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The purpose of present communication is to analyze Darcy–Forchheimer flow of viscous nanofluid by curved stretchable surface. Flow in porous medium is characterized by Darcy–Forchheimer relation. Brownian diffusion and thermophoresis are considered. Convective heat and mass boundary conditions are also used at the curved stretchable surface.

The resulting nonlinear system is solved through shooting technique.

Skin friction coefficient is enhanced for larger porosity parameter and inertia coefficient while reverse trend is noticed for curvature parameter. Local Nusselt number is enhanced for higher Prandtl number and thermal Biot number, whereas the opposite trend is seen via curvature parameter, porosity parameter, inertia coefficient, thermophoresis parameter and Brownian motion parameter. Local Sherwood number is enhanced for Schmidt number, Brownian motion parameter and concentration Biot number, while reverse trend is noticed for curvature parameter, porosity parameter, inertia coefficient and thermophoresis parameter.

To the best of author’s knowledge, no such consideration has been given in the literature yet.

This review paper aims to introduce the inkjet printing as a tool for fabrication of flexible/wearable sensors. It summarizes inkjet printing techniques including various modes of operation, commonly used substrates and inks, commercially available inkjet printers and variables affecting the printing process. More focus is on the drop-on-demand printing mode, a strongly considered printing technique for patterning conductive lines on flexible and stretchable substrates. As inkjet-printed patterns are influenced by various variables related to its conductivity, resistivity, durability and dimensions of printed patterns, the main printing parameters (e.g. printing multilayers, inks sintering, surface treatment, cartridge specifications and printing process parameters) are reported. The embedded approaches of adding electronic components (e.g. surface-mounted and optoelectronic devices) to the stretchable circuit are also included.

In this paper, inkjet printing techniques for fabrication of flexible/stretchable circuits will be reviewed. Specifically, the various modes of operation, commonly used substrates and inks and variables affecting the printing process will be presented. Next, examples of inkjet-printed electronic devices will be demonstrated. These devices will be compared to their rigid counterpart in terms of ease of implementation and electrical behavior for wearable sensor applications. Finally, a summary of key findings and future research opportunities will be presented.

In conclusion, it is evident that the technology of inkjet printing is becoming a competitor to traditional lithography fabrication techniques, as it has the advantage of being low cost and less complex. In particular, this technique has demonstrated great capabilities in the area of flexible/stretchable electronics and sensors. Various inkjet printing methods have been presented with emphasis on their principle of operation and their commercial availability. In addition, the components of a general inkjet printing process have been discussed in details. Several factors affect the resulting printed patterns in terms of conductivity, resistivity, durability and geometry.

The paper focuses on flexible/stretchable optoelectronic devices which could be implemented in stretchable circuits. Furthermore, the importance and challenges related to printing highly conductive and highly stretchable lines, as well as reliable electronic devices, and interfacing them with external circuitry for power transmission, data acquisition and signal conditioning have been highlighted and discussed. Although several fabrication techniques have been recently developed to allow patterning conductive lines on a rubber substrate, the fabrication of fully stretchable wearable sensors remains limited which needs future research in this area for the advancement of wearable sensors.

In the past 15 years stretchable electronic circuits have emerged as a new technology in the domain of assembly, interconnections and sensor circuits and assembly technologies. In the meantime a wide variety of processes with the use of many different materials have been explored in this new field. The purpose of the current contribution is for the authors to present an approach for stretchable circuits which is inspired by conventional rigid and flexible printed circuit board (PCB) technology. Two variants of this technology are presented: stretchable circuit board (SCB) and stretchable mould interconnect (SMI).

Similarly as in PCB 17 or 35 μm thick sheets of electrodeposited or rolled‐annealed Cu are structured to form the conductive tracks, and off‐the‐shelf, standard packaged, rigid components are assembled on the Cu contact pads using lead‐free solder materials and reflow processes. Stretchability is obtained by shaping the Cu tracks not as straight lines, like in normal PCB design, but as horseshoe shaped meanders. Instead of rigid or flexible board materials, elastic materials, predominantly PDMS (polydimethylsiloxane), are used to embed the conductors and the components, thus serving as circuit carrier. The authors include some mechanical modeling and design considerations, aimed at the optimization of the build‐up and combination of elastic, flexible and rigid materials towards minimal stress and maximum mechanical reliability in the structures. Furthermore, details on the two production processes are given, reliability findings are summarised, and a number of functional demonstrators, realized with the technologies, are described.

