Fluid relaxation and retardation time properties in the flow of Burgers fluid subject to modified heat and mass flux theory

In this study, the heat transport is scrutinized in the flow of magnetized Burgers fluid accelerated by stretching cylinder. Rather than, classical Fourier's and Fick's laws, the Cattaneo-Christov theory featuring the improved heat and mass conduction is utilized to investigate the energy transport. Further, the transport of thermal and solutal energy is controlled by the significant influence of heat generation/absorption and chemical reaction. The physical flow problem is modelled in the form of partial differential equations (PDEs) which are then transformed into the non-linear ordinary differential equations (ODEs) by invoking appropriate similarity variables. The numerical simulation to the system of ODE's is tackled by employing BVP-Midrich scheme in Maple. The numerical results for flow field, thermal and concentration distributions are exhibited graphically. The impact of fluid relaxation and retardation time parameters on the velocity field are observed in growing and decaying way, respectively. Both the thermal and solutal energy transport decline with higher values of retardation time parameter. The rise in Burgers fluid parameter enhances the transport of energy during the fluid motion. The effect of thermal and solutal relaxation time parameters on heat and mass transport in the fluid are noticed in the declining manner.

Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

Stagnation point flow of Jeffrey nanofluid with activation energy and convective heat and mass conditions

This research reports stagnation flow of Jeffrey nanofluid toward a permeable stretching cylinder. Brownian motion, thermophoresis, thermal radiation and viscous dissipation are explored. Convective heat-mass conditions are implemented. Moreover, activation energy is taken into account. Transformations (variables) are utilized in order to convert PDEs (Partial DIfferential Equations). (continuity, momentum, energy and concentration equation) into ODEs (Ordinary Differential Equations). Resulting systems are solved by the optimal homotopy analysis method. Behaviors of involved flow, heat and mass transport parameters for velocity, concentration and temperature are examined. Surface friction and Sherwood number and Nusselt numbers are also examined. Velocity of the fluid can be minimized by higher estimations of parameter due to ratio of relaxation and retardation time, suction and injection parameters. Decay in fluid temperature is observed for higher Prandtl number and Deborah number for relaxation time parameter. Skin friction coefficient is controlled via higher values of parameter due to ratio of relaxation and retardation time. Intensification in heat transfer rate (Nusselt number) is seen via higher values of parameter due to ratio of relaxation and retardation time, radiation parameter, Prandtl number and Deborah number for relaxation time and curvature parameter.

Analytical and numerical study for oscillatory flow of viscoelastic fluid in a tube with isosceles right triangular cross section

A theoretical investigation is carried out to analyze the oscillatory flow of second-grade fluid under the periodic pressure gradient in a long tube of isosceles right triangular cross section in the present study. The analytical expressions for the velocity profile and phase difference are obtained. The numerical solutions are calculated by using the finite difference method with Crank–Nicolson (C–N) scheme. In comparison with the Newtonian fluid (λ = 0), the effects of retardation time, Deborah number and Womersley number on the velocity profile and phase difference are discussed numerically and graphically. For smaller Womersley number, the behavior of second-grade fluid is dominated by viscosity. For larger Womersley number α = 20, the flow becomes more difficult to be generated under periodic pressure gradient with increasing retardation time. Furthermore, the analytical expressions of the mean velocity amplitude and phase difference are given explicitly for discussing.

Effects of Higher Order Retarded Gravity

In a recent paper, we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this will rely on a temporal change of galactic mass. In our previous work, we kept only second order terms of the retardation time in our analysis, while higher terms in the Taylor expansion where not considered. Here we consider analysis to all orders and show that a second order analysis will indeed suffice, and higher order terms can be neglected.

Effects of Higher Order Retarded Gravity

In a recent paper we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this will rely on a temporal change of galactic mass. In our previous work we have kept only second order terms of the retardation time in our analysis, while higher terms in the Taylor expansion where not considered. Here we consider analysis to all orders and show that indeed a second order analysis will suffice, and higher order terms can be neglected.

