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The purpose of this study is the identification of the best method to apply the body force in the lattice Boltzmann method (LBM). In the simulation of mixed convection, especially for large Richardson number flows in a square cavity.

First, three methods for applying the body force were compared to each other in the LBM. Then, an LBM-based code was written in the FORTRAN language using these three methods. Next, that code was used to simulate natural/mixed convection in a two-dimensional cavity to evaluate the methods for applying the body force. Finally, the optimum way for applying the body force was used for the simulation of free convection heat transfer in a concentric annulus with Rayleigh number in a range of 1,000 to 50,000, and mixed convection heat transfer in a concentric annulus with Rayleigh number in a range of 10,000 to 50,000 and Reynolds number in a range of 100 to 400.

Mixed convection heat transfer was simulated in a two-dimensional cavity with Richardson number in a range of 0.0001 to 100. The results which were obtained in low Richardson number flows have shown good adaptation to the available data. However, the results of large Richardson number flows, for example, Ri = 100, have shown a significant difference to the available data. Investigations revealed that this difference was due to the method of applying the body force. Therefore, the choice of the best way to apply the body force was investigated. Finally, for the large Richardson number flows, the best method to apply the body force has been identified among the several techniques.

To the authors’ knowledge, the effects of methods for applying the body force were not investigated in the cavities mixed convection, even though there are numerous investigations conducted on mixed convection with the LBM. In this study, the effects of techniques to apply the body force were investigated in large Richardson number flows. Finally, the best method to apply the body force is distinguished between several techniques for the large Richardson number mixed convection flows.

The purpose of this study is to analyze the effect of using a ceiling fan with central heating system in the winter on thermal comfort and heat transfer rate in a three-dimensional numerically.

The geometry had certain dimensions, and an occupant was modeled to be in the room. In models which were used, the flow was turbulent, and turbulence models were used for simulating turbulence. Between all the models, k-ε model had best matching.

Results show that using the ceiling fan during the winter had an efficient and considerable effect on improving the thermal comfort and energy saving inside buildings. By the use of ceiling fan, the effective room temperature has increased by 2.5°C. Furthermore, results show that by using ceiling fan in the winter, the predicted mean vote and the predicted percentage dissatisfied indexes improved. At the end, the case Room 11-0.05-15 with temperature of 87°C for radiator and normal fan velocity of o.25m/s were the optimal model that caused the complete thermal comfort and reduced energy consumption up to 28 per cent.

In the present study, the effects of using the ceiling fans on human comfort condition and heat transfer field during the winter (heating system) are studied. Following are the goals for all models: getting the appropriate temperature for radiator so that thermal comfort condition can be applied at the height of 75 cm of the room, velocity for fan so that air speed can be 0.25m/s at the height of 2 m or lower of the room and position to place the fan.

The purpose of this paper is to study the effects of using different Brownian models on natural and mixed convection fluid flow and heat transfer inside the square enclosure filled with the AlOOH–water nanofluid.

Due to fulfill of this demand, five different models for the effective thermal conductivity and viscosity of the nanofluid are considered. The following results are presented for the Ra=10⁷ to 10¹⁰ and Ri=0.01 to 100, whereas the volume fraction of the nanoparticles is varied from φ = 0.01 to 0.04.

According to the obtained results, increasing of Rayleigh number and reduction of Richardson number leads to the higher values of the average Nusselt number and entropy generation. Also, it is realized that, variation trend of the average Nusselt number and entropy generation in all cases is increasing by growing the volume fraction. It is found that the obtained average Nusselt numbers and entropy generations with Koo and Kleinstreuer are the highest among all the studied cases, and it is followed by Patel, Vajjha and Das, Corcione and Maxwell–Brinkman models, respectively.

Based on the results of present investigation, the Nusselt number difference predicted between the Maxwell–Brinkman model (as constant-property model) and Koo and Kleinstreuer model is about 7.84 per cent at 0.01 per cent volume fraction and 5.47 per cent at 0.04 per cent volume fraction for the Rayleigh number equal to 107. The entropy generation difference predicted between the two above studied model is about 8.05 per cent at 0.01 per cent volume fraction and 5.86 per cent at 0.04 per cent volume fraction for the Rayleigh number equal to 107. It is observed that using constant-property model has a significant difference in the obtained results with the results of other variable-property models.

The purpose of this paper is to apply the numerical methods to study the heap leaching process in a bed of porous and spherical ore particles. This study is performed in two stages: first, modeling the leaching process of a soluble mineral from a spherical and porous ore particle to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the particles (the particle model), and second, modeling the heap leaching of the mineral from a porous bed consisting of spherical and porous ore particles to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the bed (the bed model).

