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This investigation centers on the design and performance of a solar-assisted domestic radiator optimized for nearly zero-energy buildings (nZEBs), combining experimental and numerical approaches. The system is powered by a Photovoltaic/Thermal (PV/T) collector, customized to the climatic specifics of Elazığ, Turkey. The study introduces nano-enhanced Phase Change Materials (NEPCM) embedded with Boron Carbide (B4C) nanoparticles to improve efficiency. The NEPCM demonstrating the highest thermal conductivity and specific heat capacity, was selected for numerical analysis. These NEPCM were strategically integrated into the radiator system to maintain ambient room temperatures without additional energy input, particularly during non-solar periods like nighttime. The analysis, conducted under turbulent flow conditions using the finite volume method, reveals that NEPCM significantly improves indoor temperature regulation. The most notable temperature differential, 2.82 K, was observed between configurations with and without PCM. However, the comparison between NEPCM and pure PCM with halved thickness shows a minimal temperature difference of 0.62 K, indicating a slight improvement due to nanoparticle inclusion. These findings highlight both the potential benefits and the limitations of integrating NEPCM into domestic heating systems for sustainable building applications.

The research explores the use of iron oxide nanoparticles to enhance the thermal properties of fluids like water and ethylene glycol. These nanoparticles find applications in engineering and medicine, including wastewater treatment and coatings. The study investigates magnetic nanoparticle movement in a permeable enclosure, considering heat, magnetic field, and electromagnetic effects. Using the MAC method, dimensionless equations were solved, and results were presented through graphs, charts, and tables. Findings show nanoparticle volume significantly impacts heat transfer in nanofluids compared to base fluids. Increasing nanoparticle volume from 0 to 0.05 improved nanofluid heat transfer by 0.278% and base fluid by 0.303%. Heat absorption and generation improved nanofluid transfer by 15.819% and base fluid by 0.596%. Nusselt number increased with higher Eckert number and heat source/sink parameters in both nanofluids and base fluids.

Introduction: Nanofluids are considered a better alternative to conventional fluids in many industrial situations and unfolding new opportunities for various applications owing to the optical and thermal properties of additive nanosized materials. Objectives: In this study, the thermal and hydraulic characteristics of a Casson-based (sodium alginate) multiwall carbon nanotube (MWCNT) nanofluid were computationally investigated inside a wavy square enclosure containing a circular-shaped obstacle. The square enclosure comprised two cooled vertical walls and a wavy adiabatic top wall. The central part of the bottom wall comprised a heated wavy structure, and the remaining parts exhibited a flat and adiabatic structure. Methods: The Navier–Stokes (N–S) equations and boundary conditions were established using the non-Newtonian Casson fluid model and Rosseland thermal radiation. The present problem was numerically simulated using the Galerkin finite element method for three types of obstacles, namely, adiabatic, hot, and cold. The impacts of Casson parameter (0.001 ≤ β ≤ 0.1), Rayleigh number (103 ≤ Ra ≤ 106), nanoparticle volume fraction (0.01 ≤ φ ≤ 0.1) and radiation parameter (1 ≤ Rd ≤ 4) are analysed. A numerical code validation was performed using the available benchmark results. Results: The characteristics of the convective radiation heat transport were clearly analyzed through the stream function and isotherm plots. For all types of obstacles, the mean Nusselt number along the heated wavy wall increased with the Casson parameter, MWCNT volume fraction, Rayleigh number, and radiation parameter. Conclusion: The heat and flow characteristics of a Casson-based MWCNT nanofluid inside a wavy square enclosure were investigated. The mean Nusselt number was higher (lower) in the presence of cold (hot) obstacles.

Phase change dynamics under the rotational surface effects, area expansion and nanoparticle loading in the base fluid are explored for forced convective flow of hybrid nanofluid in a phase change packed bed installed cylindrical reactor. The study is performed with finite element method for different parameters of rotational Reynolds number, fluid stream Reynolds number and concentration of nanoparticle. The hybrid nanofluid properties are based on experimental data for binary particle of Al2O3-TiO2 in 40% ethylene–glycol. Complete phase transition time is estimated with ANFIS based model. The recirculation zone due to the area expansion within the phase change installed region is controlled by the complex interactions between the forced flow, rotation of the surface and nanoparticle amount. Higher values of Reynolds number and nanoparticle concentration result in fast phase change process at rotational Reynolds number of 0 while the effects become reverse in the presence of rotations. Complete phase transition time reduces by about 49% and 10.5% at the highest Reynolds number and at the highest concentration in the absence of rotation while it is increased by about 88% and 6.5% when rotational effects are considered at the highest rotational speed. When only rotational effects are considered, phase change process completion time reduces by about 60% at the highest speed.

