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Articular cartilage damage is a major challenge in healthcare due to the lack of long-term repair options. There are several promising regenerative implant-based approaches for the treatment, but the fixation of the implant remains a significant challenge. This study evaluated the potential for repair of an osteochondral implant produced through a novel combined bioprinting-based chondral-bone integration, with and without cells, in an equine model. Implants consisted of a melt electrowritten polycaprolactone (PCL) framework for the chondral compartment, which was firmly integrated with a bone anchor. The bone anchor was produced by extrusion-based printing of a low-temperature setting bioceramic material that had been proven to be effective for osteo-regeneration in an orthotopic, non-load bearing and non-articular site in the same species in an earlier in vivo study. Articular cartilage-derived progenitor cells were seeded into the PCL framework and cultured for 28 days in vitro in the presence of bone morphogenetic protein-9 (BMP-9), resulting in the formation of abundant extracellular matrix rich in glycosaminoglycans (GAGs) and type II collagen. The constructs were implanted in the stifle joints of Shetland ponies with cell-free scaffolds as controls. Clinical signs were monitored, and progression of healing was observed non-invasively through radiographic examinations and quantitative gait analysis. Biochemical and histological analyses 6 months after implantation revealed minimal deposition of GAGs and type II collagen in the chondral compartment of the defect site for both types of implants. Quantitative micro-computed tomography showed collapse of the bone anchor with low volume of mineralized neo-bone formation in both groups. Histology confirmed that the PCL framework within the chondral compartment was still present. It was concluded that the collapse of the osteal anchor, resulting in loss of the mechanical support of the chondral compartment, strongly

Oil spills cause environmental pollution with a serious threat to local communities and sustainable development. Accidental oil spills can be modelled as a stochastic process where each oil spill event is described by its spatial locations and incidence-time and hence allow for space-time cluster analysis. Space-time cluster analysis can detect space-time pattern distribution of oil spills which can be useful for implementing preventive measures and evidence-based decision making. This study aims to detect the space-time clusters of accidental oil spills in Rivers state, Nigeria through the Space-time Scan Statistic. The Space-time Scan Statistic was applied under the permutation model to the oil spill data (each for sabotage and operational oil spills) collected at Local Government Area (LGA)-level during the period from 2011 to 2019. The results show that the sabotage oil spill clusters have covered most of the LGAs in the southern part of the state at the start of the study period and then in 2018–2019, it moved to the west covering a single LGA. The operational oil spill clusters covered two neighboring LGAs in the south. In addition, the temporal cluster of sabotage oil spills was seen in 2019 and operational oil spills in 2011–2012. The sabotage oil spills show an increasing trend with the maximum in 2019 while the operational oil spills show a decreasing trend with the minimum in 2019. These findings assist in more effective decision-making for combating the environmental problems and controlling the future spill incidence in the cluster-regions. © 2021 Tech Science Press. All rights reserved., Funding: Yayasan Universiti Teknologi PETRONAS-Fundamental Research Grant (YUTP-FRG) with a cost center of 015LC0-013.

Oil spills cause environmental pollution with a serious threat to local communities and sustainable development. Accidental oil spills can be modelled as a stochastic process where each oil spill event is described by its spatial locations and incidence-time and hence allow for space-time cluster analysis. Space-time cluster analysis can detect space-time pattern distribution of oil spills which can be useful for implementing preventive measures and evidence-based decision making. This study aims to detect the space-time clusters of accidental oil spills in Rivers state, Nigeria through the Space-time Scan Statistic. The Space-time Scan Statistic was applied under the permutation model to the oil spill data (each for sabotage and operational oil spills) collected at Local Government Area (LGA)-level during the period from 2011 to 2019. The results show that the sabotage oil spill clusters have covered most of the LGAs in the southern part of the state at the start of the study period and then in 2018–2019, it moved to the west covering a single LGA. The operational oil spill clusters covered two neighboring LGAs in the south. In addition, the temporal cluster of sabotage oil spills was seen in 2019 and operational oil spills in 2011–2012. The sabotage oil spills show an increasing trend with the maximum in 2019 while the operational oil spills show a decreasing trend with the minimum in 2019. These findings assist in more effective decision-making for combating the environmental problems and controlling the future spill incidence in the cluster-regions. © 2021 Tech Science Press. All rights reserved., Funding: Yayasan Universiti Teknologi PETRONAS-Fundamental Research Grant (YUTP-FRG) with a cost center of 015LC0-013.

