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The purpose of this paper is to highlight the advantages of a simplified algorithm to solve the problem of heat and mass transfer in porous medium by reducing the number of partial differential equations from four to three.

The approach of the present paper is to develop a simplified algorithm to reduce the number of equations involved in conjugate heat transfer in porous medium.

Developed algorithm/method has many advantages over conventional method of solution for conjugate heat transfer in porous medium.

The current work is applicable to conjugate heat transfer problem.

The developed algorithm is useful in reducing the number of equations to be solved, thus reducing the computational resources required.

Development of simplified algorithm and comparison with conventional method.

The purpose of this study was to analyze the heat transfer in a square porous cavity that has a solid block placed at its center. The prime focus of this study is to investigate the effect of size of the square solid block and other physical parameters on the heat transfer rate from the hot surface into the porous medium. The left vertical surface of cavity is maintained at a hot temperature and the right vertical surface at a cool temperature, T_c. The finite element method is used to simplify the governing equations and is solved iteratively. It is noted that the size of the solid block plays a vital role in dictating the heat transfer from the hot surface to porous medium.

The current work is based on finite element formulation of a square porous cavity that has a solid square block placed at its center. Governing equations were solved iteratively.

The size of the solid block has a pronounced effect on the heat transfer behavior inside the porous cavity.

This study highlights the heat transfer due to a conducting square solid block at mid of porous cavity.

This paper aims to investigate the heat transfer in porous channels.

Finite element method is used to simulate the heat transfer in porous channels.

The number and width of channels play a key role in determining the heat transfer of the porous channel. The heat transfer is higher around the channel legs. Smaller base height is better to get higher heat transfer capability.

This study represents the original work to investigate heat transfer in a porous domain having multiple channels.

The purpose of this paper is to investigate the heat transfer in an arbitrary cavity filled with porous medium. The geometry of the cavity is such that an isothermal heating source is placed centrally at the bottom of the cavity. The height and width of the heating source is varied to analyses its effect on the heat transfer characteristics. The investigation is carried out for three different cases of outer boundary conditions such as two outside vertical walls being maintained at cold temperature T_o, two vertical and top horizontal surface being heated to. T_o and the third case with top surface kept at T_o but other surfaces being adiabatic.

Finite element method is used to solve the governing equations.

It is observed that the cavity exhibits unique heat transfer behavior as compared to regular cavity. The cases of boundary conditions are found to affect the heat transfer rate in the porous cavity.

This is original work representing the heat transfer in irregular porous cavity with various boundary conditions. This work is neither being published nor under review in any other journal.

The characteristics of fluid motions in micro-channel are strong fluid-wall surface interactions, high surface to volume ratio, extremely low Reynolds number laminar flow, surface roughness and wall surface or zeta potential. Due to zeta potential, an electrical double layer (EDL) is formed in the vicinity of the wall surface, namely, the stern layer (layer of immobile ions) and diffuse layer (layer of mobile ions). Hence, its competent designs demand more efficient micro-scale mixing mechanisms. This paper aims to therefore carry out numerical investigations of electro osmotic flow and mixing in a constricted microchannel by modifying the existing immersed boundary method.

The numerical solution of electro-osmotic flow is obtained by linking Navier–Stokes equation with Poisson and Nernst–Planck equation for electric field and transportation of ion, respectively. Fluids with different concentrations enter the microchannel and its mixing along its way is simulated by solving the governing equation specified for the concentration field. Both the electro-osmotic effects and channel constriction constitute a hybrid mixing technique, a combination of passive and active methods. In microchannels, the chief factors affecting the mixing efficiency were studied efficiently from results obtained numerically.

The results indicate that the mixing efficiency is influenced with a change in zeta potential (ζ), number of triangular obstacles, EDL thickness (λ). Mixing efficiency decreases with an increment in external electric field strength (Ex), Peclet number (Pe) and Reynolds number (Re). Mixing efficiency is increased from 28.2 to 50.2% with an increase in the number of triangular obstacles from 1 to 5. As the value of Re and Pe is decreased, the overall percentage increase in the mixing efficiency is 56.4% for the case of a mixing micro-channel constricted with five triangular obstacles. It is also vivid that as the EDL overlaps in the micro-channel, the mixing efficiency is 52.7% for the given zeta potential, Re and Pe values. The findings of this study may be useful in biomedical, biotechnological, drug delivery applications, cooling of microchips and deoxyribonucleic acid hybridization.

The process of mixing in microchannels is widely studied due to its application in various microfluidic devices like micro electromechanical systems and lab-on-a-chip devices. Hence, its competent designs demand more efficient micro-scale mixing mechanisms. The present study carries out numerical investigations by modifying the existing immersed boundary method, on pressure-driven electro osmotic flow and mixing in a constricted microchannel using the varied number of triangular obstacles by using a modified immersed boundary method. In microchannels, the theory of EDL combined with pressure-driven flow elucidates the electro-osmotic flow.

Nonlinear mixed-convective entropy optimized the flow of hyperbolic-tangent nanofluid (HTN) with magnetohydrodynamics (MHD) process is considered over a vertical slendering surface. The impression of activation energy is incorporated in the modeling with the significance of nonlinear radiation, dissipative-function, heat generation/consumption connection and Joule heating. Research in this area has practical applications in the design of efficient heat exchangers, thermal management systems or nanomaterial-based devices.

Suitable set of variables is introduced to transform the PDEs (Partial differential equations) system into required ODEs (Ordinary differential equations) system. The transformed ODEs system is then solved numerically via finite difference method. Graphical artworks are made to predict the control of applicable transport parameters on surface entropy, Bejan number, Sherwood number, skin-friction, Nusselt number, temperature, velocity and concentration fields.

