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This analysis explores stagnation point in Jeffery liquid flow over a stretchable cylinder. Heat and mass transfer are investigated through Cattaneo–Christov model with double stratification, heat source and thermal relaxation. Moreover, the flow of liquid is caused by stretchable cylinder. Cylindrical coordinates are used for mathematical formulations. The acquired boundary layer problems for stretchable cylinder are dealt through homotopy analysis method. Results of variables appeared in governing equations are disclosed through graphs for flow, temperature, concentration and skin friction. The findings of the study show that higher values of ratio parameter and Deborah number in terms of relaxation time reduce magnitude of drag coefficient while reverse trend is noted for larger Deborah number in terms of retardation time and curvature parameter. Comparison of present work with previous published date is presented.

Heat transfer in a time-dependent flow of incompressible viscoelastic Maxwell fluid induced by a stretching surface has been investigated under the effects of heat radiation and chemical reaction. The magnetic field is applied perpendicular to the direction of flow. Velocity, temperature, and concentration are functions of z and t for the modeled boundary-layer flow problem. To have a hereditary effect, the time-fractional Caputo derivative is incorporated. The pressure gradient is assumed to be zero. The governing equations are non-linear, coupled and Boussinesq approximation is assumed for the formulation of the momentum equation. To solve the derived model numerically, the spatial variables are discretized by employing the finite element method and the Caputo-time derivatives are approximated using finite difference approximations. It reveals that the fractional derivative strengthens the flow field. We also observe that the magnetic field and relaxation time suppress the velocity. The lower Reynolds number enhances the viscosity and thus motion weakens slowly. The velocity initially decreases with increasing unsteadiness parameter δ. Temperature is an increasing function of heat radiation parameter but a decreasing one for the volumetric heat absorption parameter. The increasing value of the chemical reaction parameter decreases concentration. The Prandtl and Schmidt numbers adversely affect the temperature and concentration profiles respectively. The fractional parameter changes completely the velocity profiles. The Maxwell fluids modeled by the fractional differential equations flow faster than the ordinary fluid at small values of the time t but become slower for large values of the time t.

This exertion is part of a liable approach for the advancement of nanotechnology and nanoscience to scrutinize the thermal and rheological aspects of the nanofluids. The conformist heat transport fluids are broadly reported to be one of the notable reasons of the reduced enactment of heat transport tools, boosting the energy charges. For this concern to be stable, nanofluids have been familiarized as probable proxies to the conformist fluids because of their intensify aptitude of heat transport coefficient. Here, the up-front goal is to investigate the aspect of nonlinear radiated and chemical reaction with aspects of Arrhenius activation energy in Carreau nanofluid. Additionally, mixed convection, MHD, and new mass flux theory is explored. The framed system is envisioned numerically via bvp4c. Temperature field intensifies against enhanced values of radiation and thermophoresis parameters, respectively. Concentration has conflicted performance for escalating activation energy and Brownian motion parameters, respectively.

Fractional MHD viscoelastic fluid flow has been discussed in this study. Two dimensional and two directional unsteady flow field is more critically analyzed via non-integer time derivatives. Three memory parameters are incorporated to explore the viscoelastic characteristics of the model. Variations in concentration occurred due to homogeneous-heterogeneous reactions in the flow domain. Change in concentrations consequently leads to one of the lasting chemical species. Heterogeneous reactions are observed at the boundary while homogeneous reactions are seen in the flowing region. We consider different orders of diffusion coefficients of chemical reacting species to tackle the wider class of physical and chemical processes. Governing equations are nonlinear in nature. Hence a recently established finite difference technique along with “L1 algorithm” is used for discretization and solution of governing fractional partial differential equations. Presence of chemical reactions in flow process made the simulations valuable for chemical industry.

