Search results for: differential type nanofluid

Authors: Abhishek Jha, Manoj Kumar

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This paper proposes a new type of two wheels differential type odometry to estimate the next position and orientation of mobile robots. The proposed odometry is composed for two independent wheels with respective encoders. The two wheels rotate independently, and the change is determined by the difference in the velocity of the two wheels. Angular velocities of the two wheels are measured by rotary encoders. A mathematical model is proposed for the mobile robots to precisely move towards the goal. Using measured values of the two encoders, the current displacement vector of a mobile robot is calculated by kinematics of the mathematical model. Using the displacement vector, the next position and orientation of the mobile robot are estimated by proposed odometry. Result of simulator experiment by the developed odometry is shown.

Keywords: mobile robot, odometry, unicycle, differential type, encoders, infrared range sensors, kinematic model

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Authors: Hicham Salhi, Mohamed Si-Ameur, Nadjib Chafai

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Natural convection of a nanofluid consisting of water and nanoparticles (Ag or TiO2) in an inclined enclosure cavity, has been studied numerically, heated by a (random temperature, based on the random function). The governing equations are solved numerically using the finite-volume. Results are presented in the form of streamlines, isotherms, and average Nusselt number. In addition, a parametric study is carried out to examine explicitly the volume fraction effects of nanoparticles (Ψ= 0.1, 0.2), the Rayleigh number (Ra=103, 104, 105, 106),the inclination angle of the cavity( égale à 0°, 30°, 45°, 90°, 135°, 180°), types of temperature (constant ,random), types of (NF) (Ag andTiO2). The results reveal that (NPs) addition remarkably enhances heat transfer in the cavity especially for (Ψ= 0.2). Besides, the effect of inclination angle and type of temperature is more pronounced at higher Rayleigh number.

Keywords: nanofluid, natural convection, inclined cavity, random temperature, finite-volume

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Authors: Eyuphan Manay

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In this study, it was aimed to determine the convective heat transfer characteristics of water-based silicon dioxide nanofluids (SiO₂) with particle volume fractions of 0.2 and 0.4% vol. Nanofluids were tested in a plate type heat exchanger with six plates. Plate type heat exchanger was manufactured from stainless steel. Water was driven in the hot flow side, and nanofluids were driven in the cold flow side. The thermal energy of the hot water was taken by nanofluids. Effect of the inlet temperature of the hot water was investigated on heat transfer performance of the nanofluids while the inlet temperature of the nanofluids was fixed. In addition, the effects of the particle volume fraction and the cold flow rate on the performance of the system were tested. Results showed that increasing inlet temperature of the hot flow caused heat transfer to enhance. The suspended solid particles into the carrier fluid also remarkably enhanced heat transfer, and, an increase in the particle volume fraction resulted in an increase in heat transfer.

Keywords: heat transfer enhancement, SiO₂-water, nanofluid, plate heat exchanger

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Authors: Md. S. Ansari, S. S. Motsa

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In this paper, an analysis has been made on the flow of non-Newtonian viscoelastic nanofluid over a linearly stretching sheet under the influence of uniform magnetic field. Heat transfer characteristics is analyzed taking into the effect of nonlinear radiation and non-uniform heat source/sink. Transport equations contain the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The relevant partial differential equations are non-dimensionalized and transformed into ordinary differential equations by using appropriate similarity transformations. The transformed, highly nonlinear, ordinary differential equations are solved by spectral local linearisation method. The numerical convergence, error and stability analysis of iteration schemes are presented. The effects of different controlling parameters, namely, radiation, space and temperature-dependent heat source/sink, Brownian motion, thermophoresis, viscoelastic, Lewis number and the magnetic force parameter on the flow field, heat transfer characteristics and nanoparticles concentration are examined. The present investigation has many industrial and engineering applications in the fields of coatings and suspensions, cooling of metallic plates, oils and grease, paper production, coal water or coal–oil slurries, heat exchangers’ technology, and materials’ processing and exploiting.

