Numerical Simulations of Bio-Convection in the Stream-Wise and Cross-Flow Directions Comprising Nanofluid Conveying Motile Microorganism: Analysis of Multiple Solutions

2021 ◽  
pp. 2150058
Author(s):  
Umair Khan ◽  
A. zaib ◽  
A. Ishak ◽  
S. Abu Bakar ◽  
Taseer Muhammad
Keyword(s):  
Differential Equations ◽  
Radiation Effects ◽  
Numerical Solutions ◽  
Cross Flow ◽  
Nanofluid Flow ◽  
Nusselt Numbers ◽  
Opposite Behavior ◽  
Flow Directions ◽  
New Variables ◽  
The Mathematical Model

This work tackles the phenomenon of motile microorganisms and nanoliquid flow in the esteem of cross-flow (CF) and stream-wise (SW) direction. The analysis exposed to viscous dissipation, Brownian motion, thermal radiation, magnetic function, and thermophoresis impacts is encountered. The mathematical model consists of the partial differential equations (PDEs) switched into nonlinear ordinary differential equations (ODEs) through proper transformations of new variables. The multiple outcomes of the flow problem are achieved through the Lobatto IIIA formula. The features of controlling constraints are sketched for the motile organism, temperature, velocities (CF and SW), and concentration fields. Also, the Sherwood and the Nusselt numbers along with motile density and friction factor are sketched. One imperative numerical outcome of this research is the existence of dual numerical solutions for the nanofluid flow. The upshots indicate that the profiles of microorganisms decelerate due to bio-convection Schmidt and Péclet numbers. The magnetic function decelerates the velocity in the directions of SW and CF in the branch of the first solution and upsurges in the branch of the second solution. The concentration profile uplifts due to [Formula: see text] in both solutions while the opposite behavior is observed for different values of [Formula: see text] in both solutions. The temperature uplifts due to magnetic and radiation effects in both solutions.

scholarly journals Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

2019 ◽  
Vol 9 (10) ◽  
pp. 2124 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Ezad Hafidz Hafidzuddin ◽  
Nadihah Wahi
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Transfer Rate ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Thermal Relaxation ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Local Skin ◽  
Flow Past

The present study emphasizes the combined effects of double stratification and buoyancy forces on nanofluid flow past a shrinking/stretching surface. A permeable sheet is used to give way for possible wall fluid suction while the magnetic field is imposed normal to the sheet. The governing boundary layer with non-Fourier energy equations (partial differential equations (PDEs)) are converted into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. The approximate relative error between present results (using the boundary value problem with fourth order accuracy (bvp4c) function) and previous studies in few limiting cases is sufficiently small (0% to 0.3694%). Numerical solutions are graphically displayed for several physical parameters namely suction, magnetic, thermal relaxation, thermal and solutal stratifications on the velocity, temperature and nanoparticles volume fraction profiles. The non-Fourier energy equation gives a different estimation of heat and mass transfer rates as compared to the classical energy equation. The heat transfer rate approximately elevates 5.83% to 12.13% when the thermal relaxation parameter is added for both shrinking and stretching cases. Adversely, the mass transfer rate declines within the range of 1.02% to 2.42%. It is also evident in the present work that the augmentation of suitable wall mass suction will generate dual solutions. The existence of two solutions (first and second) are noticed in all the profiles as well as the local skin friction, Nusselt number and Sherwood number graphs within the considerable range of parameters. The implementation of stability analysis asserts that the first solution is the real solution.

scholarly journals Numerical Solutions of Hybrid Nanofluids Flow Via Free Convection Over a Solid Sphere

2021 ◽  
Vol 83 (1) ◽  
pp. 34-45
Author(s):  
Mohammed Zaki Swalmeh
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Free Convection ◽  
Numerical Solutions ◽  
Solid Sphere ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Partial Differential ◽  
Hybrid Nanofluids

The purpose of the existing study is to examine how heat transfer enables consolidated by variations in the basic advantages of fluids in the existence of free convection with the assistance of suspended hybrid nanofluids. Iron-graphene oxide suspended in water as a hybrid nanofluid flow on a solid sphere is also considered in this work. The partial differential equations are gotten, for this problem, by transforming the mathematical governing equations using similarity equations (stream function). These partial differential equations are solved numerically by Keller-Box method and programmed by MATLAB program. the acquired numerical results are in excellent agreement with the preceding literature results. Graphical results of the influence of the hybrid nanofluid parameters on some physical quantities regarded to examine the behavior of hybrid nanofluid flow were attained, and they proved that hybrid nanofluid flow represents a more essential role in the operation of heat transfer than a regular nanofluid flow.

scholarly journals Exploration of Aluminum and Titanium Alloys in the Stream-Wise and Secondary Flow Directions Comprising the Significant Impacts of Magnetohydrodynamic and Hybrid Nanofluid

Crystals ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 679 ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
Umair Khan ◽  
Aurang Zaib ◽  
Ilyas Khan ◽  
Dumitru Baleanu
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Volume Fraction ◽  
Cross Flow ◽  
Hybrid Nanofluid ◽  
Nonlinear Odes ◽  
Soret Number ◽  
Flow Directions ◽  
Titanium Alloy Ti6al4v ◽  
Dufour Number

