been presented in discussion portion. RESULTS: Entropy generation variation near center is very small whereas in the vicinity of the channel wall is larger. Bejan number has reverse variation as observed for entropy generation. CONCLUSION: Variable characteristics of viscosity has opposite impact on velocity and temperature is observed. It is also noticed small irreversibility effects are obtained for higher varying viscosity and thermal conductivity near the vicinity of the channel walls.

Irreversibility characterization and investigation of mixed convective reactive flow over a rotating cone.

BACKGROUND: Here we investigate the mixed convective unsteady magnetohydrodynamics chemically reactive flow of viscous liquid over a rotating cone. Energy attribution are deliberated in the presence of heat generation/absorption, viscous dissipation and Joule heating. Furthermore Irreversibility analysis with thermo-diffusion (Soret) effect and binary chemical reaction are also considered. Entropy optimization rate is computed with the help of thermodynamics second law. METHOD: The partial differential expression are reduced to ordinary system by using the suitable transformation. Here we have employed Newton built in shooting technique to get computational results for proposed nonlinear system. RESULTS: Influences of different interesting parameters on entropy optimization, velocity, Bejan number, concentration and temperature are discussed through graphs. The computational results of skin friction coefficient, gradient of temperature and Sherwood number are examined against different flow parameters through tables. From obtained outcome it is noticed that velocity and temperature have opposite behaviors for magnetic parameter and unsteadiness parameter. Concentration shows the opposite effect for Soret number and unsteadiness parameter. Bejan number and entropy generation rate hold opposite via larger Brinkman number, while have similar impact of temperature difference parameters. The assertion of recent work is established by comparison with previous published literature are discussed in tabulated form and found an excellent agreement.