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MHD free convection inside a triangular-wave-shaped corrugated porous cavity with Cu-water nanofluid is numerically studied with the finite element method. The influences of the Grashof number ( 10 4 ≤ Gr ≤ 10 6 ), Hartmann number ( 0 ≤ Ha ≤ 50 ), Darcy number ( 10 − 4 ≤ Da ≤ 10 − 1 ) and solid volume fraction of the nanoparticle ( 0 ≤ ϕ ≤ 0.05 ) on the convective flow features are examined. It is observed that increasing the Grashof number and Darcy number enhances the heat transfer, while the effect is opposite for the Hartmann number. As the corrugation frequency of the triangular wave increases, the local and averaged heat transfer rates decrease, which is more effective for higher values of Grashof and Darcy numbers. Normalized total entropy generation increases as the Darcy number and solid volume fraction of the nanoparticles increase and decreases as the Hartmann number increases both for flat and corrugated wall configurations.

This study investigates time-dependent free convection heat transfer and buoyancy-assisted flow over a horizontal heated plate within a vertical channel for two distinct scenarios: one stand alone and second involving tilted plates and varying plate positions. The temperature difference between the plate and air induces buoyant airflow. The study explores the impact of plate tilt angles and positions on time-dependent heat transfer coefficients due to varying buoyant airflow. The primary focus of the research for both classes of study is on the effects of the tilt angles (which control the change in flow blockage ratio) and positions of the heated plate on the time-dependent heat transfer coefficients due to the time-dependent buoyant airflow. As the blockage ratio increases and the positions of the heated plate in the vertical channel decreases, the influence of time-dependent buoyancy on the time-dependent Nusselt number weakens. The time-dependent Richardson's number varied from 7.4 to 9.6 throughout the tests. Based on the experimental data gathered from corresponding flux geometries and test conditions, the CFD model was validated. We have also developed a set of empirical correlations for predicting time-dependent Nusselt numbers for a time-dependent Rayleigh number range of 2000 < Ra < 7500, the dimensionless height of the heated plate from 0.507 ≤  ϕ  ≤ 0.551, and a flow blockage ratio of 0.08 ≤  χ  ≤ 0.024. At orientations where γ  = π/2 and γ  = π/4 , it has been observed that the heat transfer at position ∅ 1 is higher, whereas at γ  = 0 orientation, ∅ 1 heat transfer value is lower compared to the others. When the time required for the heated plate at all positions ( ∅ ) to reach thermal equilibrium with the ambient environment is compared with respect to orientation angles, it has been observed that the γ  = π/2 orientation angle reaches thermal equilibrium in the shortest time compared to the γ  = π/0 and γ  = π/4 orientation angles.

The time-fractional free convection flow of an incompressible viscous fluid near a vertical plate with Newtonian heating and mass diffusion is investigated in presence of first order chemical reaction. The dimensionless temperature, concentration, and velocity fields, as well as the skin friction and the rates of heat and mass transfer from the plate to the fluid, are determined using the Laplace transform technique. Closed form expressions are established in terms of Robotnov-Hartley and Wright functions. The similar solutions for ordinary fluids are also determined. Finally, the influence of fractional parameter on the temperature, concentration and velocity fields is graphically underlined and discussed.