This exploration examines the nonlinear effect of radiation on magnet flow consisting of hybrid alloy nanoparticles in the way of stream-wise and cross flow. Many experimental, as well as theoretical explorations, demonstrated that the thermal conductivity of the regular liquid increases by up to 15 to 40% when nanomaterials are mixed with the regular liquid. This change of the thermal conductivity of the nanoliquid depends on the various characteristics of the mixed nanomaterials like the size of the nanoparticles, the agglomeration of the particles, the volume fraction, etc. Researchers have used numerous nanoparticles. However, we selected water-based aluminum alloy (AA7075) and titanium alloy (Ti6Al4V) hybrid nanomaterials. This condition was mathematically modeled by capturing the Soret and Dufour impacts. The similarity method was exercised to change the partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). Such nonlinear ODEs were worked out numerically via the bvp4c solver. The influences of varying the parameters on the concentration, temperature, and velocity area and the accompanying engineering quantities such as friction factor, mass, and heat transport rate were obtained and discussed using graphs. The velocity declines owing to nanoparticle volume fraction in the stream-wise and cross flow directions in the first result and augment in the second result, while the temperature and concentration upsurge in the first and second results. In addition, the Nusselt number augments due to the Soret number and declines due to the Dufour number in both results, whereas the Sherwood number uplifts due to the Dufour number and shrinks due to the Soret number in both results.

Radiative Flow with Variable Thermal Conductivity in Porous Medium

2012 ◽  
Vol 67 (3-4) ◽  
pp. 153-159 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Muhammad Qasim ◽  
A. Alsaedi
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Differential Equations ◽  
Radiation Effect ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
Analysis Method ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Homotopy Analysis

This article considers the radiation effect on the flow of a Jeffery fluid with variable thermal conductivity. Similarity transformations are employed to convert the partial differential equations into ordinary differential equations. The resulting equations have been computed by the homotopy analysis method (HAM). The numerical values of the local Nusselt numbers are also computed. The comparison with the numerical solutions of qƟ'(0) is presented. The obtained results are displayed and physical aspects have been examined in detail

MHD Hybrid Cu-Al2O3/ Water Nanofluid Flow with Thermal Radiation and Partial Slip Past a Permeable Stretching Surface: Analytical Solution

2020 ◽  
Vol 64 ◽  
pp. 75-91 ◽  
Author(s):  
Nur Syahirah Wahid ◽  
Norihan Md Arifin ◽  
Mustafa Turkyilmazoglu ◽  
Mohd Ezad Hafidz Hafidzuddin ◽  
Nor Aliza Abd Rahmin
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Temperature Profile ◽  
Radiation Effects ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Partial Slip ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Exact Analytical Method

The influence of velocity slip and thermal radiation effects on the magnetohydrodynamic hybrid Cu-Al2O3/water nanofluid flow over a permeable stretching sheet is reported in this paper. The similarity transformation is adopted to reduce the partial differential equations to the ordinary differential equations. Exact analytical method is implemented to solve the problem. Maple program is used to facilitate the calculation process. The new additional effects which are the velocity slip and thermal radiation effects are considered towards the model to scrutinize the impacts. The effects of various parameters towards the velocity and temperature profiles are demonstrated through graphs, meanwhile the skin friction coefficient and the local Nusselt number are exhibited through the tabulation of data. The existence of velocity slip reduced the velocity profile but enhanced the temperature profile. The thermal radiation effect has increased the temperature profile. The heat transfer rate are enhanced for the case of hybrid nanofluid compared to the mono nanofluid.

scholarly journals Thermal Radiation Effects on Unsteady Stagnation Point Nanofluid Flow in View of Convective Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Haroon Ur Rasheed ◽  
Saeed Islam ◽  
Zeeshan Khan ◽  
Sayer O. Alharbi ◽  
Waqar A Khan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Mass Conservation ◽  
Present Communication ◽  
Nanofluid Flow ◽  
Convective Boundary ◽  
Nonlinear Odes ◽  
Layer Flow ◽  
Mathematica Software

The present communication particularizes nonlinear convective non-Newtonian stagnation point flow and heat transference effects in stretchable flow of nanofluid. Magnetohydromagnetic steady viscous flow of nanofluid is examined. Heat transfer attributes of nanofluids are addressed via a numerical algorithm. Conductivity and diffusivity characteristics of fluid are depending on temperature and concentration and furthermore, on mass conservation, momentum, energy, and concentration yield partial differential equations (PDEs). The boundary layer flow concept pioneered by Prandtl has been employed to simplify the nonlinear constitutive flow laws which are then changed to ordinary differential equations. A built-in bvp4c algorithm in Mathematica software yields convergent outcomes of nonlinear (ODEs) systems. A comprehensive analysis has been made elucidating the physical significance of various governing parameters effects presented graphically. Additionally, the flow nature was confirmed versus streamlines.