Keywords: magnetic field, nonlinear radiation, non-uniform heat source/sink, similar solution, spectral local linearisation method, Rosseland diffusion approximation

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Authors: Lina Wu, Ye Li, Jia Liu

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We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite in non-L^q space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Keywords: differential forms, holder inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series

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Authors: Sina Movafagh, Younes Bakhshan

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Heat transfer of coolant flow through the automobile radiators is of great importance for the optimization of fuel consumption. In this study, the heat transfer performance of the automobile radiator is evaluated numerically. Different concentrations of nanofluids have been investigated by the addition of Al2O3 nano-particles into the water. Also, the effect of the inlet temperature of nanofluid on the performance of radiator is studied. Results show that with an increase of inlet temperature the outlet temperature and pressure drop along the radiator increase. Also, it has been observed that increase of nono-particle concentration will result in an increase in heat transfer rate within the radiator.

Keywords: heat transfer, nanofluid, car radiator, CFD simulation

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: Ibtisam Masmali, Edwin Beggs

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In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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Authors: Moulay Youssef El Hafidi

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In this research, an enhanced room-temperature magnetic refrigerator based on nanofluid, consisting of permanent magnets as a magnetism source, gadolinium as magnetocaloric material, water as base liquid, and carbon nanotubes (CNT) as nanoparticles, has been designed. The magnetic field is supplied by NdFeB permanent magnets and is about 1.3 Tesla. Two similar heat exchangers are employed to absorb and expel heat. The cycle performance of this self-designed device is analyzed theoretically. The results provide useful data for future optimization of room-temperature magnetic refrigeration using nanofluids.

Keywords: magnetic cooling, nanofluid, gadolinium, permanent magnets, heat exchange

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: G. Sarojamma, K. Vendabai

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An analysis is carried out to investigate the effect of magnetic field and heat source on the steady boundary layer flow and heat transfer of a Casson nanofluid over a vertical cylinder stretching exponentially along its radial direction. Using a similarity transformation, the governing mathematical equations, with the boundary conditions are reduced to a system of coupled, non –linear ordinary differential equations. The resulting system is solved numerically by the fourth order Runge – Kutta scheme with shooting technique. The influence of various physical parameters such as Reynolds number, Prandtl number, magnetic field, Brownian motion parameter, thermophoresis parameter, Lewis number and the natural convection parameter are presented graphically and discussed for non – dimensional velocity, temperature and nanoparticle volume fraction. Numerical data for the skin – friction coefficient, local Nusselt number and the local Sherwood number have been tabulated for various parametric conditions. It is found that the local Nusselt number is a decreasing function of Brownian motion parameter Nb and the thermophoresis parameter Nt.

Keywords: casson nanofluid, boundary layer flow, internal heat generation/absorption, exponentially stretching cylinder, heat transfer, brownian motion, thermophoresis

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Authors: F. Hekmatipour, M. A. Akhavan-Behabadi, B. Sajadi

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In this paper, the combined free and forced convection heat transfer of the Copper Oxide-Heat Transfer Oil (CuO-HTO) nanofluid flow in horizontal and inclined microfin tubes is studied experimentally. The flow regime is laminar, and pipe surface temperature is constant. The effect of nanoparticle and microfin tube on the heat transfer rate is investigated with the Richardson number which is between 0.1 and 0.7. The results show an increasing nanoparticle concentration between 0% and 1.5% leads to enhance the combined free and forced convection heat transfer rate. According to the results, five correlations are proposed to provide estimating the free and forced heat transfer rate as the increasing Richardson number from 0.1 to 0.7. The maximum deviation of both correlations is less than 16%. Moreover, four correlations are suggested to assess the Nusselt number based on the Rayleigh number in inclined tubes from 1800000 to 7000000. The maximum deviation of the correlation is almost 16%. The Darcy friction factor of the nanofluid flow has been investigated. Furthermore, CuO-HTO nanofluid flows in inclined microfin tubes.

Keywords: nanofluid, heat transfer oil, mixed convection, inclined tube, laminar flow

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Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar

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This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.

