Numerical simulation for bioconvectional flow of burger nanofluid with effects of activation energy and exponential heat source/sink over an inclined wall under the swimming microorganisms

AbstractNanofluids has broad applications such as emulsions, nuclear fuel slurries, molten plastics, extrusion of polymeric fluids, food stuffs, personal care products, shampoos, pharmaceutical industries, soaps, condensed milk, molten plastics. A nanofluid is a combination of a normal liquid component and tiny-solid particles, in which the nanomaterials are immersed in the liquid. The dispersion of solid particles into yet another host fluid will extremely increase the heat capacity of the nanoliquid, and an increase of heat efficiency can play a significant role in boosting the rate of heat transfer of the host liquid. The current article discloses the impact of Arrhenius activation energy in the bioconvective flow of Burger nanofluid by an inclined wall. The heat transfer mechanism of Burger nanofluid is analyzed through the nonlinear thermal radiation effect. The Brownian dispersion and thermophoresis diffusions effects are also scrutinized. A system of partial differential equations are converted into ordinary differential equation ODEs by using similarity transformation. The multi order ordinary differential equations are reduced to first order differential equations by applying well known shooting algorithm then numerical results of ordinary equations are computed with the help of bvp4c built-in function Matlab. Trends with significant parameters via the flow of fluid, thermal, and solutal fields of species and the area of microorganisms are controlled. The numerical results for the current analysis are seen in the tables. The temperature distribution increases by rising the temperature ratio parameter while diminishes for a higher magnitude of Prandtl number. Furthermore temperature-dependent heat source parameter increases the temperature of fluid. Concentration of nanoparticles is an decreasing function of Lewis number. The microorganisms profile decay by an augmentation in the approximation of both parameter Peclet number and bioconvection Lewis number.

Download Full-text

Numerical Simulation For Bioconvectional Flow of Burger Nanofluid With Effects of Activation Energy and Exponential Heat Source/Sink Over an Inclined Wall Under The Swimming Microorganisms

10.21203/rs.3.rs-146009/v1 ◽

2021 ◽

Author(s):

Hassan Waqas ◽

Umar Farooq ◽

Aqsa Ibrahim ◽

Zahir Shah ◽

Poom Kumam

Keyword(s):

Heat Transfer ◽

Differential Equation ◽

Activation Energy ◽

Numerical Results ◽

Solid Particles ◽

Nonlinear Thermal Radiation ◽

Liquid Component ◽

Source Sink ◽

Bioconvective Flow ◽

The Impact

Abstract A nanofluid is a combination of a normal liquid component and tiny-solid particles, in which the nanomaterials are immersed in the liquid. The dispersion of solid particles into yet another host fluid will extremely increase the heat capacity of the nanoliquids, and an increase of heat efficiency can play a significant role in boosting the rate of heat transfer of the host liquid. The current article discloses the impact of Arrhenius activation energy in the bioconvective flow of Burger nanofluid by an inclined wall. The heat transfer mechanism of Burger nanofluid is analyzed through the nonlinear thermal radiation effect. The Brownian dispersion and thermophoresis diffusions effects are also scrutinized. Established partial differential equation expressions are updated by a similarity transformation of the ordinary differential equation ODE. The numerical results are given by the built-in bvp4c function Matlab also applies the Labotto-IIIa formula for the shooting scheme. Trends with significant parameters via the flow of fluid, thermal, and solutal fields of species and the area of microorganisms are controlled. The numerical results for the current analysis are seen in the tables.

Download Full-text

Unsteady Convective MHD Flow and Heat Transfer of a Viscous Nanofluid across a Porous Stretching/Shrinking Surface: Existence of Multiple Solutions

Crystals ◽

10.3390/cryst11111359 ◽

2021 ◽

Vol 11 (11) ◽

pp. 1359

Author(s):

Nawal A. Alshehri ◽

Awatef Abidi ◽

Muhammad Riaz Khan ◽

Yanala Dharmendar Reddy ◽

Saim Rasheed ◽

...

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Heat Source ◽

Heat Transfer Rate ◽

Transfer Rate ◽

Mhd Flow ◽

Velocity Slip ◽

Solid Particles ◽

Friction Drag ◽

Shrinking Surface

The suspension of tiny solid particles inside the energy transport liquids could enhance their thermal conductivity as well as provide an efficient and inventive approach to significantly improve their properties of heat transport. Therefore, our aim is to explore the radiative two-dimensional unsteady flow of a viscous nanofluid about an aligned magnetic field that includes the joint effect of suction, velocity slip, and heat source across a porous convective stretching/shrinking surface. Initially, using non-dimensional variables, the nonlinear governing partial differential equations (PDEs) were transformed into ordinary differential equations (ODEs) which were subsequently solved with the help of bvp4c built-in package in MATLAB. The results declare that escalating the values of the unsteadiness parameter escalates the friction drag whereas it reduces with the escalation of the slip parameter. Furthermore, the heat transfer rate escalates with the escalation of radiation and concentration parameter, and the escalation of the heat source parameter causes to reduce the heat transfer rate. Finally, it is found that the rate of heat transfer and friction drag continuously improve and decline against the rising rates of stretching, respectively.