The capability of LBM in the determination of entropy during power-law ferrofluid-free convection in the presence of effective factors is depicted in this research. Uniform absorption/production of heat and magnetic field in different types/angles affects the current inside a 2D chamber. Evaluation of the influence of thermal radiation through modeling with three separate distribution functions on the characteristics of the flow within the chamber with variable aspect ratio under various internal and external factors is among the features of this research, which has not been inquired so far. Application in the design of electronic coolers and solar collectors is one of the practical cases of this numerical evaluation. According to the results, the improvement in heat transfer due to the imposition of radiation on the system is more evident for fluid with higher viscosity. The enhancement of the power-law coefficient, further reducing the average Nusselt number value, diminishes the effectiveness of the magnetic field in reducing the entropy and the heat transfer rate. It is possible to achieve the current strength and the mean Nusselt value up to 40% and 61% more, respectively, by exerting a vertical magnetic field in a non-uniform type. Although for the generation of heat, there will be the lowest value of the thermal performance index and the average Nusselt number value, the greatest influence of the magnetic field is observed. The effectiveness of the addition of nanoparticles on the system thermal characteristics is more evident in cases where the conductivity effects are greater, such as the strong presence of the magnetic field in the high viscosities of the fluid. One of the effective ways to reduce the effect of the phenomenon of heat absorption/production is exposing the system to the shear thickening fluid. With this action, the changes in the average Nusselt number value for increasing the value of the heat absorption/generation parameter is about 59% lower than when a shear thinning fluid is considered. By designing the chamber in a smaller aspect ratio, in addition to enhancing the thermal performance system index, it is also feasible to decline the Bejan number.

Purpose This paper aims to theoritically investigate the free convection flow and heat transfer of a non-Newtonian fluid with pseudoplastic behavior in a cylindrical vertical cavity partially filled with a layer of a porous medium. Design/methodology/approach The non-Newtonian behavior of the pseudoplastic liquid is described by using a power-law non-Newtonian model. There is a temperature difference between the internal and external cylinders. The porous layer is attached to the internal cylinder and has a thickness of D. Upper and lower walls of the cavity are well insulated. The governing equations are transformed into a non-dimensional form to generalize the solution. The finite element method is used to solve the governing equations numerically. The results are compared with the literature results in several cases and found in good agreement. Findings The influence of the thickness of the porous layer, Rayleigh number and non-Newtonian index on the heat transfer behavior of a non-Newtonian pseudoplastic fluid is addressed. The increase of pseudoplastic behavior and increase of the thickness of the porous layer enhances the heat transfer. By increase of the porous layer from 0.6 to 0.8, the average Nusselt number increased from 0.15 to 0.25. The increase of non-Newtonian effects (decrease of the non-Newtonian power-law index) enhances the heat transfer rate. Originality/value The free convection behavior of a pseudoplastic-non-Newtonian fluid in a cylindrical enclosure partially filled by a layer of a porous medium is addressed for the first time.

Numerical study of various physical phenomena in three dimensions has become a necessity to better understand the physical process than in two dimensions. Thus, in this paper, the code is elaborated to be adapted to the simulation of heat transfer in three dimensions. The numerical simulations are performed using a hybrid method. This method is based on the lattice Boltzmann approach for the computation of velocities, and on the finite difference technique for the calculation of temperature. The used numerical code is validated by examining the free convection in a cubic enclosure filled with air. Then, the analysis of the heat exchange between two cold vertical walls and a heated block located at the center of a cubic cavity is considered.  The performed simulations showed that for a small value of the Rayleigh number (Ra=103 for example), the fluid exchanges its heat almost equally with all hot surfaces of the obstacle. However, for large values of Ra (Ra≥104), the numerical results found showed that the heat exchange rate is greater on the bottom face compared to the other faces of the obstacle.

Transient conjugate free convection in flexible enclosure is examined numerically. Isoflux heat sources are mounted in a left wall of finite thermal conductivity while a right wall is assumed to be hyper-flexible. The finite element method (FEM) is adopted to solve the governing partial differential equations, an arbitrary Lagrangian–Eulerian (ALE) approach inherent in the unstructured mesh. The governing parameters under consideration are: the number of the heat source, 1 ≤ n ≤ 3 , the thickness of the heat source, 0 ≤ a ≤ 0 . 25 , and the Rayleigh number, 10 5 ≤ Ra ≤ 10 8 . It is determined that the development of conjugate convection heat transfer experiences through an initial phase, a transition phase, and a steady state phase. Each phase interval is shifted by adjusting the thickness of the heat source. Higher number and thicker of heat source cases had an ignorant effect on the shape of the flexible wall, but they tend to suppress the heat transfer rate. Increasing the block amplitude by 25% for n = 1 , 2 , 3 results in reductions of the values of Nu ¯ to 24%, 20%, and 28% respectively.