Oil spills cause environmental pollution with a serious threat to local communities and sustainable development. Accidental oil spills can be modelled as a stochastic process where each oil spill event is described by its spatial locations and incidence-time and hence allow for space-time cluster analysis. Space-time cluster analysis can detect space-time pattern distribution of oil spills which can be useful for implementing preventive measures and evidence-based decision making. This study aims to detect the space-time clusters of accidental oil spills in Rivers state, Nigeria through the Space-time Scan Statistic. The Space-time Scan Statistic was applied under the permutation model to the oil spill data (each for sabotage and operational oil spills) collected at Local Government Area (LGA)-level during the period from 2011 to 2019. The results show that the sabotage oil spill clusters have covered most of the LGAs in the southern part of the state at the start of the study period and then in 2018–2019, it moved to the west covering a single LGA. The operational oil spill clusters covered two neighboring LGAs in the south. In addition, the temporal cluster of sabotage oil spills was seen in 2019 and operational oil spills in 2011–2012. The sabotage oil spills show an increasing trend with the maximum in 2019 while the operational oil spills show a decreasing trend with the minimum in 2019. These findings assist in more effective decision-making for combating the environmental problems and controlling the future spill incidence in the cluster-regions. © 2021 Tech Science Press. All rights reserved., Funding: Yayasan Universiti Teknologi PETRONAS-Fundamental Research Grant (YUTP-FRG) with a cost center of 015LC0-013.

Oil spills cause environmental pollution with a serious threat to local communities and sustainable development. Accidental oil spills can be modelled as a stochastic process where each oil spill event is described by its spatial locations and incidence-time and hence allow for space-time cluster analysis. Space-time cluster analysis can detect space-time pattern distribution of oil spills which can be useful for implementing preventive measures and evidence-based decision making. This study aims to detect the space-time clusters of accidental oil spills in Rivers state, Nigeria through the Space-time Scan Statistic. The Space-time Scan Statistic was applied under the permutation model to the oil spill data (each for sabotage and operational oil spills) collected at Local Government Area (LGA)-level during the period from 2011 to 2019. The results show that the sabotage oil spill clusters have covered most of the LGAs in the southern part of the state at the start of the study period and then in 2018–2019, it moved to the west covering a single LGA. The operational oil spill clusters covered two neighboring LGAs in the south. In addition, the temporal cluster of sabotage oil spills was seen in 2019 and operational oil spills in 2011–2012. The sabotage oil spills show an increasing trend with the maximum in 2019 while the operational oil spills show a decreasing trend with the minimum in 2019. These findings assist in more effective decision-making for combating the environmental problems and controlling the future spill incidence in the cluster-regions. © 2021 Tech Science Press. All rights reserved., Funding: Yayasan Universiti Teknologi PETRONAS-Fundamental Research Grant (YUTP-FRG) with a cost center of 015LC0-013.

Oil spills cause environmental pollution with a serious threat to local communities and sustainable development. Accidental oil spills can be modelled as a stochastic process where each oil spill event is described by its spatial locations and incidence-time and hence allow for space-time cluster analysis. Space-time cluster analysis can detect space-time pattern distribution of oil spills which can be useful for implementing preventive measures and evidence-based decision making. This study aims to detect the space-time clusters of accidental oil spills in Rivers state, Nigeria through the Space-time Scan Statistic. The Space-time Scan Statistic was applied under the permutation model to the oil spill data (each for sabotage and operational oil spills) collected at Local Government Area (LGA)-level during the period from 2011 to 2019. The results show that the sabotage oil spill clusters have covered most of the LGAs in the southern part of the state at the start of the study period and then in 2018–2019, it moved to the west covering a single LGA. The operational oil spill clusters covered two neighboring LGAs in the south. In addition, the temporal cluster of sabotage oil spills was seen in 2019 and operational oil spills in 2011–2012. The sabotage oil spills show an increasing trend with the maximum in 2019 while the operational oil spills show a decreasing trend with the minimum in 2019. These findings assist in more effective decision-making for combating the environmental problems and controlling the future spill incidence in the cluster-regions. © 2021 Tech Science Press. All rights reserved., Funding: Yayasan Universiti Teknologi PETRONAS-Fundamental Research Grant (YUTP-FRG) with a cost center of 015LC0-013.

