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Convective flowing and heat transference of non-Newtonian liquid comprising nano-encapsulated phase-changing material (NEPCM) suspensions, filled in a square cavity, is numerically investigated. The molecules of NEPCM are cored with n-octadecane, shelled by polymethyl-methacrylate, and suspended in non-Newtonian fluid. The enclosure is insulated horizontally and heated vertically. Finite element method (FEM) is implemented for the numerical solution under different variables such as nanoparticles volume fraction (0 < ∅ < 0. 0 5), Stefan number (Ste = 0. 2 , 0. 3 1 3 , 0. 5), the heat capacity ratio (λ) of about (0.4), the temperature of fusion of the NEPCM (0 < θ f < 1) and the density ratio ( ρ P ∕ ρ f ) (0. 7 < ρ P ∕ ρ f ≤ 0. 9). The results show that the Nusselt quantity is related to the fusion temperature. An improvement in heat transference is observed when the fusion temperature deviates from the wall temperature, which is in the range of 0. 2 5 < θ f < 0. 7 5. For all power law index values (n), a linear increase of the Nusselt number with the solid volume fraction is detected. The shear-thinning nanofluid (n = 0. 6) demonstrates higher Nusselt number values than those of n = 1 and 1.4. [ABSTRACT FROM AUTHOR]

Latent heat storage in a shell-tube is a promising method to store excessive solar heat for later use. The shell-tube unit is filled with a phase change material PCM combined with a high porosity anisotropic copper metal foam (FM) of high thermal conductivity. The PCM-MF composite was modeled as an anisotropic porous medium. Then, a two-heat equation mathematical model, a local thermal non-equilibrium approach LTNE, was adopted to consider the effects of the difference between the thermal conductivities of the PCM and the copper foam. The Darcy–Brinkman–Forchheimer formulation was employed to model the natural convection circulations in the molten PCM region. The thermal conductivity and the permeability of the porous medium were a function of an anisotropic angle. The finite element method was employed to integrate the governing equations. A neural network model was successfully applied to learn the transient physical behavior of the storage unit. The neural network was trained using 4998 sample data. Then, the trained neural network was utilized to map the relationship between control parameters and melting behavior to optimize the storage design. The impact of the anisotropic angle and the inlet pressure of heat transfer fluid (HTF) was addressed on the thermal energy storage of the storage unit. Moreover, an artificial neural network was successfully utilized to learn the transient behavior of the thermal storage unit for various combinations of control parameters and map the storage behavior. The results showed that the anisotropy angle significantly affects the energy storage time. The melting volume fraction MVF was maximum for a zero anisotropic angle where the local thermal conductivity was maximum perpendicular to the heated tube. An optimum storage rate could be obtained for an anisotropic angle smaller than 45°. Compared to a uniform MF, utilizing an optimum anisotropic angle could reduce the melting time by about 7% without impacting the unit's thermal energy storage capacity or adding weight. [ABSTRACT FROM AUTHOR]

Cooling of two parallel surfaces with different temperatures is encountered in marine equipment. This requires a compact heat exchanger of two separated fluids, which counts on the double-passage channel. The present study uses a flexible separator to isolate two vertical passages, each partially filled with a porous layer. The permeability of the porous layers (Darcy number, Da), Reynolds number of each passage, temperature ratio, and the modulus of elasticity of the separator are scrutinized. Finite element method with the coupled ALE approach is employed in the numerical treatises. Results show that the strain energy of the elastic separator promotes the overall performance of the heat transfer, where at Da = 10−4, the left wall Nusselt number elevates by 10.4% and that of the right wall by 16.25% when the separator is changed from rigid to a flexible one. As the porous layers meet high permeability, energy transfer from the hot surfaces to the cold fluid upgrades notably, where the Nusselt number increases by 138% for the left wall and 96% for the right wall when Da is increased from 10−5 to 10−1. It is found in a high permeable layer, the flexible separator showcases higher performance than the rigid separator. • The paper investigates the energy exchange through a double-passage channel. • Each passage composed of clear and porous layers. A flexible strained wall separates the passages. • The elastic separator promotes the performance of the heat transfer in the channel. • The higher permeability porous layer promotes the Nusselt number. • The encountered buoyancy within the right passage lowers the Nusselt number in this passage. [ABSTRACT FROM AUTHOR]