This article elucidates viscoelastic fractional fluid flow along with homogeneous-heterogeneous reactions. Non-integer derivatives are important for the systems having hereditary behavior as they depend on the past conditions along with the local conditions. Viscoelastic fluids keep memory of old deformations and their behavior is related to these deformations. The fractional derivatives are more adequate in predicting the characteristics of viscoelastic fluids than the ordinary derivatives. In this paper we have examined characteristics of fractional homogeneous-heterogeneous reactions with variable concentrations of both the reactant species. Flow is induced by the variable moving surface. Diffusion coefficients of reactants and auto catalyst are of comparable size. For better understanding of hereditary properties, non integer Caputo time derivatives have been incorporated in mathematical formulation of the flow regime. Unsteady motion of a magnetohydrodynamic incompressible viscoelastic fluid is governed by highly nonlinear fractional partial differential equations. Flux conditions are imposed on the chemical species at the boundary. Governing flow equations with suitable initial and boundary conditions have been discretized using finite difference-finite element scheme. Proposed numerical scheme is flexible for the solution of non-linear flow problems. Skin friction coefficients are calculated for fractional viscoelastic model. Flow field is demonstrated for different values of involved parameters. The acquired results revealed that with the increase of fractional exponent α concentration of chemical specie decreases for the final time t = 2 . It is also noted that concentration gradients of chemical specie increase with the increase of α at both the boundaries of flow configuration. In literature no such result exits with non integer Caputo fractional derivatives. Various viscoelastic flows particularly in chemical, plastics and polymer industries can be modeled in a similar manner.

In this communication we have examined the magneto-hydrodynamic flow of viscoelastic liquid with revise version of thermal flux. Thermal conductivity of the fluid is variable. Effects of body forces such as gravity are also examined in terms of convection. Non-integer time derivatives are used for the better understanding of viscoelastic flow characteristics. In literature, these derivatives have been proved suitable for the predictions of hereditary systems such as viscoelastic flows. Heat transfer is analyzed in the flow field via modified fractional thermal gradient. Temperature gradient exists between the flow boundaries and increases with the passage of time. Flow is generated by the variable movement of flow boundary. All the segments of numerical modeling are completely addressed in this paper i.e. physical system, mathematical model, simulation, prediction, validation and verification. Unsteady motion of in-compressible fluid is directed by differential equations with fractional partial derivatives, for the solutions of these equations numerical techniques are necessary to use. Governing equations with appropriate flow conditions have been discretized by finite difference along with finite element algorithms. Theoretical error appraisals are hypothesized and created numerical plan has been approved by doing error investigations numerically regarding spatial directions. We have shown the estimate error and plotted the error curves in logarithmic scales of L 2 ( Ω ) and H 1 ( Ω ) norms by taking absolute approximations of the space discretization. Local Nusselt number and coefficients of skin friction are determined for non-integer viscoelastic model. Flow field is simulated for various values of physical parameters. The obtained results showed that fractional exponent α has opposite effects on the velocity, temperature profiles for time t = 2 . It is also noted that temperature gradient increases by the increase of fractional number α and thermal relaxation parameter γ . Viscoelastic flows in polymer and plastics industries can be addressed by similar technique.

This article presents unsteady, magneto-hydrodynamic (MHD) flow of viscoelastic fluid through porous medium. Constitutive relationship for this model is established by fractional calculus approach. Flow is considered between two parallel plates of infinite length. Finite element-finite difference scheme is used for the solution of the governing nonlinear partial differential equation. Influence of the fractional flow parameters on the velocity profile and skin friction coefficient is shown by graphical illustrations. Numerical values are also computed for the skin friction coefficient. It is expected that present work helps as a motivation for modeling further porous medium flows that involve catalytic converters, gas turbines and condensers.

Bimodal porous structures were prepared by combining conventional sacrificial template and partial sintering methods. These porous structures were analysed by comparing pore characteristics and gas permeation properties of alumina/mullite specimens sintered at different temperatures. The pore characteristics were investigated by SEM, mercury porosimetry, and capillary flow porosimetry. A bimodal pore structure was observed. One type of pore was induced by starch, which acted as a sacrificial template. The other pore type was due to partial sintering. The pores produced by starch were between 2 and 10 µm whereas those produced by partial sintering exhibited pore size of 0.1–0.5 µm. The effects of sintering temperature on porosity, gas permeability, and mullite phase formation were studied. The formation of the mullite phase was confirmed by XRD. Compressive strengths of 37.9 MPa and 12.4 MPa with porosities of 65.3% and 70% were achieved in alumina and mullite specimens sintered at 1600 °C.