Performance features of a thermoelectric system mounted in a chaotic channel with non-Newtonian power law fluid are numerically explored with finite element method. The analysis is performed for different values of Re number of the hot and cold fluid streams (250⩽Re⩽1000), power law indices (0.75⩽n⩽1.25) and solid volume fraction of alumina (0⩽ϕ⩽4%) in water. It is observed that the fluid type with different power law indices significantly affected the electric potential variations and power generation of the thermoelectric system. Impacts of Re number on the power generation enhancement amount depends upon the power law index. The power rises by about 123.78%, 94.13% and 52.30% at the highest Re for different power law index combinations of (0.75,0.75), (0.75,12.5) and (1.25,1.25), respectively. Thermoelectric power reduces by about 39.71% for shear thinning fluids in both channels while it rises by about 43.48% for shear thickening fluids in chaotic channels. The potential of using nanofluids is more when both channels contain shear thinning fluids. Nanofluids rise the power of thermoelectric system by about 31%, 29% and 28% for the case when the hot side fluid is shear thinning, Newtonian and shear thickening fluid types while the cold side chaotic channel is shear thinning. When constant and varying interface temperature configurations are compared, there is at most 3% variations in the generated power while the trends in the curves for varying parameters are similar. The computational cost of constant interface temperature and computations only in the thermoelectric domains are much cheaper as compared to high fidelity coupled computational fluid dynamics simulations. The temperature field in the whole computational domain is approximated by using POD based approach with nine modes. A polynomial type regression model is used for POD-modal coefficients while fast and accurate results for interface temperatures are obtained.

The investigation is carried to observe the impact of radiation on the MHD couple stress hybrid nanofluid over porous sheet with dissipation. The water based MHD couple stress hybrid nanofluid flow due to porous shrinking sheet with thermal radiation and viscous dissipation has range of engineering applications dealing with energy distribution, solar energy storage, chemical reactors and polymer production. The flow problem is mathematically modelled into nonlinear partial differential equations, which are transformed into set of ordinary differential equations via similarity variable. The analytical solutions are derived in the form of hypergeometric functions. These results are in line with the existing classical results. The physical insights on the impact of MHD, mass transpiration, Eckert number, Couple stress, porosity and thermal radiation on velocity and temperature profiles are provided by means of graphs.

Effects of using nanoliquid and double porous elliptic objects on the flow separation and convective heat transfer control for flow over multiple heated blocks in channel are numerically investigated by using finite element method. Spherical, brick, blade and cylindrical shaped alumina particles are used in water up to solid volume fraction of 2%. Impacts of Reynolds number (50≤Re ≤ 500), permeability of the porous ellipses (10−5≤Da1≤5 × 10−2 and 10−5≤Da2≤5 × 10−2), aspect ratio of the ellipses (0.25≤AR1≤1.5, 0.25≤AR2≤1.5), distance between the ellipses (0.2H ≤ sx ≤ 1.6H) and distance of the first ellipse from inlet (−H ≤ mx ≤ H) on the hydro-thermal performance are explored. The highest performance improvement is obtained by using the cylindrical shaped particles in the base heat transfer fluid at the highest solid volume fraction and the amount of heat transfer enhancement are 33% and 40.5% for hot blocks while negligible pressure drop is observed. Varying the aspect ratio of the ellipses in the perpendicular direction to the flow, up to 25% and 30% heat transfer increment are obtained for hot block with slight rise of pressure coefficient. However, when varying the horizontal location of the porous ellipses in the channel and permeability of them, there is considerable rise of pressure drop. Variation of the average heat transfer from the hot blocks with varying permeability of the ellipses are obtained as 32% and 25%. Successful hydro-thermal performance estimation results are achieved by using artificial neural networks with feed-forward network architecture of 1 hidden layer and 17 neurons.