Oil spills cause environmental pollution with a serious threat to local communities and sustainable development. Accidental oil spills can be modelled as a stochastic process where each oil spill event is described by its spatial locations and incidence-time and hence allow for space-time cluster analysis. Space-time cluster analysis can detect space-time pattern distribution of oil spills which can be useful for implementing preventive measures and evidence-based decision making. This study aims to detect the space-time clusters of accidental oil spills in Rivers state, Nigeria through the Space-time Scan Statistic. The Space-time Scan Statistic was applied under the permutation model to the oil spill data (each for sabotage and operational oil spills) collected at Local Government Area (LGA)-level during the period from 2011 to 2019. The results show that the sabotage oil spill clusters have covered most of the LGAs in the southern part of the state at the start of the study period and then in 2018–2019, it moved to the west covering a single LGA. The operational oil spill clusters covered two neighboring LGAs in the south. In addition, the temporal cluster of sabotage oil spills was seen in 2019 and operational oil spills in 2011–2012. The sabotage oil spills show an increasing trend with the maximum in 2019 while the operational oil spills show a decreasing trend with the minimum in 2019. These findings assist in more effective decision-making for combating the environmental problems and controlling the future spill incidence in the cluster-regions. © 2021 Tech Science Press. All rights reserved., Funding: Yayasan Universiti Teknologi PETRONAS-Fundamental Research Grant (YUTP-FRG) with a cost center of 015LC0-013.

The main purpose of the present analysis is to report the numerical solution of the thermal radiations and magnetohydrodynamic (MHD) effect on the flow of micropolar nanofluid. Further, the effect of Brownian motion and thermophoresis on the flow field are also elucidated. The combined phenomenon of heat and mass transfer is considered. Compatible similarities are implemented for the conversion of nonlinear ordinary differential equations from nonlinear partial differential equations. The numerical solution of the governing differential equations is obtained via the implicit Keller box technique. This is an efficient scheme based on the finite difference method. Findings demonstrate that the heat and mass exchange reduce with growth of the Brinkman parameter, whereas the wall shear stress enhances with improving the magnitude of the Brinkman factor. The temperature contour enhances when the radiation parameter reaches its peak, which is useful for industrial processes. The heat and mass flow rates decrease against higher magnitudes of inclination

The Brownian motion and thermophoretic impacts attained a noticeable intention of the recent researchers because these factors trigger the thermal conductivity of the nanofluid. In this study, we focus on radiation and Soret effects on a slanted stretchable sheet. Buongiorno’s model is taken into account with Brownian motion and thermophoretic effects. Compatible transformations are implemented to attain the nonlinear differential equation from the boundary value PDE’s. the physical quantities of practical interest are treated by graphically as well as numerically. For numerical results, the Keller box technique is applied. the numerical outcomes through tabulated magnitudes performed a good settlement with already existing results. Energy transfer rate against involved factor exhibited via graphs. Energy and mass transport rates enhance against increment in Soret factor while skin friction diminishes. Moreover, Nusselt number and Sherwood number decrease on improving inclination while skin friction increases

Similar to other fluids (Newtonian and non-Newtonian), micropolar fluid also exhibits symmetric flow and exact symmetric solution similar to the Navier–Stokes equation; however, it is not always realizable. In this article, the Buongiorno mathematical model of hydromagnetic micropolar nanofluid is considered. A joint phenomenon of heat and mass transfer is studied in this work. This model indeed incorporates two important e_ects, namely, the Brownian motion and the thermophoretic. In addition, the e_ects of magnetohydrodynamic (MHD) and chemical reaction are considered. The fluid is taken over a slanted, stretching surface making an inclination with the vertical one. Suitable similarity transformations are applied to develop a nonlinear transformed model in terms of ODEs (ordinary differential equations). For the numerical simulations, an effcient, stable, and reliable scheme of Keller-box is applied to the transformed model. More exactly, the governing system of equations is written in the first order system and then arranged in the forms of a matrix system using the block-tridiagonal factorization. These numerical simulations are then arranged in graphs for various parameters of interest. The physical quantities including skin friction, Nusselt number, and Sherwood number along with different effects involved in the governing equations are also justified through graphs. The consequences reveal that concentration profile increases by increasing chemical reaction parameters. In addition, the Nusselt number and Sherwood number decreases by decreasing the inclination

Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes this feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore co-dependent. The framework is general enough and fits well into a compositional model of consciousness. Interestingly, we also show how our proposal may become a step towards avoiding the hard problem of consciousness, and thereby address the combination problem of conscious experiences., Comment: 19 pages

In this study, we attempt to obtain all probable multiple solutions of the magnetohydrodynamic (MHD) steady flow of micropolar nanofluid on an exponentially shrinking surface by the consideration of concentration slip, thermal radiation, and convective boundary condition with help of the revised model of Buongiorno. The significance of the mass suction on the existence of multiple solutions is integrated. The suitable pseudo‐exponential similarity variables have been adopted to transfer the system of nonlinear partial differential equations into a system of nonlinear quasi‐ordinary ordinary differential equations. The resultant system has been solved by employing the Runge–Kutta fourth‐order method along with the shooting method. Three different ranges of solutions are noticed, namely triple solutions and single solution. When ranges of the suction parameter are

In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of Sc≤S and Mc≤M (Sc>S and Mc>M). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised.