A numerical attempt of the two-phase (non-homogeneous) nanofluid approach towards the convection heat transfer within a 3D wavy direct absorber solar collector is reported. The solar collector is permeated by a water- Al 2 O 3 nanofluid and contains a wavy glass top surface that is exposed to the ambient atmosphere and a flat steel bottom surface. The left and right surfaces are maintained adiabatic. The governing equations of the Navier–Stokes and energy equations for the nanofluid are transformed into a dimensionless pattern and then solved numerically using the Galerkin weighted residual finite-element technique. Validations with experimental and numerical data are performed to check the validity of the current code. Impacts of various parameters such as the number of oscillations, wave amplitude, Rayleigh number and the nanoparticles volume fraction on the streamlines, isotherms, nanoparticle distribution, and heat transfer are described. It is found that an augmentation of the wave amplitude enhances the thermophoresis and Brownian influences which force the nanoparticles concentration to display a nonuniform trend within the examined region. Furthermore, the heat transfer rate rises midst the growing wave amplitude and number of oscillations. More importantly, such enhancement is observed more significantly with the variation of the wave amplitude. [ABSTRACT FROM AUTHOR]

• The phase change heat transfer of nano-enhanced PCMs is addressed. • Mesoporous silica particles are adopted to enhance the thermal conductivity of PCM. • The non-Newtonian behavior of PCM is taken into account using a power-law model. • The results show using the nanoparticles suppresses the convective heat transfer. • Using 5% mass fraction of nanoparticles reduces the heat transfer by 50%. In the present study, the melting phase-change heat transfer of nano-enhanced phase-change octadecane by using mesoporous silica particles is investigated in an inclined cavity, theoretically. The presence of mesoporous silica particles induces non-Newtonian effects in the molten octadecane. A phase-change interface-tracking approach, deformed mesh technique, is employed to track the phase-change interface and heat transfer in the cavity. The Arbitrary Lagrangian-Eulerian (ALE) moving mesh technique along with the finite element method is adopted to solve the governing equations for conservation of mass, momentum, and energy during the phase-change process. A re-meshing technique and an automatic time step control approach are employed to control the quality of the deformed mesh and the computed numerical solution. The effect of various mass fractions of nanoparticles and various inclination angles of the enclosure on the heat transfer and phase-change behavior of nano-enhanced octadecane are addressed. The outcome reveals that using the mesoporous silica particles diminish the heat transfer in the enclosure. Although the presence of nanoparticles improved the conductive heat transfer, a reduction in the phase-change heat transfer performance of the enclosure can be observed, which is due to the increase of the viscosity (consistency parameter) of the liquid and suppression of natural convective flows. Moreover, the presence of nanoparticles reduces the latent heat capacity of octadecane as they do not contribute to the phase-change energy storage. Dispersing 5% mass fraction of nanoparticles in octadecane can reduce the heat transfer up to 50% and increase the consistency parameter by three folds. The angle of inclination of the cavity also plays an important role in the heat transfer characteristics. Tilting the cavity by -75° leads to an 80% reduction in the heat transfer. [ABSTRACT FROM AUTHOR]