Keywords: load frequency control, fuzzy-pid controller, type 2 fuzzy system, harmony search algorithm

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Authors: Yacine Arioua

Abstract:

In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: Yohannes Yirga, Daniel Tesfay

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The convective heat and mass transfer in nanofluid flow through a porous media due to a permeable stretching sheet with magnetic field, viscous dissipation, and chemical reaction and Soret effects are numerically investigated. Two types of nanofluids, namely Cu-water and Ag-water were studied. The governing boundary layer equations are formulated and reduced to a set of ordinary differential equations using similarity transformations and then solved numerically using the Keller box method. Numerical results are obtained for the skin friction coefficient, Nusselt number and Sherwood number as well as for the velocity, temperature and concentration profiles for selected values of the governing parameters. Excellent validation of the present numerical results has been achieved with the earlier linearly stretching sheet problems in the literature.

Keywords: heat and mass transfer, magnetohydrodynamics, nanofluid, fluid dynamics

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: Farhad Hekmatipour, M. A. Akhavan-Behabadi, Farzad Hekmatipour

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In this paper, experiments were conducted to investigate the heat transfer of Copper Oxide-Heat Transfer Oil (CuO-HTO) nanofluid laminar flow in vertical smooth and microfin tubes as the surface temperature is constant. The effect of adding the nanoparticle to base fluid and Richardson number on the heat transfer enhancement is investigated as Richardson number increases from 0.1 to 0.7. The experimental results demonstrate that the combined forced-natural convection heat transfer rate may be improved significantly with an increment of mass nanoparticle concentration from 0% to 1.5%. In this experiment, a correlation is also proposed to predict the mixed convection heat transfer rate of CuO-HTO nanofluid flow. The maximum deviation of both correlations is less than 14%. Moreover, a correlation is presented to estimate the Nusselt number inside vertical smooth and microfin tubes as Rayleigh number is between 2´105 and 6.8´106 with the maximum deviation of 12%.

Keywords: mixed convection, heat transfer, nanofluid, vertical tube, microfin tube

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Authors: M. Insiat Islam Rabby, M. Mahbubur Rahman, Eshanul Islam, A. K. M. Sadrul Islam

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The numerical and simulative analysis of laminar heat exchange convection of aluminum oxide (Al₂O₃) - water nanofluid for the developed region through two parallel plates is presented in this present work. The second order single phase energy equation, mass and momentum equation are solved by using finite volume method with the ANSYS FLUENT 16 software. The distance between two parallel plates is 4 mm and length is 600 mm. Aluminum oxide (Al₂O₃) is used as nanoparticle and water is used as the base/working fluid for the investigation. At the time of simulation 1% to 5% volume concentrations of the Al₂O₃ nanoparticles are used for mixing with water to produce nanofluid and a wide range of interval of Reynolds number from 500 to 1100 at constant heat flux 500 W/m² at the channel wall has also been introduced. The result reveals that for increasing the Reynolds number the Nusselt number and heat transfer coefficient are increased linearly and friction factor decreased linearly in the developed region for both water and Al₂O₃-H₂O nanofluid. By increasing the volume fraction of Al₂O₃-H₂O nanofluid from 1% to 5% the value of Nusselt number increased rapidly from 0.7 to 7.32%, heat transfer coefficient increased 7.14% to 31.5% and friction factor increased very little from 0.1% to 4% for constant Reynolds number compared to pure water. At constant heat transfer coefficient 700 W/m2-K the pumping power advantages have been achieved 20% for 1% volume concentration and 62% for 3% volume concentration of nanofluid compared to pure water.

Keywords: convective heat transfer, pumping power, constant heat flux, nanofluid, nanoparticles, volume concentration, thermal conductivity

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Authors: M. Khalid, W. Rashmi, L. L. Kwan