< p>In this paper, the lattice Boltzmann approach is carried out to study the double-diffusive natural convection in a space encapsulating liquid metal is presented. The Uniform magnetic field is applied horizontally at the square domain and an insulated rectangular block is kept stationary at the center of the cavity. The linear increment of temperature and concentration is used at the left wall and cold temperature is applied at the right wall. Horizontal walls are adiabatic conditions. Horizontal walls are adiabatic conditions. The numerical analysis is performed at the range of Rayleigh number (103 ≤ Ra ≤ 105), Lewis number (2 ≤ Le ≤ 10), buoyancy ratio (-2 ≤ N ≤ 2), Hartmann number (0 ≤ Ha ≤ 50) with Prandtl number (Pr) = 0.054. Results show that the increase in Ra tends to maximize heat and mass transfer rate while increasing Ha, decreases the same. The rise in Le diminishes heat transfer marginally but increasing the mass transfer significantly. The effect of N differs with different operating conditions, in general, the rate of heat and mass transfer is found to decrease with a decrease of N value.

This study presents the numerical results relative to the development of heat transfer and pressure drop inside a corrugated channel, under constant heat flux conditions applied to the walls; the working fluid is air. The test section is a channel with two plates having trapezoidal-shaped corrugations with V-folds. The corrugated plates were placed inside a 12.5 m high channel and tested for three different inclination angles, i.e. 20°, 40° and 60°. The model was simulated for a heat flux of 0.58 kW /m2, while the Reynolds numbers were considered within the interval ranging from 600 to 1400. The standard turbulent model (k-ε) was employed to simulate the flow and heat transfer developments within the channel. In addition, the governing equations were solved using the finite volume method in a structured uniform grid arrangement. Moreover, the effects of the geometric parameters on heat transfer and flow evolution were discussed as well. It is also worth noting that the corrugated surface had a significant impact on the enhancement of heat transfer and pressure drop due to breakage and destabilization occurring in the thermal boundary layer.

It is important to consider the thermal management of lithium-ion batteries to overcome their limitations in usage and improve their performance and life cycles. In this study, a novel cooling system for the thermal management of lithium-ion battery packs is proposed by using an inner cylinder in the cooling channel and different-shaped nanoparticles in the base fluid, which is used as the cooling medium. The performance improvements in a 20 Ah capacity battery are compared by using a water–boehmite alumina (AlOOH) nanofluid, considering cylinder-, brick-, and blade-shaped nanoparticles up to a solid volume fraction of 2%. The numerical analysis is conducted using the finite element method, and Reynolds numbers between 100 and 600 are considered. When the efficacy of the coolants utilized is compared, it is apparent that as the Reynolds number increases, both cooling media decrease the highest temperature and homogenize the temperatures in the battery. The utilization of the cylinder in the mini-channel results in a 2 °C temperature drop at Re = 600 as compared to the flat channel. A boehmite alumina nanofluid with a 2% volume fraction reduces the maximum temperature by 5.1% at Re = 200. When the shape effect of the nanofluid is examined, it is noted that the cylinder-shaped particle improves the temperature by 4.93% as compared to blade-shaped nanoparticles and 7.32% as compared to brick-shaped nanoparticles. Thus, the combined utilization of a nanofluid containing cylindrical-shaped nanoparticles as the cooling medium and a cylinder in the mini-channel of a battery thermal management system provides an effective cooling system for the thermal management of the battery pack. The outcomes of this work are helpful for further system design and optimization studies related to battery thermal management.

Heat transfer augmentation is a modern challenge in various engineering fields including heat exchangers, electronics, chemical and bio reactors, and others. Nanofluids as a new heat transfer liquids can be considered as effective media for increment of energy transport. Such gain is getting due to an increase in the effective thermal conductivity and change in the fluid flow dynamics. In the case of hybrid nanofluids when we can include two or several nanoadditives to the host liquid one can obtain more essential enhancement of transport processes. Therefore, this paper deals with the energy augmentation using hybrid nanofluids. The objective is to find exact analytical solutions to the unsteady hybrid nanofluid flow with heat transfer past an infinite flat vertical plate with a ramped temperature profile concerning time. The effects of various hybrid nanofluids on the unsteady flow and heat transfer features in the presence of the magnetic field, thermal radiation and a temperature-dependent heat source are explored. Results of radiation parameter, heat source parameter, magnetic parameter and nanoparticle volume fraction obtained by employing the Laplace transform technique for engineering variables such as skin friction coefficient and Nusselt number along with velocity and temperature profiles are analyzed using graphs. It has been found that a growth of the average Nusselt number occurs with the nanoparticle volume fraction, while this augmentation can be improved with use of hybrid nanofluid.

