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

Mathematics ◽  
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.

scholarly journals Thermal Characterization of Coolant Maxwell Type Nanofluid Flowing in Parabolic Trough Solar Collector (PTSC) Used Inside Solar Powered Ship Application

Coatings ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1552
Author(s):  
Wasim Jamshed ◽  
Ceylin Şirin ◽  
Fatih Selimefendigil ◽  
MD. Shamshuddin ◽  
Yasir Altowairqi ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Solid Particles ◽  
Engine Oil ◽  
Working Fluid ◽  
Parabolic Trough ◽  
Partial Differential ◽  
Solar Powered

Parabolic trough solar collectors (PTSCs) are generally utilized to reach high temperatures in solar-thermal applications. The current work investigates entropy production analysis and the influence of nano solid particles on a parabolic trough surface collector (PTSC) installed within a solar powered ship (SPS). For the current investigation, the non-Newtonian Maxwell type, as well as a porous medium and Darcy–Forchheimer effects, were used. The flow in PTSC was produced by a nonlinear stretching surface, and the Cattaneo–Christov approach was used to assess the thermal boundary layer’s heat flux. Similarity transformation approach has been employed to convert partial differential equations into solvable ordinary differential equations allied to boundary conditions. Partial differential and the boundary conditions have been reduced into a group of non-linear ordinary differential equations. A Keller-box scheme applied to solve approximate solutions of the ordinary differential equations. Single-walled carbon nanotubes -engine oil (SWCNT-EO) and Multiwalled carbon nanotubes/engine oil (MWCNT-EO) nanofluids have been utilized as working fluid. According to the findings, the magnetic parameter led to a reduction in the Nusselt number, as well as an increment in skin friction coefficient. Moreover, total entropy variance over the domain enhanced for flow rates through Reynolds number and viscosity fluctuations were monitored by using Brinkman number. Utilizing SWCNT-EO nanofluid increased the thermal efficiency between 1.6–14.9% in comparison to MWCNT-EO.

scholarly journals Investigation of heat transfer enhancement in an annular conduit with angled fins using functionalized GNP colloidal suspension

2021 ◽  
Vol 945 (1) ◽  
pp. 012058
Author(s):  
Sayshar Ram Nair ◽  
Cheen Sean Oon ◽  
Ming Kwang Tan ◽  
S.N. Kazi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Exchanger ◽  
Heat Exchangers ◽  
Power Plants ◽  
Colloidal Suspension ◽  
Industrial Applications ◽  
Point Of View ◽  
Solid Particles ◽  
Working Fluid

Abstract Heat exchangers are important equipment with various industrial applications such as power plants, HVAC industry and chemical industries. Various fluids that are used as working fluid in the heat exchangers such as water, oil, and ethylene glycol. Researchers have conducted various studies and investigations to improve the heat exchanger be it from material or heat transfer point of view. There have been attempts to create mixtures with solid particles suspended. This invention had some drawbacks since the pressure drop was compromised, on top of the occurrence of sedimentation or even erosion, which incurs higher maintenance costs. A new class of colloidal suspension fluid that met the demands and characteristics of a heat exchanger was then created. This novel colloidal suspension mixture was then and now addressed as “nanofluid”. In this study, the usage of functionalized graphene nanoplatelet (GNP) nanofluids will be studied for its thermal conductivity within an annular conduit with angled fins, which encourage swirling flows. The simulation results for the chosen GNP nanofluid concentrations have shown an enhancement in thermal conductivity and heat transfer coefficient compared to the corresponding base fluid thermal properties. The data from this research is useful in industrial applications which involve heat exchangers with finned tubes.

scholarly journals Numerical study of magnetohydrodynamic free convective heat transfer flow along a vertical flat plate with temperature dependent thermal conductivity

2010 ◽  
Vol 6 (1) ◽  
pp. 16-29 ◽  
Author(s):  
M. M. Rahman ◽  
M. A. Alim
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Flat Plate ◽  
Temperature Dependent ◽  
Implicit Finite Difference ◽  
Transfer Flow ◽  
Temperature Dependent Thermal Conductivity ◽  
Vertical Flat Plate