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This work provides an overview on the experimental and numerical simulations of various nanofluids and their flow and heat transfer behavior. It was further extended to study the effect of nanoparticle concentration, fluid flow rates and thermo-physical properties on the heat transfer enhancement of Al2O3/water nanofluid in a turbulent flow circular conduit using ANSYS FLUENT™ 14.0. Single-phase approximation (homogeneous model) and two-phase (mixture and Eulerian) models were used to simulate the nanofluid flow behavior in the 3-D horizontal pipe. The numerical results were further validated with experimental correlations reported in the literature. It was found that heat transfer of nanofluids increases with increasing particle volume concentration and Reynolds number, respectively. Results showed good agreement (~9% deviation) with the experimental correlations, especially for a single-phase model with constant properties. Among two-phase models, mixture model (~14% deviation) showed better prediction compared to Eulerian-dispersed model (~18% deviation) when temperature independent properties were used. Non-drag forces were also employed in the Eulerian two-phase model. However, the two-phase mixture model with temperature dependent nanofluid properties gave slightly closer agreement (~12% deviation).

Keywords: nanofluid, CFD, heat transfer, forced convection, circular conduit

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Authors: Sujoy Das, M. M. Ghosh

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The thermal conductivity of a fluid can be significantly enhanced by dispersing nano-sized particles in it, and the resultant fluid is termed as "nanofluid". A theoretical model for estimating the thermal conductivity of a nanofluid has been proposed here. It is based on the mechanism that evenly dispersed nanoparticles within a nanofluid undergo Brownian motion in course of which the nanoparticles repeatedly collide with the heat source. During each collision a rapid heat transfer occurs owing to the solid-solid contact. Molecular dynamics (MD) simulation of the collision of nanoparticles with the heat source has shown that there is a pulse-like pick up of heat by the nanoparticles within 20-100 ps, the extent of which depends not only on thermal conductivity of the nanoparticles, but also on the elastic and other physical properties of the nanoparticle. After the collision the nanoparticles undergo Brownian motion in the base fluid and release the excess heat to the surrounding base fluid within 2-10 ms. The Brownian motion and associated temperature variation of the nanoparticles have been modeled by stochastic analysis. Repeated occurrence of these events by the suspended nanoparticles significantly contributes to the characteristic thermal conductivity of the nanofluids, which has been estimated by the present model for a ethylene glycol based nanofluid containing Cu-nanoparticles of size ranging from 8 to 20 nm, with Gaussian size distribution. The prediction of the present model has shown a reasonable agreement with the experimental data available in literature.

Keywords: brownian dynamics, molecular dynamics, nanofluid, thermal conductivity

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Authors: K. Y. Tseng, C. Y. Wu

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This paper employs a heuristic algorithm to solve engineering problems including truss structure optimization and optimal chiller loading (OCL) problems. Two different type algorithms, real-valued differential evolution (DE) and modified binary differential evolution (MBDE), are successfully integrated and then can obtain better performance in solving engineering problems. In order to demonstrate the performance of the proposed algorithm, this study adopts each one testing case of truss structure optimization and OCL problems to compare the results of other heuristic optimization methods. The result indicates that the proposed algorithm can obtain similar or better solution in comparing with previous studies.

Keywords: differential evolution, Truss structure optimization, optimal chiller loading, modified binary differential evolution

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Authors: Ratheesh Radhakrishnan, P. C. Sreekumar, K. Krishnamoorthy

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Heat transfer augmentation techniques ultimately results in the reduction of thermal resistance in a conventional heat exchanger by generating higher convective heat transfer coefficient. It also results in reduction of size, increase in heat duty, decrease in approach temperature difference and reduction in pumping power requirements for heat exchangers. Present study deals with compound augmentation technique, which is not widely used. The study deals with the use of Alumina (Al2O3)/water nanofluid and baffled twisted tape inserts in double pipe heat exchanger as compound augmentation technique. Experiments were conducted to evaluate the heat transfer coefficient and friction factor for the flow through the inner tube of heat exchanger in turbulent flow range (8000Keywords: enhancement, heat transfer coefficient, friction factor, twisted tape, nanofluid

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Authors: Houda Jalali, Hassan Abbassi