In the present work, coupled effects of forced convection, rotational conic surface and magnetic field on the phase change dynamics are numerically explored by using finite element method for a phase change material (PCM) filled 3D cylindrical reactor. The PCM filled region has a conic shape and it is rotating. The study is conducted for various values of rotational Re number (between 0 and 2500), magnetic field strength (Hartmann number between 0 and 30) and conic surface aspect ratio (between 1 and 2). It is observed that the coupled interactions between the rotational surface and magnetic field significantly affect the phase change process dynamics and convective heat transfer between different phases. Optimum value of rotational Reynolds number for minimum complete phase transition time is achieved at Rew = 1000. The magnetic field has a positive impact on the phase change process while it is impact is profound without surface rotation. There are 98% and 65% reductions in the complete phase transition times when configurations at Rew = 1000 are compared with motionless conic surface case in the absence and presence of magnetic field. The effects of rotation are profound when different aspect ratios of the PCM filled region is considered. The transition time is increased up to 553% without rotation while this value is only 86% when cases with lowest and highest aspect ratio are compared. A modal analysis with 30 mode is used to capture the phase change dynamics and coupled interactions between the rotational surface and magnetic field on the variation of liquid fraction.

Three-dimensional computational analysis has been performed to investigate the melting time of the phase change material (PCM) in a sinusoidal pipe inserted into another pipe. The other pipe is filled with PCM and the system is heated from the inner sinusoidal pipe at different temperatures. The main aim of the study is to control the melting time. The finite volume method (FVM) is used to solve time-dependent governing equations. Four different cases are chosen for the sinusoidal wall to see the effects of geometry on melting. After the analysis, it is observed that melting time can be controlled via an adjustment of the geometrical parameter, namely a passive technique, without spending extra energy.

In this study, impacts of using a sinusoidal shape encapsulated phase change material (PCM) packed bed (PB) system on the phase change and thermal performance are analyzed in multi-port vented cavity under a partially active magnetic field during hybrid nanoliquid convection. The current study is performed for different magnetic field strengths of domains (Hartmann number between 0 and 50), wave number (between 1 and 8), wave amplitude (between 0.01 H and 0.15 H), and nanoparticle loading (between 0 and 2%) by using the finite element method. The sinusoidal shape of the PCM-PB zone and varying its geometrical form are both found to affect the phase change process and thermal performance. When wave amplitude (Hp) rises from 0.01 H to 0.15 H, full phase change time (t-fr) increases by about 33% while average Nu increases by about 55%. When a partially active magnetic field is imposed at the highest value, up to 30.3% reduction in t-fr is obtained, while average Nu rises by about 9% at t = 18 min. The value of t-fr is reduced by about 15% while spatial average Nu rises by about 55% at the highest nanoparticle loading.

This review is about non-Newtonian nanofluid applications for convection in cavities under a magnetic field. Convection in cavities is an important topic in thermal energy system, and diverse applications exist in processes such as drying, chemical processing, electronic cooling, air conditioning, removal of contaminates, power generation and many others. Some problems occur in symmetrical phenomena, while they can be applicable to applied mathematics, physics and thermal engineering systems. First, brief information about nanofluids and non-Newtonian fluids is given. Then, non-Newtonian nanofluids and aspects of rheology of non-Newtonian fluids are presented. The thermal conductivity/viscosity of nanofluids and hybrid nanofluids are discussed. Applications of non-Newtonian nanofluids with magnetohydrodynamic effects are given. Different applications of various vented cavities are discussed under combined effects of using nanofluid and magnetic field for Newtonian and non-Newtonian nanofluids. The gap in the present literature and future trends are discussed. The results summarized here will be beneficial for efficient design and thermal optimization of vented cavity systems used in diverse energy system applications.

In this study, numerical analysis and optimization for the convective heat transfer and fluid flow over a facing step in the presence of an elliptic shaped porous object located downstream of the step are considered. The COBYLA optimization algorithm is used to find the optimum location and size of the porous object in order to maximize average Nu number. Air and nano-diamond/Fe3O4 hybrid nanofluid as the coolant in the thermo-fluid system. It is observed that the presence of the obstacle, varying its permeability, aspect ratio and location in the channel profoundly affect the fluid flow features and improvement amount in the heat transfer rate. The average Nu number is first reduced by about 14.7% and then increased by about 6.8% when the permeability of the object is increased. The optimum value of the Nu number is found as 2.037 while the optimum location and sizes are found as (Sx, Sy, r1, r2)=(0.538H,0.4509H,0.2138H, 0.348H) when air is used as heat transfer fluid. The average heat transfer rate is reduced with higher aspect ratio while the value of Nu number at the optimum point is 33% higher as compared to case with aspect ratio of 0.5. The average Nu number variation shows non-monotonic behavior for horizontal location of the object. When the object is closer to the top wall, the average Nu number becomes higher while the value at the optimum point is 19.8% higher in the parametric study. At the optimum operating point, hybrid nanoparticle addition in the fluid brings further enhancement of 28.4% in the average heat transfer.