The governing equations are derived for the particle model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised on a uniform spherical grid fitted to the particle using finite difference method. The resulting algebraic equations are solved using Tri‐Diagonal Matrix Algorithm, and the governing equations are derived for the bed model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised explicitly on a one‐dimensional and uniform grid fitted to the bed. The unknown quantities are evaluated using the corresponding values at the previous time interval.

The results obtained from numerical modeling show that, when the particle has a low diffusion resistance or a high chemical resistance, the reaction takes place slowly and homogeneously throughout the ore particle. On the other hand, when the bed has a low convection resistance, the reaction takes place homogeneously throughout the bed. As the convection resistance increases, the non‐homogeneous (local) behavior predominates. It is also noticed that, when the chemical reaction resistance is high, the reaction takes place homogeneously throughout the bed.

The dynamic diffusion and movement of solution in the ore particles and ore bed are not modeled and volumetric ratio of solution in the particles and the bed and also vertical velocity of solution in the bed are assumed to be fixed constants.

This study shows that the reaction takes place homogeneously throughout the bed when the convection resistance is low, the diffusion resistance is high, the concentration resistance is low, and the chemical reaction resistance is high.

Homogeneous reaction conditions being suitable for heap leaching operations are identified. Thus, it is recommended to approach the above conditions when preparing ore heaps and designing the relevant operation.

The purpose of this paper is to investigate thermohydraulic characteristics of turbulent flow of water (4,000 = Re = 10,000) in a rectangular channel equipped with perforated chevron plat-fin (PCPF) with different vortex generators (VGs) shapes.

First, three general shapes of VGs including rectangular, triangular and half circle, are compared to each other. Then, the various shapes of rectangular VGs, (horizontal, vertical and square) and triangular VGs, (forward, backward and symmetric) are evaluated. To comprehensively evaluate the thermohydraulic performance of the PCPF with various VG shapes, the relationship between the Colburn factor and the friction factor (j/f) is presented, then a performance index (η) is applied using these factors.

Results show that the enhanced models of the PCPF, which are equipped with VGs, have higher values of j/f ratio and η as compared with the reference model (R). Further, the half-circle VG with the lowest pressure drop values (about 2.4% and 4.9%, averagely as compared with the S and ST vortex generators), shows the highest thermohydraulic performance among the proposed shapes. The maximum of performance index of 1.14 is found for the HC vortex generator at Re = 4,000. It is also found that the square and forward triangular VGs, have the best thermohydraulic performance among the rectangular and triangular VGs respectively and the highest performance index of 1.13 and 1.11 are reported for these VGs.

The thermohydraulic performance of the PCPF with different vortex generators VGs shapes have been investigated.

The aim of this study is to investigate the effects of two-phase nanofluid model on mixed convection in a double lid-driven square cavity in the presence of a magnetic field. The authors believe that this work is a good contribution for improving the thermal performance and the heat transfer enhancement in some engineering instruments.

The current work investigates the problem of mixed convection heat transfer in a double lid-driven square cavity in the presence of magnetic field. The used cavity is filled with water-Al₂O₃ nanofluid based on Buongiorno’s two-phase model. The bottom horizontal wall is maintained at a constant high temperature and moves to the left/right, while the top horizontal wall is maintained at a constant low temperature and moves to the right/left. The left and right vertical walls are thermally insulated. The dimensionless governing equations are solved numerically using the Galerkin weighted residual finite element method.

The obtained results show that the heat transfer rate enhances with an increment of Reynolds number or a reduction of Hartmann number. In addition, effects of thermophoresis and Brownian motion play a significant role in the growth of convection heat transfer.

According to above-mentioned studies and to the authors’ best knowledge, there has no study reported the MHD mixed convection heat transfer in a double lid-driven cavity using the two-phase nanofluid model. Thus, the authors of the present study believe that this work is valuable. Therefore, the aim of this comprehensive numerical study is to investigate the effects of two-phase nanofluid model on mixed convection in a double lid-driven square cavity in the presence of a magnetic field. The authors believe that this work is a good contribution for improving the thermal performance and the heat transfer enhancement in some engineering instruments.

The purpose of this paper is to predict the plate heat exchanger performance when axial conduction in plates and in flow channels are present and fluids' viscosities are temperature dependent.

