Narrow Results

The process of convective thermal management in the radiative flow of Oldroyd-B fluid over the stretching cylinder is investigated in this paper. In engineering and applied sciences, the viewpoint of fluid flow due to vertically stretched cylinder covers both theoretical and practical significances. Nonlinear ordinary differential equations are first transformed from their corresponding partial differential equations, then rebuilt using sufficient transformations to produce a system of nondimensional equations, using a proper similarity technique, which is then calculated. The MATLAB built-in technique BVP4C, a standard numerical process, is used to solve the regulating flow equations. A comprehensive graphical depiction was used for characteristics like unsteadiness and curvature, Prandtl number, and thermal diffusivity. The relevant flow characteristics of the governing problem are depicted in graphs.

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partial differential equations, which then give rise to a set of highly nonlinear coupled ordinary differential equations using similarity transformations. The nonlinearity in the differential equations is dealt with quasilinearization technique. The resultant equations are numerically solved using Chebyshev wavelet collocation method. The effects of magnetic field, radiation, chemical reaction and buoyancy parameters are investigated. The numerical values of local skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated and analyzed. We observe that the increase in buoyancy parameters enhances the velocity profiles and larger values of magnetic field decrease the velocity profiles but increases the temperature and concentration profiles. Error analysis has been done to check the convergence of the numerical scheme.

This paper aims to investigate the time-dependent stagnation point flow of an Oldroyd-B fluid subjected to the modified Fourier law. The flow into a vertically stretched cylinder at the stagnation point is discussed. The heat flux model of a non-Fourier is intended for the transfer of thermal energy in fluid flow. The study is carried out on the surface heating source, namely the surface temperature. The developed nonlinear partial differential equation for regulating fluid flow and heat transport is transformed via appropriate similarity variables into a nonlinear ordinary differential equation. The development and analysis of convergent series solutions were considered for velocity and temperature. Prandtl number numerical values are computed and investigated. This study’s findings are compared to the previous findings. By making use of the bvp4c Matlab method, numerical solutions are obtained. Besides, high buoyancy parameter values are found to increase the fluid velocity for the stimulating approach. By improving the thermal relaxation time parameter values, heat transfer in the fluid flow decreases. The temperature field effects are displayed graphically.

The role of non-Newtonian fluids can’t be denied owing to their immense industrial and engineering applications. Taking this point in mind, the motivation of the current investigation is to examine the influence of a magnetic dipole on two-dimensional nonelectrical conducting Oldroyd-B fluid flow in the existence of thermophoretic particle deposition along a linearly stretching surface. The exponential space-based thermal source and the temperature-dependent heat source/sink are incorporated into the thermal equation. The fluid concentration is strengthened with binary activation energy and Arrhenius chemical reaction. The set of ordinary differential equations that are attained after applying the similarity transformations is resolved numerically by the bvp4c approach of MATLAB software. The impact of diverse parameters on velocity, temperature, and concentration are graphically examined. The quantities of physical importance are also computed and analyzed numerically. The results revealed that fluid velocity and temperature have opposing trends for the ferromagnetic interaction parameter. It is also witnessed that the fluid concentration arguments for the chemical reaction parameter. The validation of the model in the limiting case is also given.

In this research, the authors precisely focus on the analysis of the chaotic behavior in an Oldroyd-B fluid saturated anisotropic porous medium via a feedback control technique. A four-dimensional (4D) weakly nonlinear system emerging from a Galerkin method of the constitutive and preservation equations is developed to accord with a convective stabilization with various Darcy numbers (Da) and feedback control gain value $({\widehat{F}}_g)$. The chaotic dynamic convection is governed by the Darcy–Rayleigh number ($R_n$) and feedback control, while the Da has a significant impact on system stabilization. Their results reveal the effects of the feedback gain parameter $({\widehat{F}}_g)$, stress relaxation parameter ($\mathrm{\Gamma }$), strain retardation parameter ($\mathrm{\Lambda }$), Darcy number (Da), mechanical ($\zeta$) and thermal ($\chi$) anisotropy parameter on the stability and destabilization of thermal convection. Stabilization of thermal convection are important in cooling, nuclear power, and a range of technical, biological and engineering processes. In particular, feedback control gain values are discovered to be the preferred mode for the controlled onset of oscillatory convection. Finally, a graphical representation is presented to demonstrate that the feedback control approach is more effective in regulating the entire system when aperiodic external disturbances occur.

Roll coating is a popular method for applying a thin coating film to a continuous substrate, such as paper or foil. This study aims to investigate analytically the fluid flow through counter rotating rolls using a non-Newtonian model. The governing equation for the constitutive of the Oldroyd-B as a non-Newtonian fluid with momentum equation has been discovered. The nondimensionalizing of the fluid flow equations is done by using suitable dimensionless parameters. The equations are then simplified by using Lubrication Approximation Theory (LAT) to obtain the solution for various quantities. Analytical solutions for the velocity distribution, pressure and pressure gradients have been obtained by regular perturbation method. Numerical integration has been used to calculate separation point, coating thickness, separation force and power input of the fluid. The effect of involved parameter such as Weissenberg number We and viscosity on velocities, pressure gradient and pressure is presented in a variety of graphs and several other results are shown in tables. It has been observed that as the modified capillary number $N_{C{a}_2}$ increases, the separation point moves toward the nip region, whereas the coating thickness declines. It has been witnessed that the We serves as the controlling parameter for flow rate, pressure distribution and power input, whereas for the coating thickness, the separation force increases, which are important for coating industries.

