Defect and Diffusion Forum Vol. 424

Abstract: This study is based on the exploration of MHD Casson fluid flow past a stretching cylinder in the presence of non-uniform heat generation, thermal radiation and Joule heating. Boussinesq approximation is also put into consideration due to density difference in the fluid. The governing equations and their corresponding boundary conditions are changed into system of ordinary differential equations with the aid of appropriate similarity variables. The obtained ordinary differential equations are solved numerically using Runge-Kutta Fehlberg method alongside shooting technique. The flow and thermal fields are investigated in the presence of emerging parameters, namely Grashof number, Prandtl number, radiation parameter, curvature parameter, Eckert number, Casson parameter, permeability parameter, magnetic number, space and temperature dependent heat generation parameter. In this study, enhancement in velocity distributions is noticed as values of Grashof number grow but velocity profiles are depreciated by permeability parameter and curvature parameter.

Abstract: This work presents a computational analysis of the heat-exchange characteristics in a double-cylinder (also known as a double-pipe) geometrical arrangement. The heat-exchange is from a hotter viscoelastic fluid flowing in the core (inner) cylinder to a cooler Newtonian fluid flowing in the shell (outer) annulus. For optimal heat-exchange characteristics, the core and shell fluid flow in opposite directions, the so-called counter-flow arrangement.The mathematical modelling of the given problem reduces to a system of nonlinear coupled Partial Differential Equations (PDEs). Specifically, the rheological behaviour of the core fluid is governed by the Giesekus viscoelastic constitutive model. The governing system of coupled nonlinear PDEs is intractable to analytic treatment and hence is solved numerically using Finite Volume Methods (FVM). The FVM numerical methodology is implemented via the open-source software package OpenFOAM. The numerical methods are stabilized, specifically to address numerical instabilities arising from the High Weissenberg Number Problem (HWNP), via a combination of the Discrete Elastic Viscous Stress Splitting (DEVSS) technique and the Log-Conformation Reformulation (LCR) methodology. The DEVSS and LCR stabilization techniques are integrated into the relevant viscoelastic fluid solvers. The novelties of the study center around the simulation and analysis of the optimal heat-exchange characteristics between the heated Giesekus fluid and the coolant Newtonian fluid within a double-pipe counter-flow arrangement. Existing studies in the literature have either focused exclusively on Newtonian fluids and/or on rectangular geometries. The existing OpenFOAM solvers have also largely focused on non-isothermal viscoelastic flows. The relevant OpenFOAM solvers are modified for the present purposes by incorporating the energy equation for viscoelastic fluid flow. The flow characteristics are presented qualitatively (graphically) via the fluid pressure, temperature, velocity, and the polymer-stress components as well as the related normal stress differences. The results illustrate the required decrease in the core fluid temperature in the longitudinal direction due to the cooling effects of the shell fluid, whose temperature predictably increases in the counter-flow direction.

Abstract: In this article we consider heat transfer models prescribed by reaction-diffusion equations. The diffusivity term and internal heat generator are given by the power law. The differential transform method (DTM) is utilized to construct the approximate analytical solutions. These solutions are generated using one- and two-dimensional DTM for the steady state and the transient problem, respectively. The effects of parameters appearing in the model are presented and explained.

Abstract: In this paper, we report the effects of fractional relaxation time on the parameters of blood flow together with magnetic particles through straight circular cylindrical arterial segment. A mathematical model of blood flow subject to pulsatile pressure gradient in the axial direction with external magnetic field applied normal to the direction of flow is presented. Combining the momentum equation together with the Maxwell model parameter appropriately, leads to the governing fractional partial differential equation which permits to obtain the velocity profile of blood along with magnetic particles. By adopting the non-dimensionalized form of the new version of the governing fractional partial differential equation allowed us to obtain the dimensionless relaxation time parameter λ₁ which controls blood flow conditions. Solving the fractional partial differential equations using Laplace and finite Hankel transforms we found that the influence of the order of Caputo's fractional time-derivative and fractional relaxation time on the blood flow parameters with magnetic particles are enormous. The graphical results plotted of different influential parameters are presented and discussed in details. The velocities of blood flow and that of magnetic particles are reduced under the influence of the external magnetic field and the relaxation time parameter. The magnetic particles are assumed to be uniformly distributed within the blood, since they are flowing in the same axial direction designated by along a circular cylindrical coordinates of radius. This is a very good indication that blood velocity can be controlled by the application of external magnetic field as well as the relaxation time parameter during treatment to avoid tissues damage. The present study has important applications in magnetic field control of biotechnological processes, bio magnetic device technology, biomedical engineering and pathology. Keywords: Arterial segment, Blood flow, Relaxation time, Magnetic field, Magnetic particles