Download Full-text

Approximate Analytical Analysis of Unsteady MHD Mixed Flow of Non-Newtonian Hybrid Nanofluid over a Stretching Surface

Fluids ◽

10.3390/fluids6040138 ◽

2021 ◽

Vol 6 (4) ◽

pp. 138

Author(s):

Ali Rehman ◽

Zabidin Salleh

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Base Fluid ◽

Research Work ◽

Hybrid Nanofluid ◽

Stretching Surface ◽

Optimal Homotopy Analysis Method ◽

Analytical Analysis ◽

Transfer Ratio ◽

The Impact

This paper analyses the two-dimensional unsteady and incompressible flow of a non-Newtonian hybrid nanofluid over a stretching surface. The nanofluid formulated in the present study is TiO2 + Ag + blood, and TiO2 + blood, where in this combination TiO2 + blood is the base fluid and TiO2 + Ag + blood represents the hybrid nanofluid. The aim of the present research work is to improve the heat transfer ratio because the heat transfer ratio of the hybrid nanofluid is higher than that of the base fluid. The novelty of the recent work is the approximate analytical analysis of the magnetohydrodynamics mixed non-Newtonian hybrid nanofluid over a stretching surface. This type of combination, where TiO2+blood is the base fluid and TiO2 + Ag + blood is the hybrid nanofluid, is studied for the first time in the literature. The fundamental partial differential equations are transformed to a set of nonlinear ordinary differential equations with the guide of some appropriate similarity transformations. The analytical approximate method, namely the optimal homotopy analysis method (OHAM), is used for the approximate analytical solution. The convergence of the OHAM for particular problems is also discussed. The impact of the magnetic parameter, dynamic viscosity parameter, stretching surface parameter and Prandtl number is interpreted through graphs. The skin friction coefficient and Nusselt number are explained in table form. The present work is found to be in very good agreement with those published earlier.

Download Full-text

Parametric analysis of the heat transfer behavior of the nano-particle ionic-liquid flow between concentric cylinders

Advances in Mechanical Engineering ◽

10.1177/16878140211024009 ◽

2021 ◽

Vol 13 (6) ◽

pp. 168781402110240

Author(s):

Rehan Ali Shah ◽

Hidayat Ullah ◽

Muhammad Sohail Khan ◽

Aamir Khan

Keyword(s):

Heat Transfer ◽

Ionic Liquid ◽

Partial Differential Equations ◽

Differential Equations ◽

Heat Source ◽

Ordinary Differential Equations ◽

Heat Transfer Rate ◽

Transfer Rate ◽

Volume Fraction ◽

Concentric Cylinders

This paper investigates the enhanced viscous behavior and heat transfer phenomenon of an unsteady two di-mensional, incompressible ionic-nano-liquid squeezing flow between two infinite parallel concentric cylinders. To analyze heat transfer ability, three different type nanoparticles such as Copper, Aluminum [Formula: see text], and Titanium oxide [Formula: see text] of volume fraction ranging from 0.1 to 0.7 nm, are added to the ionic liquid in turns. The Brinkman model of viscosity and Maxwell-Garnets model of thermal conductivity for nano particles are adopted. Further, Heat source [Formula: see text], is applied between the concentric cylinders. The physical phenomenon is transformed into a system of partial differential equations by modified Navier-Stokes equation, Poisson equation, Nernst-Plank equation, and energy equation. The system of nonlinear partial differential equations, is converted to a system of coupled ordinary differential equations by opting suitable transformations. Solution of the system of coupled ordinary differential equations is carried out by parametric continuation (PC) and BVP4c matlab based numerical methods. Effects of squeeze number ( S), volume fraction [Formula: see text], Prandtle number (Pr), Schmidt number [Formula: see text], and heat source [Formula: see text] on nano-ionicliquid flow, ions concentration distribution, heat transfer rate and other physical quantities of interest are tabulated, graphed, and discussed. It is found that [Formula: see text] and Cu as nanosolid, show almost the same enhancement in heat transfer rate for Pr = 0.2, 0.4, 0.6.

Download Full-text

Nonlinear mixed convective Williamson nanofluid flow with the suspension of gyrotactic microorganisms

International Journal of Modern Physics B ◽

10.1142/s0217979221501459 ◽

2021 ◽

pp. 2150145

Author(s):

Shuang-Shuang Zhou ◽

M. Ijaz Khan ◽

Sumaira Qayyum ◽

B. C. Prasannakumara ◽

R. Naveen Kumar ◽

...