• A suspension of Nano–Encapsulated Phase Change Materials (NEPCMs) is modeled. • A glass-ball porous medium is saturated with the NEPCM suspension. • The nanoparticles are consist of a PCM core (nonadecane) and a shell (polyurethane). • The unsteady behavior thermal behavior of the NEPCM suspension is investigated. • There is a range of optimal fusion temperature for NEPCM nanoparticles. The free convection phase change heat transfer of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous space is theoretically addressed. The core of the nanoparticles is made of a phase change material and encapsulated in a thin shell. Hence, the core of the nanoparticles of the suspension undergoes a phase change at its fusion temperature and release/store large amounts of latent heat. The phase change of nanoparticles is modeled using a sine shape temperature-dependent heat capacity function. Darcy-Brinkman model is used to model the flow in the porous medium. The governing equations including the conservation of mass, momentum, and heat are transformed into a non-dimensional form before being solved by the finite element method in a structured non-uniform mesh. The influence of the porosity, Darcy number, Rayleigh number, fusion temperature of nanoparticles, and the unsteady time-periodic boundary conditions on the thermal behavior of the porous medium in the presence of NEPCM particles is investigated. The results show that the presence of NEPCM particles improves the heat transfer. The increase of porosity improves the heat transfer when the volumetric concentrations of NEPCM particles are higher than 3%. There exists an optimal dimensionless fusion temperature of NEPCM nanoparticles for the interval [0.25; 0.75]. [ABSTRACT FROM AUTHOR]

Non-Newtonian behavior of a Phase Change Material (PCM) inside a porous coaxial pipe is studied by utilizing the deformed mesh technique. The inner and outer pipes are subjected to the high and low temperatures of T h and T c , while the bottom and upper surfaces are thermally insulated. The Finite Element Method (FEM), implemented in the Arbitrary Eulerian-Lagrangian (ALE) moving grid technique, is applied to solve the weakened forms of the governing equations. Stefan's condition is employed to track the solid-liquid interface of the PCM during the melting process. Grid independency test is conducted, and the verifications of the results are evaluated through comparisons with several test cases published in the literature. The simulations show that an increment of Stefan's number can significantly improve the melting rate. As the Stefan number reaches from 0.014 to 0.01, the full melting non-dimensional time declines from 1.313 to 0.937. Also, an extreme increase in the melting rate can be found while decreasing the power-law index. When the power-law index decrease from 1 to 0.6, the full melting time subsequently is reduced to 54%. [ABSTRACT FROM AUTHOR]

Current investigation aims to analyze the conjugate free convection inside a porous square cavity occupied with Ag-MgO hybrid nanofluid using the local thermal non-equilibrium (LTNE) model. Hybrid nanofluids are a novel kind of enhanced working fluids, engineered with enhanced thermo-physical and chemical properties. Two solid walls located between the horizontal bounds in two sides of cavity play the role of a conductive interface between the hot and cold walls, and moreover, the top and bottom bounds have been insulated. The governing differential equations are obtained by Darcy model and then for better representation of the results, converted into a dimensionless form. The finite element method is utilized to solve the governing equations. To evaluate the correctness and accuracy of the results, comparisons have been performed between the outcomes of this work and the previously published results. The results indicate that using the hybrid nanoparticles decreases the flow strength and the heat transfer rate. The heat transfer rate augments when Rk rises and the flow strength augments when Ra grows. Enhancing the porosity increases strongly the size and strength of the vortex composed inside the porous medium. When Kr is low, the heat transfer rate is low and by increasing Kr, thermal fields become closer to each other. The effect of hybrid nanoparticles on thermal fields with the thinner solid walls is more than that the thicker ones. An increment in H eventuates the enhancement of heat transfer and hence, the thermal boundary layer thickness. By increasing the volume fraction of the hybrid nanoparticles, Nuhnf and Nus decrease in constant Ra. Besides, increase in Ra enhances the Nuhnf and Nus. For a certain d, the reduction of Nus due to using the hybrid nanoparticles is more than that for Nuhnf. The increment of d lessens Nuhnf for all values of Kr and has not specific trends for Nus. Utilizing hybrid nanoparticles decreases Nus (except d = 0.4), rises Nus when Kr < 18, while it can increase Nus for Kr > 42. In constant d, increment of H, respectively, decreases and boosts Nuhnf and Nus. For all values of d, increment of ε declines Nuhnf. In low value of d, the increase in ε reduces Nus, whereas at higher values, Nus has continuously enhancing trend. For different values of d, the increase in ε scrimps Nuhnf. The increment of d and also ε, and H are, respectively, decreases and increases the heat transfer rate. [ABSTRACT FROM AUTHOR]

