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 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 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.

scholarly journals A Significant Solar Energy Note on Powell-Eyring Nanofluid with Thermal Jump Conditions: Implementing Cattaneo-Christov Heat Flux Model

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2669
Author(s):  
Nidal H. Abu-Hamdeh ◽  
Radi A. Alsulami ◽  
Muhyaddin J. H. Rawa ◽  
Mashhour A. Alazwari ◽  
Marjan Goodarzi ◽  
...  
Keyword(s):  
Heat Flux ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Frictional Coefficient ◽  
Approximate Solutions ◽  
Engine Oil ◽  
Partial Differential ◽  
Boundary Constraints ◽  
Solar Thermal Applications

PTSCs (parabolic trough solar collectors) are widely employed in solar-thermal applications to attain high temperatures. The purpose of this study is to determine how much entropy is created when Powell-Eyring nanofluid (P-ENF) flows across porous media on a horizontal plane under thermal jump circumstances. The flow in PTSC was generated by nonlinear surface stretching, thermal radiation, and Cattaneo-Christov heat flux, which was utilized to compute heat flux in the thermal boundary layer. Using a similarity transformation approach, partial differential equations were converted into ordinary differential equations with boundary constraints. Then, the boundary restrictions and partial differential equations were merged to form a single set of nonlinear ordinary differential equations. To obtain approximate solutions to ordinary differential equations, the Keller-Box approach is utilized. Nanofluids derived from silver- and copper-based engine oil (EO) has been employed as working fluids. The researchers observed that changing the permeability parameter reduced the Nusselt number while increasing the skin frictional coefficient. Total entropy variation was also calculated using the Brinkman number for flow rates with Reynolds number and viscosity changes. The key result is that thermal efficiency is inversely proportional to particular entropy production. For example, using Cu-EO nanofluid instead of Ag-EO nanofluid increased the heat transport rate efficiency to 15–36%.

scholarly journals Method of additional unknown functions in heat conductivity problems with variable physical properties of the medium

Vestnik IGEU ◽  
2019 ◽  
pp. 59-70 ◽  
Author(s):  
E.V. Kotova ◽  
A.V. Eremin ◽  
V.A. Kudinov ◽  
V.K. Tkachev ◽  
A.E. Kuznetsova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Physical Properties ◽  
Ordinary Differential Equations ◽  
High Precision ◽  
Analytical Solutions ◽  
Time Range ◽  
Partial Differential ◽  
Additional Boundary Conditions ◽  
Gamma Functions

Finding analytical solutions to the problems of thermal conductivity with variable physical properties of the medium by classical analytical methods is very complicated mathematically. The known expressions repre-senting complex infinite series including two types of Bessel functions and gamma-functions are, in fact, numerical as they require a numerical solution to complex transcendental equations with eigenvalues of the boundary problem. Such solutions can hardly be used in engineering applications, especially in cases when a solution to a certain problem is only an intermediate stage in other problems (such as thermoelasticity and control problems, inverse problems, etc.) which can be solved effectively only by finding analytical solutions to the initial problems. Therefore, an urgent problem now is to develop new methods of obtaining analytical solutions to the abovementioned problems, at least approximate ones. The study employed methods of additional boundary conditions and additional unknown functions in the integral method of heat balance. High-precision approximate analytical solutions to the transient heat conduction problem with nonhomogeneous physical properties of the medium for an infinite plate under symmetric boundary conditions of the first type have been obtained. The initial problem for partial differential equations is reduced to two problems in which ordinary differential equations are integrated. Additional boundary conditions are defined in such a way that their fulfillment in accordance with the new method is equivalent to the result of solving the initial partial differential equation at the boundary points and at the temperature perturbation front (for the first stage of the process). By combining methods with finite and infinite heat propagation rate we have been able to obtain high-precision analytical solutions for the whole time range of the unsteady process including its small and ultra small values. The solutions look like simple algebraical polynomials not including special functions (Bessel, Legendre, gamma-functions and others). Since it is not necessary to directly integrate the initial equations by the space variable and to reduce them to ordinary differential equations with additional unknown functions, the considered method can be used for solving complex boundary problems in which differential equations do not allow distinguishing between the variables (into nonlinear, with linear boundary conditions and heat sources, etc.).

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

scholarly journals Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 74-88 ◽  
Author(s):  
Tanveer Sajid ◽  
Muhammad Sagheer ◽  
Shafqat Hussain ◽  
Faisal Shahzad
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Physical Nature ◽  
Working Fluid ◽  
Nonlinear Ordinary Differential Equations ◽  
Gyrotactic Microorganisms ◽  
Motile Gyrotactic Microorganisms ◽  
Double Diffusive

AbstractThe double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.

Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Nonlinear Partial Differential Equations ◽  
Dirichlet Boundary Conditions ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Lyapunov Inequalities ◽  
Funct Anal

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.

scholarly journals On the theory and practice of thin-walled structures

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tamaz Vashakmadze
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Complex Analysis ◽  
Theory And Practice ◽  
Linear Case ◽  
Wide Sense ◽  
Partial Differential ◽  
Thin Walled Structures ◽  
Thin Walled

Abstract The basic problem of satisfaction of boundary conditions is considered when the generalized stress vector is given on the surfaces of elastic plates and shells. This problem has so far remained open for both refined theories in a wide sense and hierarchic type models. In the linear case, it was formulated by I. N. Vekua for hierarchic models. In the nonlinear case, bending and compression-expansion processes do not split and in this context the exact structure is presented for the system of differential equations of von Kármán–Mindlin–Reisner (KMR) type, constructed without using a variety of ad hoc assumptions since one of the two relations of this system in the classical form is the compatibility condition, but not the equilibrium equation. In this paper, a unity mathematical theory is elaborated in both linear and nonlinear cases for anisotropic inhomogeneous elastic thin-walled structures. The theory approximately satisfies the corresponding system of partial differential equations and the boundary conditions on the surfaces of such structures. The problem is investigated and solved for hierarchic models too. The obtained results broaden the sphere of applications of complex analysis methods. The classical theory of finding a general solution of partial differential equations of complex analysis, which in the linear case was thoroughly developed in the works of Goursat, Weyl, Walsh, Bergman, Kolosov, Muskhelishvili, Bers, Vekua and others, is extended to the solution of basic nonlinear differential equations containing the nonlinear summand, which is a composition of Laplace and Monge–Ampére operators.

scholarly journals A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

2021 ◽  
Vol 11 (11) ◽  
pp. 4798
Author(s):  
Hari Mohan Srivastava ◽  
Sotiris K. Ntouyas ◽  
Mona Alsulami ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Arbitrary Domain ◽  
Banach Contraction ◽  
Coupled Boundary Conditions ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

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