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In this numerical work, natural convection and entropy generation of Al₂O₃–water nanofluid in square cavity have been studied. A two-dimensional steady laminar natural convection in a differentially heated square cavity of length L, filled with a nanofluid is investigated numerically. The horizontal walls are considered adiabatic. Vertical walls corresponding to x=0 and x=L are respectively maintained at hot temperature, T_h and cold temperature, T_c. The resolution is performed by the CFD code "FLUENT" in combination with GAMBIT as mesh generator. These simulations are performed by maintaining the Rayleigh numbers varied as 10³ ≤ Ra ≤ 10⁶, while the solid volume fraction varied from 1% to 5%, the particle size is fixed at dp=33 nm and a range of the temperature from 20 to 70 °C. We used models of thermophysical nanofluids properties based on experimental measurements for studying the effect of adding solid particle into water in natural convection heat transfer and entropy generation of nanofluid. Such as models of thermal conductivity and dynamic viscosity which are dependent on solid volume fraction, particle size and temperature. The average Nusselt number is calculated at the hot wall of the cavity in a different solid volume fraction. The most important results is that at low temperatures (less than 40 °C), the addition of nanosolids Al₂O₃ into water leads to a decrease in heat transfer and entropy generation instead of the expected increase, whereas at high temperature, heat transfer and entropy generation increase with the addition of nanosolids. This behavior is due to the contradictory effects of viscosity and thermal conductivity of the nanofluid. These effects are discussed in this work.

Keywords: entropy generation, heat transfer, nanofluid, natural convection

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Authors: Tamseela Habib, Muhammad Amjad, Muhammad Edokali, Masome Moeni, Olivia Pickup, Ali Hassanpour

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Nanofluid-assisted steam generation is rapidly attracting attention amongst the scientific community since it can be applied in a wide range of industrial processes. Because of its high absorption rate of solar energy, nanoparticle-based solar steam generation could be a major contributor to many applications, including water desalination, sterilization and power generation. Lithium bromide-based iron oxide nanofluids have been previously studied in steam generation, which showed promising results. However, the efficiency of the system could be improved if a more heat-conductive nanofluid system could be utilised. In the current paper, we report on an experimental investigation of the photothermal conversion properties of functionalised Copper oxide (CuO) nanoparticles used in Lithium Bromide salt solutions. CuO binary nanofluid was prepared by chemical functionalization with polyethyleneimine (PEI). Long-term stability evaluation of prepared binary nanofluid was done by a high-speed centrifuge analyser which showed a 0.06 Instability index suggesting low agglomeration and sedimentation tendencies. This stability is also supported by the measurements from dynamic light scattering (DLS), transmission electron microscope (TEM), and ultraviolet-visible (UV-Vis) spectrophotometer. The fluid rheology is also characterised, which suggests the system exhibits a Newtonian fluid behavior. The photothermal conversion efficiency of different concentrations of CuO was experimentally investigated under a solar simulator. Experimental results reveal that the binary nanofluid in this study can remarkably increase the solar energy trapping efficiency and evaporation rate as compared to conventional fluids due to localized solar energy harvesting by the surface of the nanofluid. It was found that 0.1wt% CuO NP is the optimum nanofluid concentration for enhanced sensible and latent heat efficiencies.

Keywords: nanofluids, vapor absorption refrigeration system, steam generation, high salinity

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: S. Nandal, R. Bhargava

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The paper contains a numerical study of the unsteady magneto-hydrodynamic natural convection flow of nanofluids within a symmetrical wavy walled trapezoidal enclosure. The length and height of enclosure are both considered equal to L. Two-phase nanofluid model is employed. The governing equations of nanofluid flow along with boundary conditions are non-dimensionalized and are solved using one of Meshfree technique (EFGM method). Meshfree numerical technique does not require a predefined mesh for discretization purpose. The bottom wavy wall of the enclosure is defined using a cosine function. Element free Galerkin method (EFGM) does not require the domain. The effects of various parameters namely time t, amplitude of bottom wavy wall a, Brownian motion parameter Nb and thermophoresis parameter Nt is examined on rate of heat and mass transfer to get a visualization of cooling and heating effects. Such problems have important applications in heat exchangers or solar collectors, as wavy walled enclosures enhance heat transfer in comparison to flat walled enclosures.