In this article, we reconsidered the problem of Aurangzaib et al., and reproduced the results for triple solutions. The system of governing equations has been transformed into the system of non-linear ordinary differential equations (ODEs) by using exponential similarity transformation. The system of ODEs is reduced to initial value problems (IVPs) by employing the shooting method before solving IVPs by the Runge Kutta method. The results reveal that there are ranges of multiple solutions, triple solutions, and a single solution. However, Aurangzaib et al., only found dual solutions. The effect of the micropolar parameter, suction parameter, and Prandtl number on velocity, angular velocity, and temperature profiles have been taken into account. Stability analysis of triple solutions is performed and found that a physically possible stable solution is the first one, while all leftover solutions are not stable and cannot be experimentally seen.

In this study, we attempt to obtain all probable multiple solutions of the magnetohydrodynamic (MHD) steady flow of micropolar nanofluid on an exponentially shrinking surface by the consideration of concentration slip, thermal radiation, and convective boundary condition with help of the revised model of Buongiorno. The significance of the mass suction on the existence of multiple solutions is integrated. The suitable pseudo‐exponential similarity variables have been adopted to transfer the system of nonlinear partial differential equations into a system of nonlinear quasi‐ordinary ordinary differential equations. The resultant system has been solved by employing the Runge–Kutta fourth‐order method along with the shooting method. Three different ranges of solutions are noticed, namely triple solutions and single solution. When ranges of the suction parameter are

In this article, the magnetohydrodynamic (MHD) flow of Casson nanofluid with thermal radiation over an unsteady shrinking surface is investigated. The equation of momentum is derived from the Navier–Stokes model for non-Newtonian fluid where components of the viscous terms are symmetric. The effect of Stefan blowing with partial slip conditions of velocity, concentration, and temperature on the velocity, concentration, and temperature distributions is also taken into account. The modeled equations of partial differential equations (PDEs) are transformed into the equivalent boundary value problems (BVPs) of ordinary differential equations (ODEs) by employing similarity transformations. These similarity transformations can be obtained by using symmetry analysis. The resultant BVPs are reduced into initial value problems (IVPs) by using the shooting method and then solved by using the fourth-order Runge–Kutta (RK) technique. The numerical results reveal that dual solutions exist in some ranges of different physical parameters such as unsteadiness and suction/injection parameters. The thickness of the velocity boundary layer is enhanced in the second solution by increasing the magnetic and velocity slip factor effect in the boundary layer. Increment in the Prandtl number and Brownian motion parameter is caused by a reduction of the thickness of the thermal boundary layer and temperature. Moreover, stability analysis performed by employing the three-stage Lobatto IIIA formula in the BVP4C solver with the help of MATLAB software reveals that only the first solution is stable and physically realizable.

Researchers are using different types of nanomaterials for the enhancement of the thermal performance of regular fluids such as water, kerosene oil, etc. However, these days, the researchers are more interested in hybrid nanomaterials. The purpose of this communication is to examine the stability analysis of Cu-Al2O3/water hybrid nanofluid over a non-linear shrinking sheet. The hybrid nanomaterials are composed of Cu and Al2O3. These hybridized nanomaterials are then dissolved in water taken as base fluid to form Cu-Al2O3//water hybrid nanofluid. Mathematical analysis and modeling have been attended in the presence of viscous dissipation and suction/injection effects. The governing equations of mathematical models are transformed into self-similar solutions in the form of ODEs by using similarity transformation. Solutions of the non-linear ODEs are created by employing of three-stage Lobatto IIIa formula which is built-in BVP4C function in the MATLAB software. A comparison of the current study has been done with the preceding published literature. The distributions of velocity, temperature profiles, coefficient of skin friction and heat transfer rate are presented graphically and conferred for numerous significant parameters entering into the problem. Results revealed the existence of dual solutions for a certain range of the suction/blowing parameter. Stability analysis is also done in order to obtain dual solutions stability. The smallest eigenvalues suggest that the first solution is stable from the second solution. Hybrid nanomaterials have a high scope toward nurturing our day-to-day life.

The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative).