The natural convective heat transfer of nanofluids was addressed inside a square enclosure filled by three different layers: solid, porous medium and free fluid. The behavior of the porous layer has been simulated using local thermal non-equilibrium model. The Buongiorno's model was utilized to evaluate the distribution of nanoparticles inside the enclosure that arose from the thermophoresis and Brownian motion. The governing equations were solved by the Galerkin finite element method in a non-uniform grid. The governing parameters are Rayleigh number Ra = 103-106, porosity ε = 0.3-0.9, Darcy number Da = 10−5-10−2, interface parameter Kr = 0.1-10, H = 0.1-1000; ratio of wall thermal conductivity to that of the nanofluid, Rk = 0.1-10, dimensionless length of the heater B = 0.2-0.8; dimensionless centre position height of the heater Z = 0.3-0.7 and Lewis number Le = 10-100. A considerable concentration gradient of nanoparticles was found inside the enclosure. In some studied cases, the non-dimensional volume fraction of nanoparticles is about 10% higher than the average volume fraction of nanoparticles at the region near the cold wall. The variability of Darcy and the Rayleigh numbers indicated significant effects on heat transfer rate and the concentration patterns of the nanoparticles and inward the cavity. The increase in Le and Nr amplifies and decreases the heat transfer rates through fluid and solid phases, respectively. In addition, it can be seen that the increment in heat transfer rates with Le increases as Nr increases. [ABSTRACT FROM AUTHOR]

The present paper studies the melting of nanoparticles-enhanced phase-change materials (NEPCM) in a square cavity using the finite element method. The enhancement is based on the hybrid nanofluid strategy. A linearized correlations procedure has been followed to determine the properties of the hybrid nanofluid. The Rayleigh, Prandtl, and Stefan numbers have been fixed at 10 8 , 50, and 0.1, respectively. The left wall is kept at a higher temperature T h = 40 °C, the right wall is kept at a lower temperature T c = 30 °C, while the horizontal walls are kept adiabatic. The enthalpy-porosity model is used to simulate the melting of the phase-change materials (PCM). The study is governed by tracing the liquid–solid interface by varying the total nanoparticles volume fraction ϕ = 0–5%, and four different sets of models parameters combinations ( Nc, Nν ) = (0,0), (5,18), (18,18), (18,5). The results have shown the consistency of the liquid–solid phase progress with the available experimental results, i.e. the melting process expedites when the enhancement in the thermal conductivity, which is characterized by Nc , is much greater than the enhancement of the dynamic viscosity. Compared with the available experimental data, hybrid nanoparticles composed of Mg–MgO demonstrate the best fusion performance. [ABSTRACT FROM AUTHOR]

The MHD phase change heat transfer of a phase change substance in the presence of a uniform magnetic field is theoretically studied in a cavity. A fixed grid method associated with the enthalpy–porosity method is utilized. The governing equations are transformed into a non-dimensional form and solved using the finite element method. The impacts of the crucial parameters such as the Hartmann number and the inclination angle on the phase change process are investigated. It is found that any increase in Hartmann number and the inclination angle of the cavity leads to a decrease in the rate of the melting process. [ABSTRACT FROM PUBLISHER]

This work is dealing with the natural convection heat transfer in a square filled with porous medium that has been extended according to the Nield and Kuznetsov model to tridisperse porous medium. Considering impermeable walls which the horizontal ones are insulated and vertical ones are assumed to be isothermal, the governing equations are set as the three equations for momentum and three equations for energy for three phases of porosity and are numerically solved utilizing finite element method. In this study isothermal contours, streamlines and Nusselt number values are foremost criteria which are presented for three levels of porosity. The influence of various governing parameters on the heat transfer is investigated. [ABSTRACT FROM AUTHOR]