Some analytical and numerical solutions for the safe turn manoeuvres of agricultural aircraft – an overview

2007 ◽  
Vol 111 (1123) ◽  
pp. 593-599 ◽  
Author(s):  
B. Rasuo
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Numerical Results ◽  
System Of Differential Equations ◽  
Bank Angle ◽  
Tangential Load ◽  
Load Factors ◽  
The Mathematical Model

Abstract In this paper, a theoretical study of the turn manoeuvre of an agricultural aircraft is presented. The manoeuvre with changeable altitude is analyzed, together with the, effect of the load factors on the turn manoeuvre characteristics during the field-treating flights. The mathematical model used describes the procedure for the correct climb and descent turn manoeuvre. For a typical agricultural aircraft, the numerical results and limitations of the climb, horizontal and descending turn manoeuvre are given. The problem of turning flight with changeable altitude is described by the system of differential equations which describe the influence of the normal and tangential load factors on velocity, the path angle in the vertical plane and the rate of turn, as a function of the bank angle during turning flight. The system of differential equations of motion was solved on a personal computer with the Runge-Kutta-Merson numerical method. Some analytical and numerical results of this calculation are presented in this paper.

Thermal Radiation Effects on the Mixed Convection Stagnation-Point Flow in a Jeffery Fluid

2011 ◽  
Vol 66 (10-11) ◽  
pp. 606-614 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Muhammad Qasim ◽  
Saleem Obaidat
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Deborah Number ◽  
Stagnation Point Flow ◽  
Suction Parameter

This study describes the mixed convection stagnation point flow and heat transfer of a Jeffery fluid towards a stretching surface. Mathematical formulation is given in the presence of thermal radiation. The Rosseland approximation is used to describe the radiative heat flux. Similarity transformations are employed to reduce the partial differential equations into the ordinary differential equations which are then solved by a homotopy analysis method (HAM). A comparative study is made with the known numerical solutions in a limiting sense and an excellent agreement is noted. The characteristics of involved parameters on the dimensionless velocity and temperature are also examined. It is noticed that the velocity increases with an increase in Deborah number. Further, the temperature is a decreasing function of mixed convection parameter. We further found that for fixed values of other parameters, the local Nusselt number increases by increasing suction parameter and Deborah number.

A Numerical Study of Forced Convection Casson Nanofluid Flow Past a Wedge With Melting Process

2020 ◽  
Author(s):  
Mehari Fentahun Endalew ◽  
Subharthi Sarkar
Keyword(s):  
Differential Equations ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Wedge Angle ◽  
Nanofluid Flow ◽  
Local Skin ◽  
Casson Nanofluid ◽  
Flow Past ◽  
Highly Nonlinear

Abstract A numerical investigation is carried out to analyze steady two dimensional Casson nanofluid flow past a wedge with melting. The partial differential equations that govern the nanofluid flow are transformed into highly nonlinear coupled ordinary differential equations by employing similarity transformation. Thereafter, numerical solutions of these governing equations are obtained by MATLAB routine bvp4c. A special case of the present study is compared with an existing solution in literature and is found to be in good agreement. The effects of pertinent physical entities on the nanofluid velocity, nanofluid temperature, and nanoparticle concentration are represented graphically, while skin friction, Nusselt number, and Sherwood number are recorded in tabular form. We observed that, with an increase of wedge angle parameter, nanofluid velocity and local skin friction increase. However, when the melting parameter increases, nanofluid temperature and heat transfer rate decrease. This study would be useful in unfurling novel applications of Casson nanofluids in cooling devices and heat sinks.

scholarly journals Cu-Al2O3/Water Hybrid Nanofluid Stagnation Point Flow Past MHD Stretching/Shrinking Sheet in Presence of Homogeneous-Heterogeneous and Convective Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1237
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Heterogeneous Reactions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Convective Boundary

The intent of this research was to present numerical solutions to homogeneous–heterogeneous reactions of the magnetohydrodynamic (MHD) stagnation point flow of a Cu-Al2O3/water hybrid nanofluid induced by a stretching or shrinking sheet with a convective boundary condition. A proper similarity variable was applied to the system of partial differential equations (PDEs) and converted into a system of ordinary (similarity) differential equations (ODEs). These equations were solved using Matlab’s in-built function (bvp4c) for various values of the governing parameters numerically. The present investigation considered the effects of homogeneous–heterogeneous reactions and magnetic field in the hybrid nanofluid flow. It was observed that dual solutions were visible for the shrinking sheet, and an analysis of stability was done to determine the physically realizable in the practice of these solutions. It was also concluded that hybrid nanofluid acts as a cooler for some increasing parameters. The magnetohydrodynamic parameter delayed the boundary layer separation; meanwhile, the nanoparticle volume fraction quickened the separation of the boundary layer that occurred. In addition, the first solution of hybrid nanofluid was found to be stable; meanwhile, the second solution was not stable. This study is therefore valuable for engineers and scientists to get acquainted with the properties of hybrid nanofluid flow, its behavior and the way to predict it.

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