Abstract: In this work, we consider transient electroosmotic flow of fractional Maxwell fluids model derived for both velocity and temperature in a micro-channel. We use the Poisson-Boltzmann equation to describe the potential electric field applied along the length of the micro-channel. Exact solutions of both velocity and temperature were obtained using Laplace transform combined with finite Fourier sine transform. Due to the complexity of the equations for velocity and temperature, the inverse Laplace transform was obtained using the numerical inversion formula based on Gaver Stehfest’s algorithms. The numerical solutions were simulated with the help of Mathcard software and the graphical results showing the effects of time, relaxation time, electrokinetic width and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameter on the temperature distribution in the microchannel were presented and discussed. The results show that the applied electric field, the electroosmotic force, electrokinetic width, and relaxation time play vital role on the velocity profile in the micro-channel and the fractional parameter can be used to regulate both the velocity and temperature in the micro-channel. The effects of the various influential parameters on both fluid velocity and temperature distribution were found to be useful for the design of microfluidic devices. These devices could be useful for biomedical diagnosis and analysis, for clinical detection of viruses and bacteria in biological processes. Keywords: Caputo fractional derivative, Electro kinetic width, Electroosmotic flow, Heat transfer, Zeta potential,

Abstract: This study assesses the motion and the dynamics of heat propagation in magneto-micropolar fluid along a sheet which vertically stretches on a two-dimensional plane in a porous material. The heat distribution is developed and evaluated under the condition of the prescribed wall temperature, constant magnetic field, thermal radiation, variable heat source and viscous dissipation. The main equations are re-formulated from partial to ordinary derivatives using similarity tools and consequently solved numerically by shooting and the Runge-Kutta Fehlberg approach. The parameters of interest are presented graphically to demonstrate their reactions on the velocity profiles, thermal field and heat transfer mechanism of the problem. The outcomes of the current investigation reveal that the heat transfer appreciates in the presence of higher Prandtl number, temperature exponent term and material parameter but decreases as the magnetic field term soars.Besides, the heat boundary structure expands and heat spread occurs as the thermal radiation, magnetic field and Eckert number terms escalates but a reverse trend is encountered as the Prandtl number, material micropolar term, Grashof number and heat exponent terms grows in magnitude. Under some limiting scenarios, the obtained data strongly correspond to the published studies in the open literature.

Abstract: We try through this research to present a detailed study on free convection heat transfer inside a closed space. The work is carried out in numerical way, using the method called finite volume. The governing equations are solved for numerical simulations of steady state and laminar regime. The studied domain is an annular space consisting mainly of two cylinders positioned horizontally, the inner cylinder has an elliptical shape with different aspect ratio (E) while the outer one has a single shape which is circular. The primary conditions adopted in this research are as follow: the outer cylinder has a cold surface, while the inner cylinder has a cold surface. The space between cylinders is considered to be filled with fluid of different values of thermo-physical proprieties (Pr). The fluid in the space moves under the influence of thermal buoyancy which is controlled by Ri number. The pertinent parameters for this research are: the aspect ratio of elliptical cylinder which is E = 0.1 to 1, the Prandtl number Pr = 1 to 100 and finally the Richardson number Ri = 10³, 10⁴ and 10⁵. The results of this work show that the elliptical form allows an increase in thermal transfer activity. Also, values of the number Pr have a limited effect on heat transfer.

Abstract: The present paper focuses on the effect of geometric shape of a cylindrical body submerged in an oscillating flow by means of numerical investigations. The cylindrical body has an elliptic cross-section with a variation of its elliptic ratio (ratio between major and minor axes of the elliptic section). The flow direction is oriented along the major axis. Three regimes from (Tatstuno and Bearman) maps are studied namely, a symmetric regime A and two other asymmetric regimes D and F. The flow field structures, the Morison coefficients of longitudinal forces and the root mean square (r.m.s.) of transverse forces are computed with respect to the elliptic ratio variation. For the case of cylinders with slightly elliptic cross-section, vortices and pressure fields are very similar to those of a circular cylinder. For the case of regime A, the vortex shedding is always symmetric despite the unbreakable variation of the elliptic ratio. On the other hand, the reduction of the elliptic ratio weakens the asymmetry of the flow for regimes D and F. Moreover, the flow in each regime becomes completely symmetric at a given value of the elliptic ratio. In fact, the predicted longitudinal component of the force acting on the cylinder decreases with the reduction of this ratio. This results in the same manner on the behavior of Morison coefficients. With regard to the symmetric regime A, the transverse force does not manifest itself for all considered ratios. On the other hand, the transverse force in the case of asymmetric regimes decreases rapidly with increasing the ellipticity of the cylinder. The present study showed us that the inertia coefficient is sensitive to the vortex path; however, the drag coefficient is independent of the vortex path. Both coefficients depend simultaneously on Reynolds number and the geometric shape of the body.

Abstract: This study considers the unsteady magnetohydrodynamic slip flow past a permeable stretching cylinder by taking into account the Soret and Dufour effects. Using similarity transformations, the partial differential equations governing the flow, heat, and mass transfers are transformed into a system of ordinary differential equations. These equations are numerically solved for a variety of governing parameter values using the boundary value problem solved package, bvp4c, which is available in the MATLAB software. The outcomes of the governing parameters on the skin friction coefficient, Nusselt and Sherwood numbers are also examined. Upon observation, the unsteadiness parameter influences a positive growth on the momentum, thermal and concentration boundary layers. Slip parameter can be enhanced to improve the friction drag force about 28% and the rate of cooling around 3%. Also, larger effects of Dufour leads to around 9% decay in heat transfer rate and Soret effect to cause around 11% drop in mass transfer rate. Comparison with existing results show excellent agreement which justifies the reliability of the obtained results.