It is noticed from present numerical examination that Bejan number aggravates for improved estimations of concentration-difference parameter a_2, Eckert number E_c, thermal ratio parameter ?_w and radiation parameter R_d, whereas surface entropy condenses for flow performance index n, temperature-difference parameter a_1, thermodiffusion parameter N_t and mixed convection parameter ?. Sherwood number is enriched with the amplification of pedesis-motion parameter N_b, while opposite development is perceived for thermodiffusion parameter. Lastly, outcomes are matched with formerly published data to authenticate the present numerical investigation.

To the best of the authors' knowledge, no investigation has been reported yet that explains the entropic behavior with activation energy in the flowing of hyperbolic-tangent mixed-convective nanomaterial due to a vertical slendering surface.

This paper aims to study the attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips. Numerical investigations are performed for the phase and damped velocity profiles of the wave. For numerical computation purposes, water-saturated limestone and kerosene oil saturated sandstone for the first and second porous strips, respectively. Some other peculiarities have been observed and discussed.

Dispersion and attenuation characteristic of the shear wave propagations have been studied in an inhomogeneous poro-anelastic strip of finite thickness, which is clamped between an inhomogeneous poroelastic strip of finite thickness and an elastic half-space. Both the strips are initially stressed and the half-space is self-weighted. Analytical methods are used to calculate the interior deformations of the model with the involvement of special functions. The determination of the frequency equation, which includes the Bessel’s and Whittaker functions, has been obtained using the prescribed boundary conditions.

Impacts of attenuation coefficient, dissipation factor, inhomogeneities, initial stresses, Biot’s gravity, porosity and thickness ratio parameters on the velocity profile of the wave have been demonstrated through the graphical visuals. These parameters are playing an important role and working as a catalyst in affecting the propagation behaviour of the wave.

Inclusion of the concept of doubly layered initially stressed inhomogeneous porous structure of elastic and anelastic medium bedded over a self-weighted half-space medium brings a novelty to the existing literature related to the study of shear wave. It may be helpful to geologists, seismologists and structural engineers in the development of theoretical and practical studies.

The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference r_o-r_i. Moreover, several Darcy numbers have been considered.

A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement.

For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number.

A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems.

The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility.

This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.

The purpose of this paper is to investigate the effect of Al addition on the bulk alloy microstructure and tensile properties of the low Ag‐content Sn‐1Ag‐0.5Cu (SAC105) solder alloy.

The Sn‐1Ag‐0.5Cu‐xAl (x=0, 1, 1.5 and 2 wt.%) bulk solder specimens with flat dog‐bone shape were used for tensile testing in this work. The specimens were prepared by melting purity ingots of Sn, Ag, Cu and Al in an induction furnace. Subsequently, the molten alloys were poured into pre‐heated stainless steel molds, and the molds were naturally air‐cooled to room temperature. Finally, the molds were disassembled, and the dog‐bone samples were removed. The solder specimens were subjected to tensile testing on an INSTRON tester with loading rate 10⁻³ s⁻¹. The microstructural analysis was carried out using scanning electron microscopy/Energy dispersive X‐ray spectroscopy. Electron Backscatter Diffraction (EBSD) analysis was used to identify the IMC phases. To obtain the microstructure, the solder samples were prepared by dicing, molding, grinding and polishing processes.

The addition of Al to the SAC105 solder alloy suppresses the formation of Ag₃Sn and Cu₆Sn₅ IMC particles and leads to the formation of larger Al‐rich and Al‐Cu IMC particles and a large amount of fine Al‐Ag IMC particles. The addition of Al also leads to refining of the primary β‐Sn grains. The addition of Al results in a significant increase on the elastic modulus and yield strength. On the other hand, the addition of Al drastically deteriorates the total elongation.

The addition of Al to the low Ag‐content SAC105 solder alloy has been discussed for the first time. This work provides a starting‐point to study the effect of Al addition on the drop impact and thermal cycling reliability of the SAC105 alloy.

The purpose of this paper is to investigate the effects of small additions (0.1 and 0.3 wt%) of Fe on the bulk alloy microstructure and tensile properties of low Ag‐content Sn‐1Ag‐0.5Cu lead‐free solder alloy.

Sn‐1Ag‐0.5Cu, Sn‐3Ag‐0.5Cu and Sn‐1Ag‐0.5Cu containing 1 and 3 wt.% Fe solder specimens were prepared by melting pure ingots of Sn, Ag, Cu and Fe in an induction furnace and subsequently remelting and casting to form flat dog‐bone shaped specimens for tensile testing. The solder specimens were subjected to tensile testing using an INSTRON tester with a loading rate 10‐3 s‐1. To obtain the microstructure, the solder samples were prepared by dicing, molding, grinding and polishing processes. The microstructural analysis was carried out using scanning electron microscopy/Energy Dispersive X‐ray spectroscopy. Electron backscatter diffraction (EBSD) analysis was used to identify the IMC phases.

In addition to large primary β‐Sn grains, the addition of Fe to the SAC105 alloy formed large circular shaped FeSn2 IMC particles located in the eutectic regions. This had a significant effect in reducing the elastic modulus and yield strength and maintaining the elongation at the SAC105 level. Moreover, the additions of Fe resulted in the inclusion of Fe in the Ag3Sn and Cu6Sn5 IMC particles. The additions of Fe did not have any significant effect on the melting behaviour.

The paper provides a starting‐point for studying the effect of minor additions of Fe on the drop impact and thermal cycling reliability of SAC105 alloy considering the bulk alloy microstructure and tensile properties. Further investigations should be undertaken in the future.

The effect of Fe addition on the bulk alloy microstructure and tensile properties of the SAC105 alloy has been studied for the first time. Fe‐containing SAC105 alloy may have the potential to increase the drop impact and thermal cycling reliability compared with the standard SAC105 alloy.