scholarly journals Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
M. Khan ◽  
S. Abelman ◽  
D. P. Mason ◽  
F. M. Mahomed
Keyword(s):  
Differential Equation ◽  
Fluid Velocity ◽  
Cylindrical Tube ◽  
Initial Approximation ◽  
Steady State Solution ◽  
Polar Coordinates ◽  
Sisko Fluid ◽  
Unidirectional Flow ◽  
Self Similar ◽  
Cylindrical Polar Coordinates

The governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates. The exact steady-state solution for the nonlinear problem is obtained. The reduction of the nonlinear initial value problem is carried out by using a similarity transformation. The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponentnand the material parameterbof the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented.

DISSIPATIVE HEAT TRANSFER IN SISKO FLUID PERISTALTIC FLOW THROUGH A CYLINDRICAL TUBE WITH NONLINEAR SLIP

2015 ◽  
Vol 46 (7) ◽  
pp. 643-656 ◽  
Author(s):  
Obaid Ullah Mehmood ◽  
Norzieha Mustapha ◽  
Sharidan Shafie ◽  
Muhammad Qasim
Keyword(s):  
Heat Transfer ◽  
Cylindrical Tube ◽  
Peristaltic Flow ◽  
Sisko Fluid ◽  
Dissipative Heat ◽  
Flow Through

scholarly journals Significance of Nonsimilar Numerical Simulations in Forced Convection from Stretching Cylinder Subjected to External Magnetized Flow of Sisko Fluid

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jifeng Cui ◽  
Umer Farooq ◽  
Ahmed Jan ◽  
Murtada K. Elbashir ◽  
Waseem Asghar Khan ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Frictional Heating ◽  
Fluid Velocity ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Axial Direction ◽  
High Viscosity ◽  
Heat Equations ◽  
Dimensionless Numbers ◽  
Sisko Fluid

The practice of flowing effort is participating in various industries especially in nutrition productions all around the world. These fluids practices are utilized extensively in nutrition handling productions by making use of sticky liquids to produce valuable food manufactured goods in bulk. Nevertheless, such productions ought to guarantee that involved equipment such as pipelines are maintained clean as well as are cleared out for the efficient movement of fluids. The nonsimilar characteristics of involuntary convection from circular cylinder stretching in the axial direction subjected to an external flow of Sisko fluid characterized by the freely growing boundary layers (BL) are presented in this research. A circular cylinder is submerged in a stationary fluid. The axial stretching of the cylinder causes external fluid flow. The magnetic force of strength ″ B 0 ″ is enforced in the transverse direction. Because of the fluid's high viscosity, frictional heating due to viscous dissipation is quite significant. The flow is three dimensional but with no circumferential variations. The governing equations for axisymmetric flow that include the mass balance, x -momentum, and heat equation are modeled through conservation laws. The dimensionless system is developed by employing appropriate nonsimilar transformations. The numerical analyses are presented by adapting local nonsimilarity via finite-difference (FDM)-based MATLAB algorithm bvp4c. The characteristics of dimensionless numbers are determined by graphs that are plotted on momentum and heat equations. The nonsimilar simulations have been compared with the existing local similar solutions. Fluid velocity is increased as the material and curvature parameters are increased, resulting in improved heat transfer. The deviation in skin friction and local Nusselt number against the various dimensionless numbers is also analyzed.

Numerical analysis of time-dependent stagnation point flow of Oldroyd-B fluid subject to modified Fourier’s law

2021 ◽  
pp. 2150187
Author(s):  
Foukeea Qasim ◽  
Tian-Chuan Sun ◽  
S. Z. Abbas ◽  
W. A. Khan ◽  
M. Y. Malik
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equation ◽  
Thermal Relaxation ◽  
Stagnation Point Flow ◽  
Time Dependent ◽  
Parameter Values

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.

Analytical Study of the Existence of a Hopf Bifurcation in the Tumor Cell Growth Model with Time Delay

2021 ◽  
Vol 3 (1) ◽  
pp. 20-28
Author(s):  
A. Yusnaeni ◽  
Kasbawati Kasbawati ◽  
Toaha Syamsuddin
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Immune System ◽  
Hopf Bifurcation ◽  
Delay Differential Equation ◽  
Immune Cells ◽  
Steady State Solution ◽  
State Solution ◽  
Activation Process ◽  
Delay Differential

AbstractIn this paper, we study a mathematical model of an immune response system consisting of a number of immune cells that work together to protect the human body from invading tumor cells. The delay differential equation is used to model the immune system caused by a natural delay in the activation process of immune cells. Analytical studies are focused on finding conditions in which the system undergoes changes in stability near a tumor-free steady-state solution. We found that the existence of a tumor-free steady-state solution was warranted when the number of activated effector cells was sufficiently high. By considering the lag of stimulation of helper cell production as the bifurcation parameter, a critical lag is obtained that determines the threshold of the stability change of the tumor-free steady state. It is also leading the system undergoes a Hopf bifurcation to periodic solutions at the tumor-free steady-state solution.Keywords: tumor–immune system; delay differential equation; transcendental function; Hopf bifurcation. AbstrakDalam makalah ini, dikaji model matematika dari sistem respon imun yang terdiri dari sejumlah sel imun yang bekerja sama untuk melindungi tubuh manusia dari invasi sel tumor. Persamaan diferensial tunda digunakan untuk memodelkan sistem kekebalan yang disebabkan oleh keterlambatan alami dalam proses aktivasi sel-sel imun. Studi analitik difokuskan untuk menemukan kondisi di mana sistem mengalami perubahan stabilitas di sekitar solusi kesetimbangan bebas tumor. Diperoleh bahwa solusi kesetimbangan bebas tumor dijamin ada ketika jumlah sel efektor yang diaktifkan cukup tinggi. Dengan mempertimbangkan tundaan stimulasi produksi sel helper sebagai parameter bifurkasi, didapatkan lag kritis yang menentukan ambang batas perubahan stabilitas dari solusi kesetimbangan bebas tumor. Parameter tersebut juga mengakibatkan sistem mengalami percabangan Hopf untuk solusi periodik pada solusi kesetimbangan bebas tumor.Kata kunci: sistem tumor–imun; persamaan differensial tundaan; fungsi transedental; bifurkasi Hopf.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

On the Dynamics and Stability of a Viscoelastic Pipe Conveying a Non-Newtonian Fluid

2009 ◽  
Author(s):  
Vincent O. S. Olunloyo ◽  
Charles A. Osheku ◽  
Sidikat I. Kuye
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Newtonian Fluid ◽  
Elevated Temperatures ◽  
Fluid Velocity ◽  
Flow Induced Vibration ◽  
Partial Differential ◽  
Flow Parameters ◽  
Sea Bed ◽  
Internal Fluid

Flow induced vibration of pipeline and riser systems are strongly dependent on internal fluid flow parameters as well as the mechanical properties of the conveyance vessel. The effect of variability of flow parameters especially at elevated temperatures can lead to instability, buckling and bursting of these systems. In this paper, the effect of high temperature fluid transmission on the vibration and stability of an offshore viscoelastic pipeline conveying a non-Newtonian fluid is investigated analytically. By idealising the viscoelastic pipeline resting on the sea bed as a viscoelastic beam that is resting on an elastic continuum, a non-linear boundary value partial differential equation governing the fluid-structure-soil interaction mechanics is formulated. In particular, formal linearization of the governing partial differential equation, under slight perturbation of the internal fluid velocity and other flow variables revealed their impact, on the natural frequency and stability of the system which can then be computed for design analysis and applications.

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