This article presents the phase dynamics of an inline long Josephson junction in voltage state under the influence of constant external magnetic field. Fractional calculus approach is used to model the evolution of the phase difference between the macroscopic wave functions of the two superconductors across the junction. The governing non-linear partial differential equation is then solved using finite difference-finite element schemes. Other quantities of interest like Josephson current density and voltage across the junction are also computed. The effects of various parameters in the model on phase difference,Josephson current density and voltage are analyzed graphically with the help of numerical simulations.

In the arena of pharmaceutical, nanotechnology and nanoscience numerous scientists are fascinated to explore the notion of nanofluid because nanofluids are two-phase ingredients comprising of disreputable fluid and nanoparticles which have notable possessions of heat transportation. Nanofluids are of boundless worth due to the higher enactment on progress of thermal act. This exertion sightsee the thought of new mass flux and activation energy in magnetized transient Carreau nanofluid with variable conductivity. The convective phenomenon, heat sink-source and chemical reaction are also scrutinized. The bvp4c algorithm exploited for solutions of ODEs. The outcomes of influential parameters are sketched graphically and in tabular shape. The temperature field escalates for Biot number and falloff for Prandtl number. The thermophoretic and activation energy parameters have analogous influence on concentration scattering and intensify the concentration field. Furthermore, the comparative fallouts are acknowledged and attained outstanding agreement.

Influence of electric and magnetic fields in a nonlinear viscoelastic flow is studied in this communication. Microscopic description of Joule heating can be seen with the proposed model. Fractional formulation of the problem with Cattaneo–Maxwell model leads to oscillation and relaxation processes that show memory and delay of thermal and diffusing flux. Abrupt change in temperature and concentration in MHD flow can be controlled with this formalism. Time-dependent flow is governed by highly nonlinear fractional differential equations. Finite-element–finite-difference algorithm is used to solve the fractional coupled fields and flow dynamics problem. Remarkable physical parameters are calculated to signify the importance of problem under observation. Modeled problem can be tackled in numerous ways to obtain accurate simulations in polymer and electromagnetic casting industries.

Heat transfer through a Forchheimer medium in an unsteady magnetohydrodynamic (MHD) developed differential-type fluid flow is analyzed numerically in this study. The boundary layer flow is modeled with the help of the fractional calculus approach. The fluid is confined between infinite parallel plates and flows by motion of the plates in their own plane. Both the plates have variable surface temperature. Governing partial differential equations with appropriate initial and boundary conditions are solved by employing a finite-difference scheme to discretize the fractional time derivative and finite-element discretization for spatial variables. Coefficients of skin friction and local Nusselt numbers are computed for the fractional model. The flow behavior is presented for various values of the involved parameters. The influence of different dimensionless numbers on skin friction and Nusselt number is discussed by tabular results. Forchheimer medium flows that involve catalytic converters and gas turbines can be modeled in a similar manner.

Convective phenomena in a nanofluid flow under the influence of gravitational and magnetic body forces is analyzed in this communication. Nanofluid is of viscoelastic nature that preserves viscosity as well as elasticity. In order to capture the more realistic behavior of the convective phenomena Caputo fractional derivative and fractional relaxation time are introduced in the Buongiorno nanofluid model. Fractional derivative and relaxation time are used for controlled flow mechanism and to overcome infinite propagation speed for the temperature and concentration. The proposed model will also help to understand the hereditary and memory properties of the viscoelastic nanofluid. In order to more closely analyze the buoyancy forces nonlinear convection is introduced in the mathematical modeling of the flow problem. Finite difference-finite element numerical computations are carried out for the governing nonlinear partial differential equations. Quantities of physical interest are computed and discussed for the fractional model. The proposed fractional model can be used to realistically simulate various flow problems in polymer and chemical industries.