A numerical study was carried out to examine the magnetohydrodynamic (MHD) flow of micropolar fluid on a shrinking surface in the presence of both Joule heating and viscous dissipation effects. The governing system of non-linear ordinary differential equations (ODEs) was obtained from the system of partial differential equations (PDEs) by employing exponential transformations. The resultant equations were transformed into initial value problems (IVPs) by shooting technique and then solved by the Runge-Kutta (RK) method. The effects of different parameters on velocity, angular velocity, temperature profiles, skin friction coefficient, and Nusselt number were obtained and demonstrated graphically. We observed that multiple solutions occurred in certain assortments of the parameters for suction on a surface. The stability analysis of solutions was performed, and we noted that the first solution was stable while the remaining two solutions were not. The results also showed that the velocity of the fluid increased as the non-Newtonian parameter rose in all solutions. Furthermore, it was detected that the temperature of fluid rose at higher values of the Eckert number in all solutions.

Brownian motion and thermophoresis diffusions are the fundamental ideas of abnormal upgrading in thermal conductivity via binary fluids (base fluid along with nanoparticles). The influence of Brownian motion and thermophoresis are focused on in the Buongiorno model. In this problem, we considered the Buongiorno model with Brownian motion and thermophoretic effects. The nonlinear ordinary differential equations are recovered from the partial differential equations of the boundary flow via compatible similarity transformations and then employed to the Kellerbox scheme for numerical results. The physical quantities of our concern including skin friction, Nusselt number, and Sherwood number along with velocity, temperature and concentration profile against involved effects are demonstrated. The impacts of the involved flow parameters are drawn in graphs and tabulated forms. The inclination effect shows an inverse relation with the velocity field. Moreover, the velocity profile increases with the growth of the buoyancy effect

In this article, the effects of a Casson Nanofluid boundary layer flow, over an inclined extending surface with Soret and Dufour, is scrutinized. The model used in this study is based on the Buongiorno model of the thermal efficiencies of the fluid flows in the presence of Brownian motion and thermophoresis properties. The non-linear problem for Casson Nanofluid flow over an inclined channel is modeled to gain knowledge on the heat and mass exchange phenomenon, by considering important flow parameters of the intensified boundary layer. The governing non-linear partial differential equations are changed to non-linear ordinary differential equations and are afterward illustrated numerically by the Keller-Box scheme. A comparison of the established results, if the incorporated effects are lacking, is performed with the available outcomes of Khan and Pop [1] and recognized in a nice settlement. Numerical and graphical results are also presented in tables and graphs

The key objective of the study under concern is to probe the impacts of Brownian motion and thermophoresis diffusion on Casson nanofluid boundary layer flow over a nonlinear inclined stretching sheet, with the effect of convective boundaries and thermal radiations. Nonlinear ordinary differential equations are obtained from governing nonlinear partial differential equations by using compatible similarity transformations. The quantities associated with engineering aspects, such as skin friction, Sherwood number, and heat exchange along with various impacts of material factors on the momentum, temperature, and concentration, are elucidated and clarified with diagrams. The numerical solution of the present study is obtained via the Keller-box technique and in limiting sense are reduced to the published results for accuracy purpose

The prime aim of this paper is to probe the flow of micropolar nanofluid towards an inclined stretching surface adjacent to the stagnation region with Brownian motion and thermophoretic impacts. The chemical reaction and heat generation or absorption are also taken into account. The energy and mass transport of the micropolar nanofluid flow towards an inclined surface are discussed. The numerical solution is elucidated for the converted non-linear ordinary differential equation from the set of partial nonlinear differential equations via compatible similarity transformations. A converted system of ordinary differential equations is solved via the Keller-box scheme. The stretching velocity and external velocity are supposed to change linearly by the distance from the stagnation point. The impacts of involved parameters on the concerned physical quantities such as skin friction, Sherwood number, and energy exchange are discussed. These results are drawn through the graphs and presented in the tables. The energy and mass exchange rates show a direct relation with the stagnation point. In the same vein, skin friction diminishes with the growth of the stagnation factor. Heat and mass fluxes show an inverse correspondence with the inclination factor

The principal objective of the current study is to analyze the Brownian motion and thermophoretic impacts on micropolar nanofluid flow over a nonlinear inclined stretching sheet taking into account the Soret and Dufour effects. The compatible similarity transformations are applied to obtain the nonlinear ordinary differential equations from the partial differential equations. The numerical solution of the present study obtained via the Keller-Box technique. The physical quantities of interest are skin friction, Sherwood number, and heat exchange, along with several influences of material parameters on the momentum, temperature, and concentration are elucidated and clarified with diagrams. A decent settlement can be established in the current results with previously published work in the deficiency of incorporating e_ects. It is found that the growth of the inclination and nonlinear stretching factor decreases the velocity profile. Moreover, the growth of the Soret e_ect reduces the heat flux rate and wall shear stress

