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In the framework of this paper, nanofluid flow and heat transfer in a square enclosure containing a rectangular heated body is investigated computationally. The fluid in the cavity is a water-based nanofluid containing four different types of metal and metal-oxide nanoparticles: alumina (Al2O3), copper (Cu), silver (Ag) and titania (TiO2). The effective viscosity and thermal conductivity of the nanofluid are calculated by the Brinkman model and Maxwell–Garnett (MG), respectively. The Lattice Boltzmann Method (LBM) has been adopted to solve this problem. The effects of various governing parameters such as nanofluid type, Rayleigh number, volume fraction of nanoparticles and height of the rectangular heated body contained in the cavity on hydrothermal characteristics are studied. The results indicate that both the Nusselt number and dimensionless entropy generation are increasing functions of the Rayleigh number and nanoparticle volume fraction of the nanofluid. Furthermore, the effect of nanoparticle volume fraction is found to be more pronounced for a low Rayleigh number as compared to a high Rayleigh number. Excellent accuracy is achieved with the LBM code.

No abstract is provided for this article.

Influence of Lorentz forces and radiative term on nanoparticles treatment through a porous semi annulus has been displayed in current article. An innovative numerical method was employed to portray the roles of radiative term, Rayleigh number and Lorentz forces. Working fluid is Al2O3-H2O nanofluid with various shapes. Results display that inner wall temperature reduces with rise of Rd. The best shape of nanoparticle in view of hydrothermal treatment is Platelet shape.

Nanofluid heat transfer augmentation in a heat exchanger equipped with helical twisted tape turbulator is simulated numerically via Finite volume method. Impacts of width ratio, Reynolds number and pitch ratio on nanofluid hydrothermal behavior were illustrated. Related formulas for Nusselt number and Darcy factor are provided according to obtained results. Outputs show that thermal boundary layer thickness decreases with augment of width ratio due to stronger secondary flow. Better nanofluid mixing can be obtained for lower values of pitch ratio.

In this study natural convection heat transfer in a cold outer circular enclosure containing a hot inner sinusoidal cylinder is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both circular enclosure and inner cylinder are maintained at constant temperature and air filled the enclosure. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The calculations were performed for different governing parameters such as the Rayleigh number (Ra = 103, 104, 105 and 106), values of amplitude (A = 0.1, 0.3 and 0.5) and the number of undulations of the inner cylinder (N = 2, 3, 5 and 6). The results show that streamlines, isotherms, and the number, size and formation of the cells inside the enclosure strongly depend on the Rayleigh number, values of amplitude and the number of undulations of the enclosure.

Magnetic field effect on CuO–water nanofluid flow and heat transfer in an enclosure which is heated from below is investigated. Lattice Boltzmann method is applied to solve the governing equations. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. In this model effect of Brownian motion on the effective thermal conductivity is considered. Effect of active parameter such as: Hartmann number, heat source length, nanoparticle volume fraction and Rayleigh numbers on the flow and heat transfer characteristics have been examined. The results reveal that the enhancement in heat transfer increases as Hartmann number and heat source length increase but it decreases with increase of Rayleigh number. Also it can be found that effect of Hartmann number and heat source length is more pronounced at high Rayleigh number.

Recently, new-nanometer sized particles have been dispersed in the base fluid in heat transfer fluids. The fluids containing the solid nanometer-sized particle dispersion are called “nanofluids.” Two main categories were discussed in detail. Single-phase modeling is the combination of a nanoparticle and a base fluid and is considered as a single-phase mixture with steady properties. Two-phase modeling is that in which the nanoparticle properties and behaviors are considered separately from the base fluid properties and behaviors. Moreover, nanofluid flow and heat transfer can be studied in the presence of thermal radiation, electric field, magnetic field, and porous media. In this chapter, definition of nanofluid and its application have been presented.

Natural convection heat transfer of a nanofluid in the presence of an electric field is investigated. The control volume finite element method (CVFEM) is utilized to simulate this problem. A Fe3O4–ethylene glycol nanofluid is used as the working fluid. The effect of the electric field on nanofluid viscosity is taken into account. Numerical investigation is conducted for several values of Rayleigh number, nanoparticle volume fraction, and the voltage supplied. The numerical results show that the voltage used can change the flow shape. The Coulomb force causes the isotherms to become denser near the bottom wall. Heat transfer rises with increase in the voltage supplied and Rayleigh number. The effect of electric field on heat transfer is more pronounced at low Rayleigh numbers due to the predomination of the conduction mechanism.