The approach to achieve the objective of the paper is deriving the governing equations and developing a computer program based on finite differences to solve them. The governing equations become dimensionless defining reference values and then discretized using FTBCS and FTCS methods. To solve the governing equations, the flow channel is divided into small elements in axial direction. Physical properties are constant for each element, while viscosity changes from one element to another one.

The effect of axial conduction in plates as well as in flow channels on temperature distributions, are studied individually and simultaneously. The program is run under four different conditions, namely: no axial conduction, axial conduction in the plates and in the flow channels, axial conduction in the plates only, and axial conduction in the flow channels only.In all the above cases, temperature distributions are achieved and characteristic curves are plotted. The numerical results are validated by comparing them with those published in an established reference carried out ignoring the effect of axial conduction, using the same plate geometry and flow details.

This paper gives valuable information and offers practical help to plate heat exchanger design engineer in order to choose the proper material for the plates as well as the right service and product fluids.

This paper aims to to simulate the flow and heat transfer during free convection in a square cavity using double-multi-relaxation time (MRT) lattice Boltzmann method.

The double-MRT lattice Boltzmann method is used, and the natural convection fluid flow and heat transfer under influence of different parameters are analyzed. The D2Q5 model and D2Q9 model are used for simulation of temperature field and flow field, respectively. The cavity is filled with CuO-water nanofluid; in addition, the thermo-physical properties of nanofluid and the effect of nanoparticles’ shapes are considered using Koo–Kleinstreuer–Li (KKL) model. On the other hand, the cavity is included with an internal active hollow with constant thermal boundary conditions at its walls and variable dimensions. It should be noted that the dimensions of the internal hollow will be determined by as aspect ratio.

The Rayleigh number, nanoparticle concentration and the aspect ratio are the governing parameters. The heat transfer performance of the cavity has direct relationship with the Rayleigh number and solid volume fraction of CuO-water nanofluid. Moreover, the configuration of the cavity is good controlling factor for changing the heat transfer performance and entropy generation.

The originality of this work is using double-MRT lattice Boltzmann method in simulating the free convection fluid flow and heat transfer.

The purpose of this paper is to study problem of conjugate MHD natural convection of Al₂O₃-water nanofluid in a square cavity with conductive inner block using Buongiorno’s two-phase model numerically.

An isothermal heater is placed on the left wall of the square cavity, while the right wall is maintained at a constant cold temperature. The horizontal top and bottom walls are kept adiabatic. The boundaries of the annulus are assumed to be impermeable, the fluid within the cavity is a water-based nanofluid having Al₂O₃ nanoparticles. The Boussinesq approximation is applicable. The governing equations subject to the boundary conditions are solved using the finite difference method.

Numerical results are presented graphically in the form of streamlines, isotherms and nanoparticles distributions as well as the local and average Nusselt numbers. The results show that the effect of the nanoparticles addition on the average Nusselt number is essential for low Rayleigh, high Hartmann and high values of length ratio when attenuated the convective flow.

According to exist studies and to the authors’ best knowledge, so far, there have been no studies of conjugate natural convection of Al₂O₃-water nanofluid in a square cavity with a conductive inner block using Buongiorno’s two-phase model with the effect of the magnetic field. Thus, the authors believe that this work is new and valuable. The aim of this study is to investigate the MHD natural convection of Al₂O₃-water nanofluid in a square cavity with conductive inner block using Buongiorno’s two-phase model.

The purpose of this study is to numerically analyze the mixed convection and entropy generation in an annulus with a rotating heated inner cylinder for single-wall carbon nanotube (SWCNT)–water nanofluid flow using local thermal nonequilibrium (LTNE) model. An examination of the system behavior is presented considering the heat-generating solid phase inside the porous layer partly filled at the inner surface of the outer cylinder.

The discretized governing equations for nanofluid and porous layer by means of the finite volume method are solved by using the SIMPLE algorithm.

It is found that the buoyancy force and rotational effect have an important impact on the change of the strength of streamlines and isotherms for nanofluid flow. The minimum average Nusselt number on the inner cylinder is obtained at Ra$_E$ = 10$^4$, and the minimum total entropy generation is found at Re = 400 for given parameters. The entropy generation minimization is determined in case of different nanoparticle volume fractions. It is observed that at the same external Rayleigh numbers, the LTNE condition obtained with internal heat generation is very different from that without heat generation.

To the best of the authors’ knowledge, there is no previous paper presenting mixed convection and entropy generation of SWCNT–water nanofluid in a porous annulus under LTNE condition. The addition of nanoparticles to based fluid leads to a decrease in the value of minimum total entropy generation. Thus, using nanofluid has a significant role in the thermal design and optimization of heat transfer applications.