The present numerical work describes the effect of the magnetohydrodynamic (MHD) free convective heat transfer flow along a vertical flat plate with temperature dependent thermal conductivity and heat conduction. The governing equations reduce to local non-similarity boundary layer equations using suitable transformation have been integrated by employing an implicit finite difference method together with the Keller box technique. Comparison with previously published work is performed and excellent agreement is observed. Profiles of the dimensionless velocity and temperature distributions as well as the local skin friction coefficient and surface temperature distribution are shown graphically for various values of the magnetic parameter M, thermal conductivity variation parameter g and Prandtl number Pr.Keywords: Implicit finite difference method, free convection flow, vertical flow, vertical flat plate, temperature dependent thermal conductivityDOI: 10.3329/jname.v6i1.2654Journal of Naval Architecture and Marine Engineering Vol.6(1) 2009 16-29

scholarly journals NUMERICAL APPROACHES FOR A MATHEMATICAL MODEL OF AN FCCU REGENERATOR

2008 ◽  
Vol 7 (1) ◽  
pp. 71
Author(s):  
J. C. Penteado ◽  
C. O. R. Negrao ◽  
L. F. S. Rossi
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Finite Difference Methods ◽  
Implicit Finite Difference ◽  
Conservation Principles ◽  
Continuously Stirred Tank Reactor ◽  
Time Changes ◽  
Numerical Approaches

This work discusses a mathematical model of an FCCU (Fluid Catalytic Cracking Unit) regenerator. The model assumes that the regenerator is divided into two regions: the freeboard and the dense bed. The latter is composed of a bubble phase and an emulsion phase. Both phases are modeled as a CSTR (Continuously Stirred Tank Reactor) in which ordinary differential equations are employed to represent the conservation of mass, energy and species. In the freeboard, the flow is considered to be onedimensional, and the conservation principles are represented by partial differential equations to describe space and time changes. The main aim ofthis work is to compare two numerical approaches for solving the set of partial and ordinary differential equations, namely, the fourth-order Runge-Kutta and implicit finite-difference methods. Although both methods give very similar results, the implicit finite-difference method can be much faster. Steady-state results were corroborated by experimental data, and the dynamic results were compared with those in the literature (Han and Chung, 2001b). Finally, an analysis of the model’s sensitivity to the boundary conditions was conducted.

Instability of Variable Thermal Conductivity Magnetohydrodynamic Nanofluid Flow in a Vertical Porous Channel of Varying Width

2017 ◽  
Vol 378 ◽  
pp. 85-101
Author(s):  
Md. Sarwar Alam ◽  
Oluwole Daniel Makinde ◽  
Md. Abdul Hakim Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Porous Wall ◽  
Variable Thermal Conductivity ◽  
Physical Parameters

A numerical investigation is performed into the heat transfer and entropy generation of a variable thermal conductivity magnetohydrodynamic flow of Al2O3-water nanofluid in a vertical channel of varying width with right porous wall, which enable the fluid to enter. The effects of the Lorentz force, buoyancy force, viscous dissipation and Joule heating are considered and modeled using the transverse momentum and energy balance equations respectively. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using power series with Hermite-Padé approximation method. A stability analysis has been performed for the local rate of shear stress and Nusselt number that indicates the existence of dual solution branches. Numerical results are achieved for the fluid velocity, temperature as well as the rate of heat transfer at the wall and the entropy generation of the system. The present results are original and new for the flow and heat transfer past a channel of varying width in a nanofluid which shows that the physical parameters have significant effects on the flow field.

scholarly journals Empirical correlations to predict thermophysical and heat transfer characteristics of nanofluids

2008 ◽  
Vol 12 (2) ◽  
pp. 27-37 ◽  
Author(s):  
Vasu Velagapudi ◽  
Krishna Konijeti ◽  
Kumar Aduru
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Ethylene Glycol ◽  
Volume Fraction ◽  
Solid Particles ◽  
Engine Oil ◽  
Fluid Temperature ◽  
Flow Conditions ◽  
Thermophysical Characteristics ◽  
Laminar And Turbulent Flow