Key conclusions of the work are that: supporting the metal meanders with a flexible carrier prior to embedding in an elastic substrate substantially increases the reliability under mechanical stress (cyclic uniaxial stretching) of the stretchable interconnect and the transition areas between rigid components and stretchable interconnects are the zones which are most sensitive to failure under mechanical stress. Careful design and technology implementation is necessary, providing a gradual transition from rigid to flexible to stretchable parts of the circuit.

Technologies for stretchable circuits, with the same level of similarity to standard PCB manufacturing and assembly, and thus with the same high potential for transfer to an industrial environment and for mass production, have not been shown before.

The aim of this study is to elaborate three dimensional rotating flow of nanoliquid induced by a stretchable sheet subject to Darcy–Forchheimer porous space. Thermophoretic diffusion and random motion aspects are retained. Prescribed surface heat flux and prescribed surface mass flux conditions are implemented at stretchable surface. Convergent series solutions have been derived for velocities, temperature and concentration.

Optimal homotopy analysis method is implemented for the solution development.

The current solution demonstrates very good agreement with those of the previously published studies in the special cases of regular fluid and nanofluids. Graphical results are presented to investigate the influences of the titania and copper nanoparticle volume fractions and also the nodal/saddle indicative parameter on flow and heat transfer characteristics. Here, the thermal characteristics of hybrid nanofluid are found to be higher in comparison to the base fluid and fluid containing single nanoparticles, respectively. An important point to note is that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids.

To the best of the authors’ knowledge, no such consideration has been given in the literature yet.

The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface.

A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method.

The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior.

This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.

To explore the fusion of dust particles and of polymers in a viscous liquid is the main purpose of this article. Newtonian fluid as a base fluid is considered and the mutual presence of polymers and dusty bodies is investigated. It discusses the steady laminar flow and heat transportation of a polymeric dusty liquid induced by a uniformly heated, penetrable and stretchable surface inside the boundary layer.

The mathematical system incorporates separate equations of energy and momentum for dusty bodies and for fluid. The classical Oldroyd-B model is chosen for exploring polymer presence. For the fluid phase, this model adds another stress to the conservation law of momentum. Appropriate similarity variables are introduced to transform the system of partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs). The problem is solved by introducing a numerical iterative procedure which turned out to be fastly converging.

Expeditious changes inside the boundary layer cause polymers to deform. No changes outside the boundary layer are noticed on account of polymer stretching. The dependence of heat transfer rate and skin friction on the parameter of polymer concentration and Weissenberg number is analyzed and displayed graphically against interaction parameters for temperature and velocity, dust particles’ mass concentration, Eckert and Prandtl numbers. Combining effects of polymers and dust particles cause skin friction to decrease and heat transfer rate to increase. Increasing values of interaction parameter for velocity, dust particles’ mass concentration and Eckert number reduces the drag coefficient and local Nusselt number. On the other hand, the Prandtl number and interaction parameter of temperature magnify the heat flux at the wall.

This article studies the infinite extensibility of polymers. FENE and FENE-P models can be used to investigate the polymer presence in dusty fluids in the future.

In this article, the authors’ aim is to study the combined presence of polymers and dusty bodies. Keeping the existing literature in view, this type of fusion is not studied yet. Polymer inclusion in a viscous dusty fluid is studied and the behavior of fluid flow and heat transportation is investigated within the boundary layer over a permeable linearly stretching sheet.

Nanofluid research has piqued the interest of scientists due to its intriguing applications in nanoscience, biomedical and electrical engineering, medication delivery, biotechnology, food processing, chemotherapy and other fields. This paper aims to inspect the behavior of the mixed convection magnetohydrodynamic flow and heat transfer induced by a nonlinear stretching/shrinking sheet in a nanofluid with a convective boundary condition. Tiwari and Das mathematical nanofluid model is incorporated in the analysis.

The mathematical model is initially transformed to a nondimensional form by using dimensionless variables. Then the nondimensional partial differential equations are further transformed to a set of similarity equations by using the similarity technique. These equations are solved numerically by the bvp4c function in MATLAB software.

For a certain range of the stretching/shrinking parameter, two solutions are obtained. The friction factor and the heat transfer rate escalate due to suction parameter with adding nanoparticles volume fraction by almost 27.15% and 0.153% for the upper branch solution, while the friction factor declines by almost 30.10% but the heat transfer rate augments by 0.145% for the lower branch solution. Furthermore, the behavior of the nanoparticle volume fractions on the heat transfer rate behaves differently in the presence of the mixed convection effect. The temperature of fluid augments with increasing Biot number for both solutions.

