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The purpose of this paper is to carry out a detailed investigation to study the natural convection of a non-Newtonian nanofluid flow between two vertical parallel plates. In this study, sodium alginate has been taken as a base fluid and nanoparticles that added to it are copper and silver. Maxwell–Garnetts and Brinkman models are used to calculate the effective thermal conductivity and viscosity of nanofluid, respectively.

The authors used two methods in this study, namely, Galerkin’s method and homotopy perturbation method.

This paper investigates the velocity and temperature profile of nanofluid and the real fluid flow between two vertical parallel plates. The impacts of physical parameters such as nanofluid volume fraction and dimensionless non-Newtonian viscosity are discussed.

Coupled non-linear differential equations are solved for velocity and temperature. A model is proposed in such a way that the authors may get the solution of real fluid from the nanofluid by neglecting the nano term. The authors do not require a further calculation for real fluid problem.

To study the thermal performance of both co‐current and counter‐current parallel flow heat exchangers. The hot stream is assumed to flow in the middle of two cold streams and exchange heat with them.

The dimensionless governing equations are derived based on the conservation of energy principle and solved using FEM based on subdomain collocation method and Galerkin's method. The results show that the subdomain collocation method is more accurate than the Galerkin's method, as observed when the results obtained are compared with the analytical results for the classical two‐fluid heat exchangers.

The results are presented in terms of effectiveness and number of transfer units (Ntu) for different values of the governing parameters. The governing parameters are the Ntu, the heat capacity ratios, the overall heat transfer coefficient ratio, and the inlet temperatures parameter. The results show that the effectiveness of the three‐fluid heat exchanger is always higher than that of classical two‐fluid flow heat exchanger for fixed values of the governing parameters. The results also show that for fixed values of the governing parameters, the effectiveness of the counter‐current is higher than the co‐current parallel flow three‐fluid heat exchangers.

One‐dimensional governing equations are derived based on the conservation of energy principle. The ranges of the governing parameters are: Ntu (0:5), the heat capacity ratios (0:1,000), the overall heat transfer coefficient ratio (0:2), and the inlet temperatures parameter (0:1).

Both co‐current and counter‐current parallel flow heat exchangers are used in the thermal engineering applications. The design and performance analysis of these heat exchangers are of practical importance.

This paper provides the details of the performance analysis of co‐current and counter‐current parallel flow heat exchangers, which can be used in thermal design.

The purpose of this paper is to analyse the dynamic behaviour of a three-fluid heat exchanger subjected to a step change in the temperature and velocity of the fluids at the inlet.

The analysis is carried out using the finite element methodology, adopting the Galerkin’s approach, using implicit method for transient behaviour.

The effect of step changes in the inlet temperature of hot and cold fluids show that an increase in the fluid inlet temperatures leads to increased outlet temperatures of all fluids and decreased hot fluid effectiveness. The exit temperatures of the fluids do not show any response initially for a certain period of time with the step changes. The time to reach steady state is independent of the step change in inlet temperature of the hot and the cold fluids.

The findings of this paper is limited to constant property situations.

The findings will be useful in designing control and regulation systems of heat exchangers used in different industrial processes and operations, such as in nuclear reactors, cryogenic and petrochemical process plants.

The analysis provides a time frame in which the controls and regulation systems work, so that the necessary safety precautions for the people working in the surrounding area can be taken care of.

As per the best knowledge of the authors, none of the papers so far have discussed the effect of the change in the inlet temperature and velocity of both the fluids. Performance parameters such as effectiveness, time to reach steady state, etc. have not been studied so far.

A finite element method employing Galerkin’s approach is developed to analyze free convection heat transfer in axisymmetric fluid saturated porous bodies. The method is used to study the effect of aspect ratio and radius ratio on Nusselt number in the case of a proous cylindrical annulus. Two cases of isothermal and convective boundary conditions are considered. The Nusselt number is always found to increase with radius ratio and Rayleigh number. It exhibits a maximum when the aspect ratio is around unity; maximum shifts towards lesser aspect ratios as Rayleigh number increases. Results are compared with those in the literature, wherever available, and the agreement is found to be good.

Develops a fine element method employing Galerkin’s approach for the analysis of a vertical tubular bubble absorber working with R22‐DMF as working fluid. Aims to provide an understanding of the absorption process which helps in the design of bubble absorbers. Numerical experiments have also been carried out with ammonia‐water combination for the sake of comparison with the results in the literature and the agreement is found to be good. Suggests a correlation for mass transfer coefficient for vertical tubular bubble absorbers working with R22‐DMF. The use of the correlation can either be in estimating the mass transfer rates, or in fixing up the major design parameters such as diameter and length required for complete absorption.