Here, in this research article, we have investigated an incompressible viscoelastic fluid flow over a uniform stretching surface sheet along with slip boundary conditions in the presence of porous media. The partial differential equations which govern the fluid flow are changed into ordinary differential equations through suitable similarity transformation variables. Finally, the transformed ordinary differential equations are solved with the help of a seminumerical technique known as the homotopy analysis method (HAM). The uniqueness of our study is not only to analyze and carry out the effect of the elastic parameter but also to account for viscous dissipation which is important in the case of optically transparent flow. The novel effects for the parameters which affect the flow and heat transfer, such as the Eckert number, porous medium parameter, and the velocity slip parameter, are studied through graphs. Also, the convergence analysis for the proposed method is addressed. Additionally, for the sake of validation, the present work is also compared with the already published work and an outstanding agreement is found.

Purpose: The analysis of the characteristics of particles motion is considered in this article, where a model which studies a Newtonian fluid media with specific interest on the analysis of unsteady sedimentation of particles is considered. The numerical solution of this first order differential equation model using an Obrechkoff-type block method is presented. Methodology: The algorithm for the conventional Nyström -type multistep scheme is considered with specific parameter choices in order to obtain the main k-step Obrechkoff-type block method and the required additional method. The unknown coefficients of these methods are obtained by using the concept of Taylor series expansion to obtain the required schemes for the block method which were combined as simultaneous integrators for the solution of the differential equation model.Findings: The block method gave highly accurate results as compared with the exact solution of the model. Furthermore, at selected values of the physical properties of nanoparticles, the solutions using the two-step Obrechkoff-type block method was compared with past literatures and the results were seen to be in agreement. The influence of the physical parameters on terminal velocity is also discussed.

This study investigates the numerical solutions of MHD boundary layer and heat transfer of the Williamson fluid flow on the exponentially vertical shrinking sheet, having variable thickness and thermal conductivity under effects of the velocity and thermal slip parameters. It is also assumed that shrinking/stretching velocity, as well as the wall temperature, has the exponential function form. In this study, the continuity, momentum and energy equations with buoyancy parameter and Hartmann number are incorporated especially in the Williamson fluid flow case. Similarity transformation variables have been employed to formulate the ordinary differential equations (ODEs) from partial differential equations (PDEs). The resultant ODEs are solved by shooting method with Runge Kutta of fourth order method in Maple software. The effects of the different applied non-dimensional physical parameters on the boundary layer and heat transfer flow problems are presented in graphs. The effects of Williamson parameter, Prandtl number, and slip parameters on velocity and temperature profiles have been thoroughly demonstrated and discussed. The numerical results show that the buoyancy force and the slip parameters contribute to the occurrence of the dual solutions on the boundary layer and heat transfer flow problems. Furthermore, the stability analysis suggests that the first solution is stable and physically possible.

In this study, first-order slip effect with viscous dissipation and thermal radiation in micropolar fluid on a linear shrinking sheet is considered. Mathematical formulations of the governing equations of the problem have been derived by employing the fundamental laws of conservations which then converted into highly non-linear coupled partial differential equations (PDEs) of boundary layers. Linear transformations are employed to change PDEs into non-dimensional ordinary differential equations (ODEs). The solutions of the resultant ODEs have been obtained by using of numerical method which is presented in the form of shootlib package in MAPLE 2018. The results reveal that there is more than one solution depending upon the values of suction and material parameters. The ranges of dual solutions are S ≥ Sci , i = 0, 1, 2 and no solution is S < Sci where Sci is the critical values of S . Critical values have been obtained in the presence of dual solutions and the stability analysis is carried out to identify more stable solutions. Variations of numerous parameters have been also examined by giving tables and graphs. The numerical values have been obtained for the skin friction and local Nusselt number and presented graphically. Further, it is observed that the temperature and thickness of the thermal boundary layer increase when thermal radiation parameter is increased in both solutions. In addition, it is also noticed that the fluid velocity increases in the case of strong magnetic field effect in the second solution.

In this paper, magnetohydrodynamic (MHD) flow over a shrinking sheet and heat transfer with viscous dissipation has been studied. The governing equations of the considered problem are transformed into ordinary differential equations using similarity transformation. The resultant equations are converted into a system of fractional differential boundary layer equations by employing a Caputo derivative which is then solved numerically using the Adams-type predictor-corrector method (APCM). The results show the existence of two ranges of solutions, namely, dual solutions and no solution. Moreover, the results indicate that dual solutions exist for a certain range of specific parameters which are in line with the results of some previously published work. It is also observed that the velocity boundary layer decreases as the suction and magnetic parameters increase.