The present work considers the flow and heat transfer induced by a stretching/shrinking sheet in a nanofluid using the Tiwari–Das nanofluid model with a convective boundary condition, where the effect of the buoyancy force is taken into consideration. It is shown that two solutions are found for a certain range of the shrinking strength, while the solution is unique for the stretching case. This study is important for scientists working in the growing field of nanofluids to become familiar with the flow properties and behaviors of such nanofluids.

The purpose of this paper is to investigate the entropy optimization in magnetohydrodynamic hybrid nanomaterials flows toward a stretchable surface. The energy expression is modeled subject to dissipation, heat generation/absorption and Joule heating. Here silicon dioxide (SiO₂) and molybdenum disulfide (MoS₂) as nanoparticles and propylene glycol (C₃H₈O₂) as base fluid, respectively. Furthermore, the authors discussed the comparative study of molybdenum disulfide and silicon dioxide diluted in propylene glycol. The total entropy optimization rate is computed through implementation of the second law of thermodynamics.

The nonlinear partial differential system is reduced to an ordinary one through implementation of transformation. Newton built-in shooting method is used for computational results for the given system. Influences of various flow variables on the temperature, Bejan number, velocity, concentration and entropy generation rate are examined graphically for both nanoparticles (SiO₂ and MoS₂). Gradients of velocity and temperature are computed numerically for various physical parameters. Also, take the comparison between the present and previously published results in tabulated form.

For higher estimation of ϕ both temperature and velocity are enhanced. Entropy optimization and Bejan number have the opposite outcome for viscosity parameter. Temperature and velocity have opposite behaviors for larger values of magnetic parameter. Molybdenum disulfide (MoS₂) is more efficient than silicon dioxide (SiO₂).

No such work is yet published in the literature.

In this article, we consider the magnetohydrodynamic (MHD) nanofluid flow over a rotating stretchable disk through porous medium. For porous medium, Darcy’s relation is used. It also encompassed the impact of nanoparticles shape on MHD nanofluid flow and heat transfer. The effect of thermal radiation and Joule heating is also being considered.

Three categories of nanoparticles are taken into deliberation, i.e. copper, silver and titanium oxide. The nanofluid is made of pure water and various types of sphere- and lamina-shaped nanoparticles. By using appropriate similarity transformation, the governing partial differential equations are transformed to ordinary one. The coupled ordinary differential equations system is tackled numerically by bvp4c method.

The impact of various pertinent parameters, i.e. solid volume fraction, Hartman number, thermal radiations parameter, Reynolds number, Eckert number, porosity parameter and ratio parameter, on flow and Nusselt number with a fixed value of Prandtl number at 6.2 is discussed in details. The obtained results are presented in the concluding section. The lamina shape of nanoparticles in silver-water performed an excellent role on temperature distribution. The heat transfer rate of lamina shape in copper-water was found to be greater in the system of flow regime.

The authors have discussed the shape effect of nanoparticles on MHD nanofluid flow over a rotating stretchable disk through porous medium using three categories of nanoparticles, such as copper, silver and titanium oxide. To the best of the authors’ knowledge, this is the first study on mass and heat transfer nanofluid flow and no such study is yet published in literature. A detailed mathematical analysis has also to be carried out to prove the regularity of model. The authors believe that the numerical results are original and have not been copied from any other sources.

The purpose of this paper is to analyze the heat transfer effects on the stretched flow of Oldroyd-B fluid in a rotating frame. Cattaneo–Christov heat conduction model is considered, which accounts for the influence of thermal relaxation time.

Based on scale analysis, the usual boundary layer approximations are used to simplify the governing equations. The equations so formed have been reduced to self-similar forms by similarity transformations. A powerful analytic approach, namely, homotopy analysis method (HAM), has been applied to present uniformly convergent solutions for velocity and temperature profiles.

Suitable values of the so-called auxiliary parameter in HAM are obtained by plotting h-curves. The results show that boundary layer thickness has an inverse relation with fluid relaxation time. The rotation parameter gives resistance to the momentum transport and enhances fluid temperature. Thermal boundary layer becomes thinner when larger values of thermal relaxation time are chosen.

To the authors’ knowledge, this is the first attempt to study the three-dimensional rotating flow and heat transfer of Oldroyd-B fluid.