The present paper aims to analyze the thermal convective heat transport and generated irreversibility of water-Cu-Al2O3 hybrid nanosuspension in an odd-shaped cavity. The side walls are adiabatic, and the internal and external borders of the enclosure are isothermally kept at high and low temperatures of Th and Tc, respectively. The control equations based on conservation laws are formulated in dimensionless form and worked out employing the Galerkin finite element technique. The outcomes are demonstrated using streamlines, isothermal lines, heatlines, isolines of Bejan number, as well as the rate of generated entropy and the Nusselt number. Impacts of the Rayleigh number, the hybrid nanoparticles concentration (ϕhnf), the volume fraction of the Cu nanoparticles to ϕhnf ratio (ϕr), width ratio (WR) have been surveyed and discussed. The results show that, for all magnitudes of Rayleigh numbers, increasing nanoparticles concentration intensifies the rate of entropy generation. Moreover, for high Rayleigh numbers, increasing WR enhances the rate of heat transport. [ABSTRACT FROM AUTHOR]

In the current study, free convection heat transfer of a suspension of Nano–Encapsulated Phase Change Materials (NEPCMs) is simulated and discussed in an inclined porous cavity. The phase change materials are capsulated in nano-shells layers, while the core stores/releases large amounts of energy during melting/solidification in the vicinity of the hot/cold walls. The governing equations are introduced and transformed into non–dimensional form before being solved by using the finite element method. Simulation results are validated thoroughly. Thereafter, the consequences of the fusion temperature and the Stefan number on the distributions of streamlines, isotherms, and the heat capacity ratio, as well as the heat transfer characteristics, are analyzed for different inclination angles of the cavity. Inspection of the results demonstrates that the best heat transfer performance occurs for the non–dimensional fusion temperature of 0.5 and the inclination angle of 42°. It is found that a decrease in the Stefan number improves heat transfer. The results also show that the presence of the NEPCM particles generally leads to heat transfer improvement. • Heat transfer of nano–encapsulated phase change materials (NEPCMs) is addressed. • The porous cavity is filled with a suspension of NEPCM particles. • The finite element method is employed to solve the phase change governing equations. • The effect of fusion temperature on the thermal behaviour of the cavity is examined. • Using NEPCM particles could enhance the heat transfer up to 28%. [ABSTRACT FROM AUTHOR]

The present investigation addressed the entropy generation, fluid flow, and heat transfer regarding Cu-Al 2 O 3 -water hybrid nanofluids into a complex shape enclosure containing a hot-half partition were addressed. The sidewalls of the enclosure are made of wavy walls including cold isothermal temperature while the upper and lower surfaces remain insulated. The governing equations toward conservation of mass, momentum, and energy were introduced into the form of partial differential equations. The second law of thermodynamic was written for the friction and thermal entropy productions as a function of velocity and temperatures. The governing equations occurred molded into a non-dimensional pattern and explained through the finite element method. Outcomes were investigated for Cu-water, Al 2 O 3 -water, and Cu-Al 2 O 3 -water nanofluids to address the effect of using composite nanoparticles toward the flow and temperature patterns and entropy generation. Findings show that using hybrid nanofluid improves the Nusselt number compared to simple nanofluids. In the case of low Rayleigh numbers, such enhancement is more evident. Changing the geometrical aspects of the cavity induces different effects toward the entropy generation and Bejan number. Generally, the global entropy generation for Cu-Al 2 O 3 -water hybrid nanofluid takes places between the entropy generation values regarding Cu-water and Al 2 O 3 -water nanofluids. [ABSTRACT FROM AUTHOR]