Keywords: heat transfer, meshfree methods, nanofluid, trapezoidal enclosure

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Authors: Mohsen Sheikholeslami, Zahra Khalili, Ladan Momayez

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Impacts of environmental parameters and dust deposition on the efficiency of solar panel have been scrutinized in this article. To gain thermal output, trapezoidal cooling channel has been attached in the bottom of the panel incorporating ternary nanofluid. To produce working fluid, water has been mixed with Fe₃O₄-TiO₂-GO nanoparticles. Also, the arrangement of fins has been considered to grow the cooling rate of the silicon layer. The existence of a thermoelectric layer above the cooling channel leads to higher electrical output. Efficacy of ambient temperature (Ta), speed of wind (V𝓌ᵢₙ𝒹) and inlet temperature (Tᵢₙ) and velocity (Vin) of ternary nanofluid on performance of PVT has been assessed. As Tin increases, electrical efficiency declines about 3.63%. Increase of ambient temperature makes thermal performance enhance about 33.46%. The PVT efficiency decreases about 13.14% and 16.6% with augment of wind speed and dust deposition. CO₂ mitigation has been reduced about 15.49% in presence of dust while it increases about 17.38% with growth of ambient temperature.

Keywords: photovoltaic system, CO₂ mitigation, ternary nanofluid, thermoelectric generator, environmental parameters, trapezoidal cooling channel

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Authors: Zeeshan Ahmed, Ajinkya Sarode, Pratik Basarkar, Atul Bhargav, Debjyoti Banerjee

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The use of CO₂ in oil recovery and in CO₂ capture and storage is gaining traction in recent years. These applications involve heat transfer between CO₂ and the base fluid, and hence, there arises a need to improve the thermal conductivity of CO₂ to increase the process efficiency and reduce cost. One way to improve the thermal conductivity is through nanoparticle addition in the base fluid. The nanofluid model in this study consisted of copper (Cu) nanoparticles in varying concentrations with CO₂ as a base fluid. No experimental data are available on thermal conductivity of CO₂ based nanofluid. Molecular dynamics (MD) simulations are an increasingly adopted tool to perform preliminary assessments of nanoparticle (NP) fluid interactions. In this study, the effect of the formation of a nanolayer (or molecular layering) at the gas-solid interface on thermal conductivity is investigated using equilibrium MD simulations by varying NP diameter and keeping the volume fraction (1.413%) of nanofluid constant to check the diameter effect of NP on the nanolayer and thermal conductivity. A dense semi-solid fluid layer was seen to be formed at the NP-gas interface, and the thickness increases with increase in particle diameter, which also moves with the NP Brownian motion. Density distribution has been done to see the effect of nanolayer, and its thickness around the NP. These findings are extremely beneficial, especially to industries employed in oil recovery as increased thermal conductivity of CO₂ will lead to enhanced oil recovery and thermal energy storage.

Keywords: copper-CO2 nanofluid, molecular dynamics simulation, molecular interfacial layer, thermal conductivity

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Authors: Morteza Ghanbarpour, Rahmatollah Khodabandeh

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In this study, second law of thermodynamic is employed to evaluate heat pipe thermal performance. In fact, nanofluids potential to decrease the entropy generation of cylindrical heat pipes are studied and the results are compared with experimental data. Some cylindrical copper heat pipes of 200 mm length and 6.35 mm outer diameter were fabricated and tested with distilled water and water based Al2O3 nanofluids with volume concentrations of 1-5% as working fluids. Nanofluids are nanotechnology-based colloidal suspensions fabricated by suspending nanoparticles in a base liquid. These fluids have shown potential to enhance heat transfer properties of the base liquids used in heat transfer application. When the working fluid undergoes between different states in heat pipe cycle the entropy is generated. Different sources of irreversibility in heat pipe thermodynamic cycle are investigated and nanofluid effect on each of these sources is studied. Both experimental and theoretical studies reveal that nanofluid is a good choice to minimize the entropy generation in heat pipe thermodynamic cycle which results in higher thermal performance and efficiency of the system.

Keywords: heat pipe, nanofluid, thermodynamics, entropy generation, thermal resistance

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