Many phenomena in viscoelasticity, fluid mechanics, biology, chemistry, acoustics, control theory, psychology, and other areas of science can be successfully modeled by the use of fractional order derivatives. That is because of the fact that, a realistic modeling of a physical phenomenon having dependence not only at the time instant, but also the previous time history can be successfully achieved by using fractional calculus. Some mechanical problems such as eigenvalue problem, higher-order initial problems, fractional integro-differential equations, etc., the governing equations are some complicated and cannot be solved by the traditional differential transformation method (DTM). This chapter introduces DTM for advance problems and contains the following sections: 2.1 Introduction 2.2 Differential Transformation Method for Higher-Order Initial Value Problems 2.3 Fractional Differential Transform Method 2.4 Differential Transformation Method for Integro-Differential Equation 2.5 Differential Transformation Method for Eigenvalue Problems 2.6 Two-Dimensional Differential Transformation Method for Fractional Order Partial Differential Equations 2.7 Reduced Differential Transform Method 2.8 Modified Differential Transformation Method

The differential transformation method (DTM) is an alternative procedure for obtaining an analytic Taylor series solution of differential equations. The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization and discretization, and therefore, it is not affected by errors associated with discretization. The concept of DTM was first introduced to solve linear and nonlinear problems in electrical circuits. This chapter introduces DTM generally and contains the following: 1.1 Introduction 1.2 Principle of Differential Transformation Method 1.3 Multistep Differential Transformation Method 1.4 Hybrid Differential Transformation Method and Finite Difference Method 1.5 Differential Transformation Method Applying on Initial-Value Problems and Ordinary Differential Equations 1.6 Two-Dimensional Differential Transformation Method for Partial Differential Equations 1.7 Differential Transformation Method–Padé Approximation 1.8 DTM-Padé Approximation on Singular Two-Point Boundary Value Problem

The importance of studying photovoltaic thermal (PVT) systems is underscored by their potential to harness both solar thermal and photovoltaic energy simultaneously, making them a promising avenue for sustainable power generation. The integration of a PVT system allows for enhanced energy conversion and utilization of available resources. In the context of the broader field of renewable energy, understanding and optimizing PVT systems contribute to the development of efficient and environmentally friendly power generation solutions. The introduction of CuO nanoparticles proves beneficial, contributing to an overall improvement in system performance. Throughout this exploration, the aim is to provide insights into the intricate dynamics of PVT systems under varying conditions, emphasizing the impact of key parameters on system efficiency and performance. Examining PVT systems, this study focuses on a rectangular duct equipped with a turbulator featuring rectangular cuts. The simulation considers the flow of CuO-H2O within the channel and accounts for pure conduction within the layers, employing the finite volume method with a validation test for accuracy. The mesh size has been optimized for computational efficiency. In this context, the study investigates variations in cell temperature (TPV) and efficiency components (electrical (ηPV), thermal (ηth), overall (ηPVT)) concerning key variables: wind speed (Vw (0.4, 1, 1.4 m/s)), incident irradiation (G (730, 830, 930 W/m2)), inlet velocity (0.08, 0.1, 0.12 m/s), volume fraction of CuO (ϕ = 0, 0.018). Introducing the turbulator improves TPV uniformity by about 20.43%. With increased incident irradiation in the presence of the turbulator, ηPV, ηth, and ηPVT values enhance by approximately 1.02%, 8.18%, and 4.99%, respectively. Specifically, at G = 930 W/m2, the turbulator installation leads to a 4.35% increase in ηPVT. However, certain variables demonstrate contrasting effects. Increased wind speed results in a 3.63% decrease in ηPVT for tubes equipped with a turbulator. Conversely, intensifying the inlet velocity leads to an augmentation of ηPVT by around 3.19%, coupled with a notable 16.34% improvement in the uniformity of TPV.

No abstract is provided for this article.

In this paper, magneto-hydrodynamic (MHD) Jeffery–Hamel nanofluid flow in non-parallel walls is investigated analytically using different analytical methods. Different base fluids and nanoparticle are used. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. Comparison between Differential Transformation Method (DTM), DTM–Padé and Least square method (LSM) show that LSM is more accurate than other methods. The influence of the nanofluid volume friction, Reynolds number, Hartmann number and Angle of the channel on velocity profiles are investigated. Also it can be found that skin friction coefficient is an increasing function of Reynolds number, opening angle and nanoparticle volume friction but a decreasing function of Hartmann number.