The present paper aims to investigate the influence of perforated membrane geometry on the performance of biosensors. For this purpose, a 2-D axisymmetric model of an amperometric biosensor is analyzed. The governing equations describing the reaction-diffusion equations containing a nonlinear term related to the Michaelis–Menten kinetics of the enzymatic reaction are introduced. The partial differential governing equations, along with the boundary conditions, are first non-dimensionalized by using appropriate dimensionless variables and then solved in a non-uniform unstructured grid by employing the Galerkin Finite Element Method. To examine the impact of the hole-geometry of the perforated membrane, seven different geometries—including cylindrical, upward circular cone, downward circular cone, upward paraboloid, downward paraboloid, upward concave paraboloid, and downward concave paraboloid—are studied. Moreover, the effects of the perforation level of the perforated membrane, the filling level of the enzyme on the transient and steady-state current of the biosensor, and the half-time response are presented. The results of the simulations show that the transient and steady-state current of the biosensor are affected by the geometry dramatically. Thus, the sensitivity of the biosensor can be influenced by different hole-geometries. The minimum and maximum output current can be obtained from the cylindrical and upward concave paraboloid holes. On the other hand, the least half-time response of the biosensor can be obtained in the cylindrical geometry. [ABSTRACT FROM AUTHOR]

• Free convection heat transfer in a trapezoidal enclosure is addressed. • The enclosure is divided by a flexible partition. • The Fluid–Stricture Interaction (FSI) approach with moving mesh is used. • The finite element method is utilized to solve the governing equations. • Effect of the flexibility of the partition on the thermal behavior is investigated. • The increase of Rayleigh number increases the maximum tensions in the partition. The Fluid-Structure Interaction (FSI) approach was utilized to model the displacement of a flexible partition in a trapezoidal enclosure due to interaction with an internal natural convection flow. A moving mesh technique, Arbitrary Lagrangian–Eulerian (ALE) method, is adopted to model the partition displacement and the flow and heat transfer in the enclosure. The finite element method is employed to solve the governing equations after transforming into a non-dimensional form. The effect of various non-dimensional parameters such as Rayleigh number, Prandtl number, trapezoidal walls inclination angles, and non-dimensional Young's modulus. The results show that the increase of Rayleigh number increases the heat transfer in the enclosure and the tension in the partition. Notably, raising Ra from 104 to 107 can increase the heat transfer rate in the cavity by 8 times. The inclination angle of cavity walls induces a minimal effect on the induced tensions in the partition while it influences the heat transfer. In particular, heat transfer rate in a square cavity is 15% higher than in a trapezoidal cavity having side walls with 30° angle of inclination. [ABSTRACT FROM AUTHOR]

• The melting heat transfer in an anisotropic metal foam was modeled. • The permeability and thermal conductivity tensors were used to explain the foam behavior. • The impact of anisotropic angle and foam placement on the melting heat transfer was addressed. • An anisotropic metal foam could significantly improve the charging power with no mass addition. • A tilt angle of -45° or +45° and a 0° anisotropic angle provide maximum charging power. The metal foams are a promising candidate for the enhancement of heat transfer in latent heat thermal energy storage (LHTES) units. These foams can be synthesized with engineered local properties such as improved thermal conductivity or permeability in a specified direction. However, the impact of using anisotropic metal foams for thermal energy storage has not been addressed yet. In the current research, an anisotropic metal foam was modeled mathematically with engineered local properties in perpendicular directions. The solid-liquid phase transition of the copper-coconut oil LHTES unit was simulated using the finite element method. The anisotropic metal foam was defined by using an anisotropic parameter and angle. The simultaneous impact of the mounting tilt angle and the anisotropic angle of the copper foam were addressed in the phase transition behavior and charging time of the LHTES unit. The results revealed that the anisotropic angle could notably impact the thermal energy storage power. An optimum tilt angle of -45° or +45° along with a 0° anisotropic angle could lead to the maximum charging power. Thus, designing an LHTES unit using an anisotropic metal foam could save the charging about 15% (for a -45° inclination angle) and 20% (for zero inclination angle) compared to a regular metal foam. Such save in the charging time is without any penalty on the weight increase or capacity reduction for the LHTES unit. A schematic view of an LTHES unit and its modeling approach is depicted. A solar collector absorbs the heat and transfers it to an LHTES, where the PCM modules store the heat through a melting process. Each of the storage modules can be considered a rectangular channel which was modeled as a 2D rectangle. [Display omitted] [ABSTRACT FROM AUTHOR]