—The results of numerical simulation of unsteady free convection developing near a suddenly heated plate, on which protrusions in the form of adiabatic cylinders of double height with respect to the diameter are arranged in a staggered order, are presented. The calculations were performed according to the Reynolds equations using a differential model of turbulent stresses. The range of variation of the Grashof number (plotted according to the thickness of the free convective flow), in which a significant intensification of heat transfer can be achieved, has been determined. It is shown that the best conditions for intensification are created if the longitudinal pitch in the array of protrusions is approximately twenty times the diameter of the latter.

Flow of a liquid in an enclosure with heat transfer has drawn special focus of researchers due to the abundant thermal engineering applications. So, the aim of present communication is to explore thermal characteristics of natural convective power-law liquid flow in a square enclosure rooted with a T-shaped fin. The formulation of the problem is executed in the form of partial differential expressions by incorporating the rheological relation of the power-law fluid. The lower wall of the enclosure along with the fin is uniformly heated and vertical walls are prescribed with cold temperature. For effective heat transfer within the cavity the upper boundary is considered thermally insulated. A finite element based commercial software known as COMSOL is used for simulations and discretization of differential equations and is executed incorporating a weak formulation. Domain discretization is performed by dividing it into triangular and rectangular elements at different refinement levels. A grid independence test is accomplished for quantities of engineering interest like local and average Nusselt numbers to attain accuracy and validity in results. Variation in the momentum and thermal distributions against pertinent parameters is analyzed through stream lines and isothermal contour plots. Measurement of the heat flux coefficient along with the calculation of kinetic energy against involved parameters is displayed through graphs and tables. After the comprehensive overview of attained results it is deduced that kinetic energy elevates against the upsurging magnitude of the Rayleigh number, whereas contrary behavior is encapsulated versus power-law index n. Elevation in the Nusselt number for the shear thinning case i.e., n=0.5 adheres as compared to Newtonian i.e., n=1  and shear thickening cases  i.e., n=1.5. It is perceived that by the upsurging power-law index viscosity augmentations and circulation zones increases. Heat is transferred quickly against Rayleigh number (Ra) due to production of temperature difference in flow domain.

A dispersion system fluid can convect even if the dispersoid is a solid phase. Therefore, heat exchange performance can be improved while maintaining fluidity using a material with high thermal conductivity as the dispersoid. This study presents the melting performance evaluation results of a latent heat storage material with a carbon nanotube (CNT) dispersion system with high thermal conductivity, which enhances the thermal conductivity of the latent heat storage material and does not limit free convection. Increasing the thermal conductivity and enhancing the melting convection of the heat storage material result in increased latent heat storage speed. In this study, the thermal conductivity of the latent heat storage material was successfully increased by dispersing CNTs in the material. When 0.1% (in mass) of multi-wall CNT (MWCNT) was dispersed in a paraffin-based latent heat storage material, the shear stress increased by 1.5 times at a shear rate of 500 s −1 , while taking into account the potential effects of convective inhibition. Therefore, a latent heat storage experiment was conducted in a rectangular heat storage tank using the CNT dispersion composition ratio as a parameter. A rectangular vessel with a heated vertical surface was used for the latent heat storage experiment. The melting speed was determined by comparing the amount of latent heat stored in a CNT-dispersed latent heat storage material and a single-phase latent heat storage material sample. The experimental results show that the time required for the latent heat storage material to completely melt in the heat storage tank was the shortest for the single-phase latent heat storage material sample. However, the fastest melting progress was observed for the sample with 0.02% (in mass) MWCNT content in the melting rate range of up to approximately 40% in the tank. The results indicate that this phenomenon is caused by the difference in the melting rates in the upper part of the tank. The generated data are useful for determining the shape and heat transfer surface arrangement of the latent heat storage tank.