Blood circulating efficiently inside the veins and arteries, provides essential nutrients and oxygen to tissues and organs in the entire body. To highlight the fundamental properties of blood and gain insight into the regularizing effect of various formulations, we need to develop mathematical models. In order to do this, first we present the polymer dynamics in terms of an ensemble of Hookean dumbbells with Brownian configuration fields to derive the orientation stress tensor. Then, we describe the continuity and the momentum equations for time-dependent incompressible flow and the Oldroyd-B model. Finally, we present our numerical analysis of the model and give the effect of the orientation stress tensor in a blood vessel. The development of mathematical models and numerical procedures for the approximation of the blood specific flow equations have enabled us to understand the complex behaviors of blood flows inside the vessel.

Study of heat and mass transfers is carried out for MHD Oldroyd-B fluid (OBF) over an infinite vertical plate having time-dependent velocity and with ramped wall temperature and constant concentration. It is proven in many already published articles that the heat and mass transfers do not really or always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such dynamical process very accurately, thus, a different concept of differentiation is needed to capture such process. Very recently, a new class of differential operators were introduced and have been recognized to be efficient in capturing processes following the power-law, the decay law and the crossover behaviors. For the study of heat and mass transfers, we applied the newly introduced differential operators to model such flow and compare the results with integer-order derivative. Laplace transform and inversion algorithms are used for all the cases to find analytical solutions and to predict the influences of different parameters. The obtained analytical solutions were plotted for different values of fractional orders $\alpha$ and $\beta$, $\lambda$, ${\lambda }_r$, $M$, $G_r$ and $Pr$ on the velocity field. In comparison, Atangana–Baleanu (ABC) fractional derivatives are found to be the best to explain the memory effects than the classical, Caputo (C) and Caputo–Fabrizio (CF) fractional derivatives. Some calculated values for Nusselt number and Sherwood number are presented in tables. Moreover, from the present solutions, the already published results were found as limiting cases.

The theoretical study focuses on the examination of the convective flow of Oldroyd-B fluid with ramped wall velocity and temperature. The fluid is confined on an extended, unbounded vertical plate saturated within the permeable medium. To depict the fluid flow, the coupled partial differential equations are settled by using the Caputo (C) and Caputo Fabrizio (CF) differential time derivatives. The mathematical analysis of the fractionalized models of fluid flow is performed by Laplace transform (LT). The complexity of temperature and velocity profile is explored by numerical inversion algorithms of Stehfest and Tzou. The fractionalized solutions of the temperature and velocity profile have been traced out under fractional and other different parameters considered. The physical impacts of associated parameters are elucidated with the assistance of the graph using the software MATHCAD 15. We noticed the significant influence of the fractional parameter (memory effects) and other parameters on the dynamics of the fluid flow. Shear stress at the wall and Nusselt number also are considered. It’s brought into notice the fractional-order model (CF) is the best fit in describing the memory effects in comparison to the C model. An analysis of the comparison between the solution of velocity and temperature profile for ramped wall temperature and velocity and constant wall temperature and velocity is also performed.

In this paper, we construct the exact solution of blood flow of Oldroyd-B fluids to represent the non-Newtonian characteristics of biofluids and to study the unsteady flow of blood and heat transfer through arterial segment with external magnetic field applied normal to the flow direction in the presence of thermal radiation and body acceleration. In the study, we investigate the influence of Caputo time-fractional parameter, heat transfer, external body acceleration, and magnetic field on the blood velocity and temperature distribution in a straight circular cylindrical vessel. The constitutive partial differential equation and temperature equation governing blood flow in the arterial wall are solved using Laplace and finite Hankel transforms. In addition, Gaver Stehfest’s algorithm is used for the inverse Laplace transform. The results obtained are interpreted graphically and discussed from the physiological point of view. The graphs show that the rate of heat transfer and blood velocity become less with the increase in the external magnetic field strength which is very good in regulating blood flow as well as temperature distribution during treatment. Based on the graphical representations, blood velocity and temperature distribution both decrease in ascending order of the fractional parameter as memory effect. Further, owing to the dissipation of energy caused by blood viscoelasticity and magnetic field effect, during pulsatile flow of blood, the heat transfer rate at the wall of the artery is enhanced. The significance of this study can be found in the application fields such as biomedical engineering, medicine and pathology.

The velocity field, the longitudinal and the normal tensions corresponding to the axial flow of an Oldroyd-B fluid due to an infinite circular cylinder subject to a longitudinal time-dependent stress are determined by means of the Laplace and finite Hankel transforms. The similar solutions for Maxwell, second grade or Newtonian fluids have been obtained as particular cases of the solutions for Oldroyd-B fluids. Finally, by using dimensionless variables, some characteristics of the motion as well as the influence of the material parameters on the behavior of fluid are shown by graphical illustrations.