This study aims to deal with the performance of symmetric/asymmetric slot entry hybrid journal bearing system considering the effect of three dimensional irregularities in the analysis.

The asperity profile of three-dimensional irregularities has been modeled in both circumferential and axial directions. To compute the bearing performance characteristics parameter, finite element formulation of governing Reynolds equation has been derived using Galerkin’s technique.

Based on the numerically simulated results, it has been observed that the three-dimensional irregularities enhance the value of minimum fluid film thickness (h̄_min), lubricant flow (Q̄) and fluid film damping coefficients (C̄₁₁,C̄₂₂) approximately by order of magnitude of 24-26, 43-51 and 18-66 per cent, respectively, for the case of asymmetric slot entry configuration. Whereas, the values of fluid film stiffness coefficients (S̄₁₁,S̄₂₂) and threshold speed (ω̄_th) reduces approximately by order of 1-6 and 0-3 per cent, respectively, for the case of symmetric slot entry configuration.

The present paper describes that the influence of three-dimensional irregularities on bearing surface on the performance of slot entry hybrid journal bearing is original in literature gaps. The numerically simulated results presented in this study are expected to be quite useful to the bearing designers.

Heat exchangers are devices for exchanging energy between two or more fluids. They find applications in various industries like power, process, electronics, refining, cryogenics, chemicals, metals and manufacturing sector. Even though heat exchanger designs have been reported quite extensively, they are generally limited to steady‐state performance, single phase fluids, a few of the many possible flow arrangements and only two fluid heat exchangers. While these designs encompass the majority of the heat exchanger applications, there are some designs, which involve several fluids such as in cryogenics or fault‐tolerant heat exchangers. The governing differential equations for a three‐fluid heat exchanger are written based on the conservation of energy. The finite element method is used to solve the governing differential equations along with the appropriate boundary conditions. The case of a Buoyonet heat exchanger (used for pasteurizing milk) is analysed and the results are compared with the analytical solution available in the literature. The Buoyonet heat exchanger, treated as a three‐fluid heat exchanger is also analysed. The effect of heat loss to the ambient from a parallel flow double pipe heat exchanger is also investigated and the results are compared with those available in the literature. The results are presented both in terms of the temperature distribution along the length of the heat exchanger and the variation of effectiveness with NTU. The methodology presented in this paper can be extended to heat exchangers with any number of streams and any combination of the flow arrangements.

This paper describes an efficient reduced‐order method for the analysis of cylindrical dielectric resonators with an inhomogeneous dielectric medium. The field equations are formulated using the Laplace‐domain finite element method and are reduced to lower‐order models using the complex frequency hopping (CFH) technique. CFH is a moment matching technique which has been used successfully in the circuit simulation area for the solution of a large set of ordinary differential equations. The proposed technique is faster than the conventional approach by one to three orders of magnitude. The results are compared with those of other numerical methods available in the literature.

The application of the fast multipole method reduces the computational costs and the memory requirements of the boundary element method from O(N²) to approximately O(N). In this paper we present that the computational costs can be strongly shortened, when the multipole method is not only used for the solution of the system of linear equations but also for the field computation in arbitrary points.

A computational procedure is presented for the efficient non‐linear dynamic analysis of quasi‐symmetric structures. The procedure is based on approximating the unsymmetric response vectors, at each time step, by a linear combination of symmetric and antisymmetric vectors, each obtained using approximately half the degrees of freedom of the original model. A mixed formulation is used with the fundamental unknowns consisting of the internal forces (stress resultants), generalized displacements and velocity components. The spatial discretization is done by using the finite element method, and the governing semi‐discrete finite element equations are cast in the form of first‐order non‐linear ordinary differential equations. The temporal integration is performed by using implicit multistep integration operators. The resulting non‐linear algebraic equations, at each time step, are solved by using iterative techniques. The three key elements of the proposed procedure are: (a) use of mixed finite element models with independent shape functions for the stress resultants, generalized displacements, and velocity components and with the stress resultants allowed to be discontinuous at interelement boundaries; (b) operator splitting, or restructuring of the governing discrete equations of the structure to delineate the contributions to the symmetric and antisymmetric vectors constituting the response; and (c) use of a two‐level iterative process (with nested iteration loops) to generate the symmetric and antisymmetric components of the response vectors at each time step. The top‐ and bottom‐level iterations (outer and inner iterative loops) are performed by using the Newton—Raphson and the preconditioned conjugate gradient (PCG) techniques, respectively. The effectiveness of the proposed strategy is demonstrated by means of a numerical example and the potential of the strategy for solving more complex non‐linear problems is discussed.