The incorporation of simultaneous passive and active techniques for enhancing heat transfer has been a promising area of research in the last decades. As such, in the present study, thermal convection heat transfer of a hybrid nanofluid in a square cavity subjected to simultaneous effects of gravitational and vibrational forces has been addressed. Initially, the cavity, saturated with Ag-MgO hybrid nanofluid, is stagnant and in thermal equilibrium. Then, the sidewalls of the cavity are heated isothermally, and the cavity starts vibrating in a vertical direction. The upper and lower walls are kept adiabatic. Galerkin finite element method with a very small- and adaptive-time step has been used to precisely capture the impact of vibrational force on the flow and thermal fields in high frequencies. Impacts of vibration frequency, gravitational and vibration Rayleigh numbers, and the volume fraction of hybrid nano-additives are studied. It has been revealed that the external vibration amplifies the rate of heat transfer for all the studied frequencies. Moreover, although the presence of the nanoparticles seems to have a very limited effect on the effectiveness of heating, the effect of the nanoparticle concentration on the heat transfer intensity varies with time. [ABSTRACT FROM AUTHOR]

This study aims to assess the natural convection heat transfer in a square cavity wherein the buoyancy-induced flow is generated by a thin flexible heater-plate inside the cavity. The vertical walls of the cavity are cold and the horizontal walls are adiabatic. The thin hot plate is assumed to be isothermal and fixed at an alterable point in the middle of the cavity with different inclination angles. To analysis the fluid-structure interaction (FSI), the finite element method along with the Arbitrary Lagrangian-Eulerian (ALE) technique is employed. Isotherms and streamlines, as well as the average Nusselt number, the dimensionless temperature in the cavity, and the maximum applied stress on the flexible plate, are studied. The results are presented as a function of Rayleigh number, Prandtl number, inclination angle, and different positions of the fixed point. The outcomes indicate the importance of the inclination angle and the position of the fixed point of the hot plate. The plate experiences significantly large values of stress when it is mounted horizontally. In the case of a plate fixed at its top, the highest stress occurs with an inclination angle of 40°. In contrast, the lowest stress is associated with the plate when it is positioned vertically. • Free convection in an enclosure containing a flexible hot thin-plate is addressed. • An Arbitrary Lagrangian-Eulerian technique is utilized to model fluid-structure interaction. • The plate is fixed at different locations with different inclination angles. • The influence of the location of the fixed point on the heat transfer investigated. • The position of the fixed point notably influences the deformation of plate and heat transfer. [ABSTRACT FROM AUTHOR]

• The magnetic field in non-uniform in space. • Two magnetic-sources were employed to control the flow and heat transfer. • Deformed mesh technique is employed to track the melting interface. • MHD and FHD effects due to Lorentz and Kelvin forces are taken into account. • Hartman number can drastically decline the progress of the melting front. A uniform melting of a metal or polymer is essential for the quality of products. In a melting process, the convection flows affect the heat transfer, and result in a non-uniform melting process. The presence of a magnetic-field can control the flow and heat transfer by Lorentz and Kelvin forces. The present study aims to analyze the effect of the presence of two magnetic sources on the melting flow and heat transfer in a cavity. Here, the process of heat absorption by the PCM-filled enclosure that is exposed to two non-uniform magnetic-fields is numerically studied. The strengths of two magnetic-fields are not necessarily the same. Tracking the interface of solid and fluid portions of phase change material is performed using the deformed mesh technique. Galerkin finite element method, along with the Arbitrary Lagrangian-Eulerian is applied to solve the characteristic equations. The results show that the progress of the melting front completely depends on the intensity ratio of two non-uniform magnetic-fields γ r. Besides, although the magnetic number has a slight effect on the melting, an increase in Hartman number can drastically decline the progress of the melting front. [ABSTRACT FROM AUTHOR]