Impacts of using double rotating cylinders and partly porous layers in the bifurcating channels on the hydro-thermal performance were numerically assessed. Hybrid nanoparticles were used in water and finite element method was selected as the solver. Effects of Reynolds number, rotational speeds of the cylinders and their locations in the bifurcating channels, porous layer sizes and nanoparticle solid volume fractions on the hydro-thermal performance features were explored. The contribution of different hot wall parts was changed with varying Reynolds number and rotational velocity of the cylinders. Depending upon the rotational direction of the cylinders, the vortex occurrence and size at the bifurcations change significantly. Heat transfer considering all hot walls rise with higher rotational speeds in both directions. The amount of improvement in the heat transfer rate becomes 25% and 19% with varying speeds of the cylinders as compared to motionless cylinders. The pressure coefficient reduces with increasing the second cylinder speed in clockwise direction and this is favorable for thermal performance since the heat transfer also increases. The overall impact of the varying horizontal locations of the cylinders on the heat transfer rate is slight. The separated zones at the branching depends on the porous layer sizes. The overall heat transfer behavior becomes opposite when varying the sizes of the porous layers in the horizontal and vertical channels. By using nanoparticles in the base fluid, 35.75% improvement in the heat transfer rate is achieved for vertical wall at Re = 350 while pressure drop coefficient rises by about 8.5%. The overall improvement in the heat transfer rate by using nanofluid is 26%. Owing to diverse use of bifurcating channels in thermal engineering from fuel cells to electronic cooling, the proposed methods of heat transfer enhancement techniques can be considered simultaneously for effective control the thermal performance of those systems.

This paper presents a modelling of nanofluid flow using Caputo fractional derivatives through conservative equations of mass and momentum, and provides an exact solution on un-steady convective flow over a vertical plate with the mass diffusion effect, in association with an energy equation. H2O is the base liquid with clay nanoparticles floating in it in a uniform way. Boussinessq’s approach is used in the momentum equation for pressure gradient. The non-dimensional fluid temperature, species concentration and fluid transport are derived together with Jacob Fourier sine and Laplace transform techniques in terms of exponential decay function, and the inverse is computed further in terms of the Mittag-Leffler function. The impact of various physical quantities is interpreted with the fractional order of the Caputo derivatives. The obtained temperature, transport and species concentration profiles show behaviors for 0 < α < 1, where α is the fractional parameter. The rate of heat and mass transfer coefficients for the significance of physical quantities of interest are also obtained and presented through graphs. The impact of the nanoparticle volume fraction on the flow field is observed. At larger values of the fractional parameter, the velocity, temperature, and concentration distributions grow more quickly. In addition to that, it is found the concentration profiles behave in the opposite way for the volume fraction of nanofluids.

The effects of using a partly curved porous layer on the thermal management and entropy generation features are studied in a ventilated cavity filled with hybrid nanofluid under the effects of inclined magnetic field by using finite volume method. This study is performed for the range of pertinent parameters of Reynolds number (100≤Re≤1000), magnetic field strength (0≤Ha≤80), permeability of porous region (10−4≤Da≤5×10−2), porous layer height (0.15H≤tp≤0.45H), porous layer position (0.25H≤yp≤0.45H), and curvature size (0≤b≤0.3H). The magnetic field reduces the vortex size, while the average Nusselt number of hot walls increases for Ha number above 20 and highest enhancement is 47% for left vertical wall. The variation in the average Nu with permeability of the layer is about 12.5% and 21% for left and right vertical walls, respectively, while these amounts are 12.5% and 32.5% when the location of the porous layer changes. The entropy generation increases with Hartmann number above 20, while there is 22% increase in the entropy generation for the case at the highest magnetic field. The porous layer height reduced the entropy generation for domain above it and it give the highest contribution to the overall entropy generation. When location of the curved porous layer is varied, the highest variation of entropy generation is attained for the domain below it while the lowest value is obtained at yp=0.3H. When the size of elliptic curvature is varied, the overall entropy generation decreases from b = 0 to b=0.2H by about 10% and then increases by 5% from b=0.2H to b=0.3H.