Nanofluids exhibits larger thermal conductivity due to the presence of suspended nanosized solid particles in them such as Al2O3, Cu, CuO,TiO2, etc. Varieties of models have been proposed by several authors to explain the heat transfer enhancement of fluids such as water, ethylene glycol, engine oil containing these particles. This paper presents a systematic literature survey to exploit the thermophysical characteristics of nanofluids. Based on the experimental data available in the literature empirical correlation to predict the thermal conductivity of Al2O3, Cu, CuO, and TiO2 nanoparticles with water and ethylene glycol as base fluid is developed and presented. Similarly the correlations to predict the Nusselt number under laminar and turbulent flow conditions is also developed and presented. These correlations are useful to predict the heat transfer ability of nanofluids and takes care of variations in volume fraction, nanoparticle size and fluid temperature. The improved thermophysical characteristics of a nanofluid make it excellently suitable for future heat exchange applications. .

scholarly journals The improved thermal efficiency of Prandtl–Eyring hybrid nanofluid via classical Keller box technique

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Wasim Jamshed ◽  
Dumitru Baleanu ◽  
Nor Ain Azeany Moh Nasir ◽  
Faisal Shahzad ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Differential Equations ◽  
Heat Transport ◽  
Heated Surface ◽  
Solid Particles ◽  
Engine Oil ◽  
Hybrid Nanofluid ◽  
Flow Equations ◽  
Walled Carbon Nanotubes

AbstractPrandtl–Eyring hybrid nanofluid (P-EHNF) heat transfer and entropy generation were studied in this article. A slippery heated surface is used to test the flow and thermal transport properties of P-EHNF nanofluid. This investigation will also examine the effects of nano solid tubes morphologies, porosity materials, Cattaneo–Christov heat flow, and radiative flux. Predominant flow equations are written as partial differential equations (PDE). To find the solution, the PDEs were transformed into ordinary differential equations (ODEs), then the Keller box numerical approach was used to solve the ODEs. Single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) using Engine Oil (EO) as a base fluid are studied in this work. The flow, temperature, drag force, Nusselt amount, and entropy measurement visually show significant findings for various variables. Notably, the comparison of P-EHNF's (MWCNT-SWCNT/EO) heat transfer rate with conventional nanofluid (SWCNT-EO) results in ever more significant upsurges. Spherical-shaped nano solid particles have the highest heat transport, whereas lamina-shaped nano solid particles exhibit the lowest heat transport. The model's entropy increases as the size of the nanoparticles get larger. A similar effect is seen when the radiative flow and the Prandtl–Eyring variable-II are improved.

Non-similar solution of Sisko nanofluid flow with variable thermal conductivity: a finite difference approach

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ankita Bisht ◽  
Rajesh Sharma
Keyword(s):  
Thermal Conductivity ◽  
Finite Difference ◽  
Differential Equations ◽  
Velocity Ratio ◽  
Variable Thermal Conductivity ◽  
Brownian Diffusion ◽  
Control Parameters ◽  
Nanofluid Flow ◽  
Content Type ◽  
Thermal Buoyancy

Purpose The main purpose of this study is to present a non-similar analysis of two-dimensional boundary layer flow of non-Newtonian nanofluid over a vertical stretching sheet with variable thermal conductivity. The Sisko fluid model is used for non-Newtonian fluid with an exponent (n* > 1), that is, shear thickening fluid. Buongiorno model for nanofluid accounting Brownian diffusion and thermophoresis effects is used to model the governing differential equations. Design/methodology/approach The governing boundary layer equations are converted into nondimensional coupled nonlinear partial differential equations using appropriate transformations. The resultant differential equations are solved numerically using implicit finite difference scheme in association with the quasilinearization technique. Findings This analysis shows that the temperature raises for thermal conductivity parameter and velocity ratio parameter while decreases for the thermal buoyancy parameter. The thermophoresis and Brownian diffusion parameter that characterizes the nanofluid flow enhances the temperature and reduces the heat transfer rate. Skin friction drag can be effectively reduced by proper control of the values of thermal buoyancy and velocity ratio parameter. Practical implications The wall heating and cooling investigation result in the analysis of the control parameters that are related to the designing and manufacturing of thermal systems for cooling applications and energy harvesting. These control parameters have practical significance in the designing of heat exchangers and solar thermal collectors, in glass and polymer industries, in the extrusion of plastic sheets, the process of cooling of the metallic plate, etc. Originality/value To the best of authors’ knowledge, it is found from the literature survey that no similar work has been published which investigates the non-similar solution of Sisko nanofluid with variable thermal conductivity using finite difference method and quasilinearization technique.

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