In this paper, we explore dual solutions of MHD flow, heat and mass transfer of micropolar nanofluid over a linear vertical shrinking surface with buoyancy effects, which was not considered in the previous works. The governing fluid flow equations of this problem are transformed into nonlinear boundary value problems (BVPs) of ordinary differential equations (ODEs) by applying similarity variables. The resultant BVPs are converted into initial value problems (IVPs) by using shooting method which then resolved by employing Runge Kutta of order four. The impacts of the governing parameters, such as suction parameter, material parameter, Richardson number, magnetic parameter, Prandtl number, thermophoresis and Brownian motion parameters on velocity, angular velocity, temperature, and concentration are illustrated graphically. The results indicate that the existence of a range of dual solutions and no-solutions. When Richardson number (delta) is increased, the reduction of the velocity of micropolar nanofluid has occurred in the second solution. The stability analysis on dual solutions, however, reveals that only the first solution is stable.

In this paper, the MHD flow of a micropolar nanofluid on an exponential sheet in an Extended-Darcy-Forchheimer porous medium have been considered. Buongiorno's model is considered in order to formulate a mathematical model with different boundary conditions. The governing partial differential equations (PDEs) of the nanofluid flow are changed into a third order non-linear quasi-ordinary differential equation (ODE), using the pseudo-similarity variable. The resultant ODEs of the boundary value problems (BVPs) are renewed into initial value problems (IVPs) using a shooting method, and then the IVPs are solved by a fourth order Runge-Kutta (RK) method. The effects of various physical parameters on the profiles of velocity, temperature, microrotation velocity, concentration, skin friction, couple stress coefficients, heat, and concentration transfer are demonstrated graphically. The results reveal that triple solutions appear when S ≥ 2.0337 for K = 0.1 and S ≥ 2.7148 for K = 0.2. A stability analysis has been performed to show the stability of the solutions; only the first solution is stable and physically possible, whereas the remaining two solutions are not stable.

Background and Objective: The last two and half decades are witnessed a great surge in the use convective fluids for enhancement of heat transfer of minerals ethylene glycol, oil and water due to their numerous applications in the industrial segments including chemical production, microelectronics, power generation, transportation, and air-conditioning. For this purpose, different procedures were applied to upgrade the thermal conductivity of common fluid but could not. Further, Choi and Eastman in 1995 introduced nanofluid which has good thermal properties as compared to common fluids. After that, it can be seen that researchers, mathematicians, and scientists tried to understand the principles of nanofluids and how to implicate them in many different practical applications. In this work, the Buongiorno model has been considered for nanofluid. One of the prime objectives is to consider all possible multiple solutions of the model because these solutions cannot be seen experimentally. Methods: The governing equations of fluid flow have been transformed in the form of ordinary differential equations. These equations have been solved by two methods namely, shooting method and three-stage Lobatto IIIa formula. Results: The effects of different parameters on temperature, velocity, concentration profiles, skin friction coefficient, Sherwood number, and reduced Nusselt number were obtained and presented graphically. It was noticed that four solutions existed at definite ranges of the parameters for high suction over both surfaces for the first time. The results of the stability analysis revealed that only the first solution is more stable and possess physical reliability compared to the remaining solutions. Conclusion: The graphs also indicated that the fluid velocity decreases as the thermophoresis parameter increases but the opposite behavior observed for both temperature and concentration profiles in the first solution. Furthermore, it was detected that the concentrati

Steady incompressible magnetohydrodynamic mixed convection boundary layer flow of a Casson fluid on an exponentially vertical shrinking sheet using the non‐Newtonian heating equation is investigated in this paper. There are three main objectives of this study, namely, to develop a new mathematical model, to obtain multiple solutions, and to perform stability analysis. The governing partial differential equations have been changed into nonlinear ordinary differential equations. The resultant equations of boundary value problems are then converted into the equivalent initial value problems using the shooting method before they can be solved using Runge‐Kutta of order four. The numerical results are obtained and found to be in good agreement with the published literature. The results also indicate that the velocity boundary layer becomes thinner as the magnetic, slip, and Casson parameters increase. Dual solutions for temperature and velocity distributions are obtained. Furthermore, the results suggest that the presence of the force of buoyancy (opposing flow case) would cause the occurrence of dual solutions. However, based on the stability analysis, only the first solution is stable.