Keyword(s):

Heat Source ◽

Lewis Number ◽

Solution Procedure ◽

Energy Concentration ◽

Gyrotactic Microorganisms ◽

Dimensionless Parameters ◽

Flow Equations ◽

Fluid Parameter ◽

Source Sink ◽

The Impact

This investigation aims to present the thermally developed bioconvection flow of Williamson nanoliquid over an inclined stretching cylinder in presence of linear mixed convection and nonuniform heat source/sink. The activation energy and suspension of gyrotactic microorganisms are accounted with applications of bioconvection phenomenon. Appropriate nondimensional variables are opted to attain the dimensionless form of flow equations. The resulting momentum, energy, concentration and motile density equations are abridged to highly coupled and nonlinear in nature. The numerical treatment is followed for the solution procedure by employing the shooting method. The influence of some relevant dimensionless parameters is discoursed graphically along with physical justifications. Moreover, the impact of several dimensionless parameters on skin friction and Nusselt number is obtained and listed in tables. It is observed that the velocity of fluid shows a decreasing variation for Williamson fluid parameter. The change in unsteadiness parameter and heat source parameter enhanced the nanofluid temperature. The motile microorganisms profile declines with bioconvection constant and bio-convection Lewis number.

Download Full-text

MHD and nonlinear thermal radiation effects on hybrid nanofluid past a wedge with heat source and entropy generation

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-10-2020-0636 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Fazle Mabood ◽

Anum Shafiq ◽

Waqar Ahmed Khan ◽

Irfan Anjum Badruddin

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Heat Source ◽

Thermal Radiation ◽

Entropy Generation ◽

Entropy Generation Rate ◽

Design Parameters ◽

Hybrid Nanofluid ◽

Nonlinear Thermal Radiation ◽

Content Type

Purpose This study aims to investigate the irreversibility associated with the Fe3O4–Co/kerosene hybrid-nanofluid past a wedge with nonlinear radiation and heat source. Design/methodology/approach This study reports the numerical analysis of the hybrid nanofluid model under the implications of the heat source and magnetic field over a static and moving wedge with slips. The second law of thermodynamics is applied with nonlinear thermal radiation. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved through the Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerges from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios. Findings The significant outcomes of the current investigation are that the velocity field uplifts for higher velocity slip and magnetic strength. Further, the heat transfer rate is reduced with the incremental values of the Eckert number, while it uplifts with thermal slip and radiation parameters. An increase in Brinkmann’s number uplifts the entropy generation rate, while that peters out the Bejan number. The results of this study are of importance involving in the assessment of the effect of some important design parameters on heat transfer and, consequently, on the optimization of industrial processes. Originality/value This study is original work that reports the hybrid nanofluid model of Fe3O4–Co/kerosene.

Download Full-text

Maxwell Fluids Unsteady Mixed Flow and Radiation Heat Transfer Over a Stretching Permeable Plate With Boundary Slip and Nonuniform Heat Source/Sink

Journal of Heat Transfer ◽

10.1115/1.4007891 ◽

2013 ◽

Vol 135 (3) ◽

Cited By ~ 15

Author(s):

Liancun Zheng ◽

Ning Liu ◽

Xinxin Zhang

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Heat Source ◽

Mixed Boundary ◽

Radiation Heat Transfer ◽

Radiation Heat ◽

Boundary Slip ◽

Analytical Approximations ◽

Maxwell Fluids ◽

Source Sink

This paper presents an analysis for the unsteady mixed boundary-layer flow and radiation heat transfer of generalized Maxwell fluids toward an unsteady stretching permeable surface in presence of boundary slip and nonuniform heat source/sink. The governing partial differential equations are converted into nonlinear ordinary differential equations and analytical approximations of solutions are derived by homotopy analysis method (HAM). The effects of the unsteadiness parameter, nonuniform heat source/sink parameter, suction/injection parameter, thermal radiation parameter and slip parameter on the fluid flow, and heat transfer characteristics are shown graphically and analyzed.

Download Full-text

Implicit Finite Difference Simulation of Prandtl-Eyring Nanofluid over a Flat Plate with Variable Thermal Conductivity: A Tiwari and Das Model

Mathematics ◽

10.3390/math9243153 ◽

2021 ◽

Vol 9 (24) ◽

pp. 3153

Author(s):

Nidal H. Abu-Hamdeh ◽

Abdulmalik A. Aljinaidi ◽

Mohamed A. Eltaher ◽

Khalid H. Almitani ◽

Khaled A. Alnefaie ◽

...