Unsteady stagnation-point flow of upper-convected Oldroyd-B nanofluid with variable thermal conductivity and relaxation-retardation double-diffusion model

Purpose This paper aims to examine the unsteady stagnation-point flow, heat and mass transfer of upper-convected Oldroyd-B nanofluid along a stretching sheet. The thermal conductivity is taken in a temperature-dependent fashion. With the aid of Cattaneo–Christov double-diffusion theory, relaxation-retardation double-diffusion model is advanced, which considers not only the effect of relaxation time but also the influence of retardation time. Convective heat transfer is not ignored. Additionally, experiments verify that with sodium carboxymethylcellulose (CMC) solutions as base fluid, not only the flow curve conforms to Oldroyd-B model but also thermal conductivity decreases linearly with the increase of temperature. Design/methodology/approach The suitable pseudo similarity transformations are adopted to address partial differential equations to ordinary differential equations, which are computed analytically through homotopy analysis method (HAM). Findings It is worth noting that the increase of stagnation-point parameter diminishes momentum loss, so that the velocity enlarges, which makes boundary layer thickness thinner. With the increase of thermal retardation time parameter, the nanofluid temperature rises that implies heat penetration depth boosts up and the additional time required for nanofluid to heat transfer to surrounding nanoparticles is less, which is similar to the effects of concentration retardation time parameter on concentration field. Originality/value This paper aims to explore the unsteady stagnation-point flow, heat and mass transfer of upper-convected Oldroyd-B nanofluid with variable thermal conductivity and relaxation-retardation double-diffusion model.

Time-periodic pulse electroosmotic flow of Jeffreys fluids through a microannulus

In this article, we investigate the time-periodic pulse electroosmotic flow (EOF) of Jeffreys fluids through a microannulus. By using the Laplace transform method, the velocity expression of the pulse EOF is derived. The effect of some variables on the time it takes for the fluid to go from a static state to a flowing state is analyzed. We find that increasing the relaxation time λ ¯ 1 {\bar{\lambda }}_{\text{1}} and decreasing the inner and outer radius ratio α \alpha will result in longer time for the fluid to reach the flowing state, but the retardation time λ ¯ 2 {\bar{\lambda }}_{\text{2}} and the inner and outer zeta potential ratio β \beta have little effect on it. The impact of some related parameters on the pulse EOF velocity for different inner and outer radius ratios ( α \alpha ) is discussed in detail. The results show that for a smaller inner and outer radius ratio α \alpha , the velocity amplitude increases with the relaxation time λ ¯ 1 {\bar{\lambda }}_{\text{1}} and decreases with the retardation time λ ¯ 2 {\bar{\lambda }}_{\text{2}} . As the inner and outer radius ratio α \alpha increases, the effect of relaxation time λ ¯ 1 {\bar{\lambda }}_{\text{1}} on velocity amplitude gradually weakens or even becomes insignificant, and the effect of the retardation time λ ¯ 2 {\bar{\lambda }}_{\text{2}} on the velocity amplitude remains unchanged. Moreover, the velocity amplitude will decrease with the increase in the inner and outer radius ratio α \alpha and its change range will expand from the electric double layer near the annular wall to the entire flow region.

USE OF ATANGANA–BALEANU FRACTIONAL DERIVATIVE IN HELICAL FLOW OF A CIRCULAR PIPE

There is no denying fact that helically moving pipe/cylinder has versatile utilization in industries; as it has multi-purposes, such as foundation helical piers, drilling of rigs, hydraulic simultaneous lift system, foundation helical brackets and many others. This paper incorporates the new analysis based on modern fractional differentiation on infinite helically moving pipe. The mathematical modeling of infinite helically moving pipe results in governing equations involving partial differential equations of integer order. In order to highlight the effects of fractional differentiation, namely, Atangana–Baleanu on the governing partial differential equations, the Laplace and Hankel transforms are invoked for finding the angular and oscillating velocities corresponding to applied shear stresses. Our investigated general solutions involve the gamma functions of linear expressions. For eliminating the gamma functions of linear expressions, the solutions of angular and oscillating velocities corresponding to applied shear stresses are communicated in terms of Fox- H function. At last, various embedded rheological parameters such as friction and viscous factor, curvature diameter of the helical pipe, dynamic analogies of relaxation and retardation time and comparison of viscoelastic fluid models (Burger, Oldroyd-B, Maxwell and Newtonian) have significant discrepancies and semblances based on helically moving pipe.