Mixed convection of ferrofluid filled lid driven cavity in the presence of two rotating cylinders were numerically investigated by using the finite element method. The cavity is heated from below, cooled from driven wall and rotating cylinder surfaces and side vertical walls of the cavity are assumed to be adiabatic. A magnetic dipole source is placed below the bottom wall of the cavity. The study is performed for various values of Reynolds numbers (100 ≤ Re ≤ 1000), angular rotational speed of the cylinders (−400 ≤ Ω ≤ 400), magnetic dipole strengths (0 ≤ γ ≤ 500), angular velocity ratios of the cylinders (0.25≤Ωi/Ωj≤4) and diameter ratios of the cylinders (0.5≤Di/Dj≤2). It is observed that flow patterns and thermal transport within the cavity are affected by variation in Reynolds number and magnetic dipole strength. The results of this investigation revealed that cylinder angular velocities, ratio of the angular velocities and diameter ratios have profound effect on heat transfer enhancement within the cavity. Averaged heat transfer enhancements of 181.5 % is achieved for clockwise rotation of the cylinder at Ω = −400 compared to motionless cylinder case. Increasing the angular velocity ratio from Ω2/Ω1=0.25 to Ω2/Ω1=4 brings about 91.7 % of heat transfer enhancement.

Bu çalışmada, L şeklindeki bir oyukta doğal taşınımla ısı transferi sayısal olarak incelenmiştir. Oyuğun bir tarafı soğuk, diğer taraf ise sıcak olarak alınmıştır. Tavan ve taban kısımları yalıtımlıdır. Doğal taşınım ısı transferini yöneten denklemler, bir sonlu hacim üzerinden integre edilerek tekil denklemler elde edilmiştir. SIMPLEM çözüm algoritmasını kullanan bir bilgisayar programı yapılmıştır. Hesaplamalar, Rayleigh sayısının 10 4 < Ra < 10 6 değerleri için elde edilmiştir. L şeklinin boyutları değiştirilerek hesaplamalar gerçekleştirilmiştir.

In this study, natural convection in a L-shaped enclosure was investigated numerically. The left hand side of enclosure is cooler than the right hand side of wall. Bottom and top walls are insulated. Governing equaitons for natural convection have been integrated over a finite control volume to obtain finite difference equations. For the solution a computer program was developed using SIMPLEM algorithm was used. Calculations were performed in the range of 10 4

A three dimensional computational solution has been obtained to investigate the natural convection and entropy generation of nanofluid-filled open cavities with an adiabatic diamond shaped obstacle. In the model, the finite volume technique was used to solve the governing equations. Based on the configuration, the cavity is heated from the left vertical wall and the diamond shape was chosen as adiabatic. Effects of nanoparticle volume fraction, Rayleigh number (103 ≤ Ra ≤ 106) and width of diamond shape were studied as governing parameters. It was found that the geometry of the partition is a control parameter for heat and fluid flow inside the open enclosure.

In this article, entropy generation due to natural convection in entrapped trapezoidal cavities filled with nanofluid under the influence of magnetic field was numerically investigated. The upper (lower) enclosure is filled with CuO-water (Al2O3-water) nanofluid. The top and bottom horizontal walls of the trapezoidal enclosures are maintained at constant hot temperature while other inclined walls of the enclosures are at constant cold temperature. Different combinations of Hartmann numbers are imposed on the upper and lower trapezoidal cavities. Numerical simulations are conducted for different values of Rayleigh numbers, Hartmann number and solid volume fraction of the nanofluid by using the finite element method. In the upper and lower trapezoidal cavities magnetic fields with different combinations of Hartmann numbers are imposed. It is observed that the averaged heat transfer reduction with magnetic field is more pronounced at the highest value of the Rayleigh number. When there is no magnetic field in the lower cavity, the averaged Nusselt number enhances as the value of the Hartmann number of the upper cavity increases. The heat transfer enhancement rates with nanofluids which are in the range of 10% and 12% are not affected by the presence of the magnetic field. Second law analysis of the system for various values of Hartmann number and nanoparticle volume fractions of upper and lower trapezoidal domains is performed.