Keyword(s):

Heat Transfer ◽

Thermal Conductivity ◽

Finite Difference ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Variable Thermal Conductivity ◽

Solid Particles ◽

Engine Oil ◽

Working Fluid ◽

Implicit Finite Difference

The current article presents the entropy formation and heat transfer of the steady Prandtl-Eyring nanofluids (P-ENF). Heat transfer and flow of P-ENF are analyzed when nanofluid is passed to the hot and slippery surface. The study also investigates the effects of radiative heat flux, variable thermal conductivity, the material’s porosity, and the morphologies of nano-solid particles. Flow equations are defined utilizing partial differential equations (PDEs). Necessary transformations are employed to convert the formulae into ordinary differential equations. The implicit finite difference method (I-FDM) is used to find approximate solutions to ordinary differential equations. Two types of nano-solid particles, aluminium oxide (Al2O3) and copper (Cu), are examined using engine oil (EO) as working fluid. Graphical plots are used to depict the crucial outcomes regarding drag force, entropy measurement, temperature, Nusselt number, and flow. According to the study, there is a solid and aggressive increase in the heat transfer rate of P-ENF Cu-EO than Al2O3-EO. An increment in the size of nanoparticles resulted in enhancing the entropy of the model. The Prandtl-Eyring parameter and modified radiative flow show the same impact on the radiative field.

Download Full-text

Effect of Heat Source Position in Fluid Flow, Heat Transfer and Entropy Generation in a Naturally Ventilated Room

Mathematics ◽

10.3390/math10020178 ◽

2022 ◽

Vol 10 (2) ◽

pp. 178

Author(s):

Mohammed Alghaseb ◽

Walid Hassen ◽

Abdelhakim Mesloub ◽

Lioua Kolsi

Keyword(s):

Heat Transfer ◽

Rayleigh Number ◽

Heat Source ◽

Numerical Study ◽

Temperature Fields ◽

Left Wall ◽

Heating Efficiency ◽

Discrete Heat Source ◽

Volume Method ◽

The Impact

In this study, a 3D numerical study of free ventilated room equipped with a discrete heat source was performed using the Finite Volume Method (FVM). To ensure good ventilation, two parallel openings were created in the room. A suction opening was located at the bottom of the left wall and another opening was located at the top of the opposite wall; the heat source was placed at various positions in order to compare the heating efficiency. The effects of Rayleigh number (103 ≤ Ra ≤ 106) for six heater positions was studied. The results focus on the impact of these parameters on the particle trajectories, temperature fields and on the heat transfer inside the room. It was found that the position of the heater has a dramatic effect on the behavior and topography of the flow in the room. When the heat source was placed on the wall with the suction opening, two antagonistic behaviors were recorded: an improvement in heat transfer of about 31.6%, compared to the other positions, and a low Rayleigh number against 22% attenuation for high Ra values was noted.

Download Full-text

Implication of Bio-convective Marangoni flow of non-Newtonian material towards an infinite disk subject to exponential space-based heat source

International Journal of Modern Physics B ◽

10.1142/s0217979221502520 ◽

2021 ◽

pp. 2150252

Author(s):

Hassan Waqas ◽

Sumeira Yasmin ◽

Sami Ullah Khan ◽

Sumaira Qayyum ◽

M. Ijaz Khan ◽

...

Keyword(s):

Activation Energy ◽

Heat Source ◽

Energy Parameter ◽

Lewis Number ◽

Polymer Processing ◽

Source Parameter ◽

Nonlinear Thermal Radiation ◽

Marangoni Flow ◽

Nonlinear Odes ◽

Exponential Space

In recent years, the research for enhanced thermal transportation is centered around the utilization of nanostructures to avail the prospective benefits in areas of biomedical, metallurgy, polymer processing, mechanical and electrical engineering applications, food processing, ventilation, heat storage devices, nuclear systems cooling, electronic devices, solar preoccupation, magnetic sticking, bioengineering applications, etc. The thermal aspects of nanoliquids and associated dynamics properties are still necessary to be explored. In this thermal contribution, the flow of Casson nanofluid configured by an infinite disk is analyzed. The significance of Marangoni flow with activation energy, thermal and exponential space-dependent heat source, nonlinear thermal radiation and Joule heating impacts is also incorporated. Similarly, variables are affianced to recast the governing flow expressions into highly coupled nonlinear ODEs. The numerical simulation for the prevailing model is elucidated by applying the bvp4cbuilt-in function of computational commercial software MATLAB. Consequences of sundry parameters, namely, magnetic parameter, Prandtl number, radiation parameter, exponential space-dependent heat source parameter, thermal-dependent heat source parameter, Eckert number, Dufour parameter, Soret number, Schmidt number, Marangoni number and Marangoni ratio parameter, mixed convection parameter, buoyancy ratio parameter, bioconvection Rayleigh number, activation energy parameter, thermophoresis parameter, Brownian motion parameter, bioconvection Lewis number, Peclet number microorganisms difference variable versus involved flow profiles like velocity, temperature, concentration of nanoparticles and microorganism field are obtained and displayed through graphs and tabular data.

Download Full-text