Paramount for the generation of auricular structures of clinically-relevant size is the acquisition of a large number of cells maintaining an elastic cartilage phenotype, which is the key in producing a tissue capable of withstanding forces subjected to the auricle. Current regenerative medicine strategies utilize chondrocytes from various locations or mesenchymal stromal cells (MSCs). However, the quality of neo-tissues resulting from these cell types is inadequate due to inefficient chondrogenic differentiation and endochondral ossification, respectively. Recently, a subpopulation of stem/progenitor cells has been identified within the auricular cartilage tissue, with similarities to MSCs in terms of proliferative capacity and cell surface biomarkers, but their potential for tissue engineering has not yet been explored. This study compared the in vitro cartilage-forming ability of equine auricular cartilage progenitor cells (AuCPCs), bone marrow-derived MSCs and auricular chondrocytes in gelatin methacryloyl (gelMA)-based hydrogels over a period of 56 d, by assessing their ability to undergo chondrogenic differentiation. Neocartilage formation was assessed through gene expression profiling, compression testing, biochemical composition and histology. Similar to MSCs and chondrocytes, AuCPCs displayed a marked ability to generate cartilaginous matrix, although, under the applied culture conditions, MSCs outperformed both cartilage-derived cell types in terms of matrix production and mechanical properties. AuCPCs demonstrated upregulated mRNA expression of elastin, low expression of collagen type X and similar levels of proteoglycan production and mechanical properties as compared to chondrocytes. These results underscored the AuCPCs' tissue-specific differentiation potential, making them an interesting cell source for the next generation of elastic cartilage tissue-engineered constructs.

Cell-laden hydrogels are the primary building blocks for bioprinting, and, also termed bioinks, are the foundations for creating structures that can potentially recapitulate the architecture of articular cartilage. To be functional, hydrogel constructs need to unlock the regenerative capacity of encapsulated cells. The recent identification of multipotent articular cartilage-resident chondroprogenitor cells (ACPCs), which share important traits with adult stem cells, represents a new opportunity for cartilage regeneration. However, little is known about the suitability of ACPCs for tissue engineering, especially in combination with biomaterials. This study aimed to investigate the potential of ACPCs in hydrogels for cartilage regeneration and biofabrication, and to evaluate their ability for zone-specific matrix production. Gelatin methacryloyl (gelMA)-based hydrogels were used to culture ACPCs, bone marrow mesenchymal stromal cells (MSCs) and chondrocytes, and as bioinks for printing. Our data shows ACPCs outperformed chondrocytes in terms of neo-cartilage production and unlike MSCs, ACPCs had the lowest gene expression levels of hypertrophy marker collagen type X, and the highest expression of PRG4, a key factor in joint lubrication. Co-cultures of the cell types in multi-compartment hydrogels allowed generating constructs with a layered distribution of collagens and glycosaminoglycans. By combining ACPC- and MSC-laden bioinks, a bioprinted model of articular cartilage was generated, consisting of defined superficial and deep regions, each with distinct cellular and extracellular matrix composition. Taken together, these results provide important information for the use of ACPC-laden hydrogels in regenerative medicine, and pave the way to the biofabrication of 3D constructs with multiple cell types for cartilage regeneration or in vitro tissue models.STATEMENT OF SIGNIFICANCE: Despite its limited ability to repair, articular cartilage harbors an endogeno

This work concerned to hydromagnetic mixed convection flow of Casson fluid over a wedge. It is assumed that the wedge is moving inside a porous medium. The effects of chemical reaction, slip and convective boundary conditions at velocity, temperature and concentration walls are also considered. The governing partial differential equations are converted into ordinary differential equations using similarity transformations, and then solved by implicit finite difference scheme. Comparisons with the existing literature are performed and good agreement is achieved. The influence of physical parameters on flow fields are illustrated graphically. It is observed that the velocity rises with the increment in Casson fluid parameter and magnetic parameter. It is also noticed that thickness of thermal boundary layer grows with the increase of radiation. The skin friction coefficient enhances with the increase of porosity parameter while reduces as Casson fluid and moving wedge parameters increase. Increase in heat and mass transfer rate is noticed to be enhanced with the increase in radiation and chemical reaction parameters, respectively.

This work concerned to hydromagnetic mixed convection flow of Casson fluid over a wedge. It is assumed that the wedge is moving inside a porous medium. The effects of chemical reaction, slip and convective boundary conditions at velocity, temperature and concentration walls are also considered. The governing partial differential equations are converted into ordinary differential equations using similarity transformations, and then solved by implicit finite difference scheme. Comparisons with the existing literature are performed and good agreement is achieved. The influence of physical parameters on flow fields are illustrated graphically. It is observed that the velocity rises with the increment in Casson fluid parameter and magnetic parameter. It is also noticed that thickness of thermal boundary layer grows with the increase of radiation. The skin friction coefficient enhances with the increase of porosity parameter while reduces as Casson fluid and moving wedge parameters increase. Increase in heat and mass transfer rate is noticed to be enhanced with the increase in radiation and chemical reaction parameters, respectively.