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Papers by Mohammad Bagher Ayani

Research paper thumbnail of Lattice Boltzmann simulation of diluted gas flow inside irregular shape microchannel by two relaxation times on the basis of wall function approach

Vacuum, Mar 1, 2020

Abstract The rarefied gas flow through a long microchannel with multi throats is studied in both ... more Abstract The rarefied gas flow through a long microchannel with multi throats is studied in both slip and transition flow regimes by the lattice Boltzmann method with Two Relaxation Times (TRT). The power-law analytical function is applied to improve the slippage velocity on the microchannel surfaces. The slip velocity correction at the corner point of microchannel is used. Therefore, a slip coefficient basis on the kinetic theory is considered. The Zou-He and Bounce back-Specular Reflection boundary conditions are used at the inlet-outlet of the geometry and on the microchannel wall surfaces, respectively. The present model results coincide with the Direct Simulation Monte Carlo and the Information Preservation values. The present model predicts the slippage velocity with higher accuracy as compared with the single relaxation time one. Moreover, this model has low cost and running time in comparison with the mention models.

Research paper thumbnail of Simulation of rarefied gas flow in a microchannel with backward facing step by two relaxation times using Lattice Boltzmann method – Slip and transient flow regimes

International Journal of Mechanical Sciences, Jul 1, 2019

Simulation of rarefied gas flow in a microchannel with backward facing step by two relaxation tim... more Simulation of rarefied gas flow in a microchannel with backward facing step by two relaxation times using lattice Boltzmann method-Slip and transient flow regimes, International

Research paper thumbnail of Heat transfer and deposition analysis of CuO-Water nanofluid inside a baffled channel: Two-phase Eulerian–Lagrangian method

Journal of The Taiwan Institute of Chemical Engineers, Jul 1, 2023

Research paper thumbnail of The Developed Conservation Element and Solution Element Method in Two-Dimensional Spherical Coordinate and Its Application to the Analysis of Non-Fourier Heat Conduction

Arabian journal for science and engineering, Mar 29, 2023

Research paper thumbnail of The Developed Conservation Element and Solution Element Method in Two-Dimensional Spherical Coordinate and Its Application to the Analysis of Non-Fourier Heat Conduction

Arabian Journal for Science and Engineering

Research paper thumbnail of Optimisation of plate thermal energy storage during the charging process: A numerical and experimental study

THE 6TH INTERNATIONAL CONFERENCE ON ENERGY, ENVIRONMENT, EPIDEMIOLOGY AND INFORMATION SYSTEM (ICENIS) 2021: Topic of Energy, Environment, Epidemiology, and Information System

Research paper thumbnail of Numerical study of non-Fourier heat conduction in a biolayer spherical living tissue during hyperthermia

Journal of Thermal Biology, 2016

Laser interstitial thermal therapy is one of the best methods for tumor treatment. Quality of tre... more Laser interstitial thermal therapy is one of the best methods for tumor treatment. Quality of treatment is highly influenced by the way of temperature control that depends strongly upon the living tissue thermal properties. One-dimensional dual-phase-lag (DPL) in spherical coordinate system numerically has been investigated for bioheat transfer during laser treatment in living biological tissues, which contain tumoral and normal layers. Various behaviors of heat transfer models such as wave, wavelike and diffusion are studied by adjusting the relaxation parameters. Effect of different phase lags values of the heat flux and the temperature gradient and thermal diffusivity on the behavior of heat transfer overshooting phenomenon is also investigated as well. Results indicate variation of the time lag and the thermal diffusivity of the normal and tumoral tissues. Also it has cleared that the geometrical conditions have significant effects upon the thermal response and overshooting phenomenon in biological tissue.

Research paper thumbnail of بررسی و مطالعه عددی انتقال حرارت در سیل های مکانیکی

Research paper thumbnail of Analyses of non-Fourier heat conduction in 1-D spherical biological tissue based on dual-phase-lag bio-heat model using the conservation element/solution element (CE/SE) method: A numerical study

International Communications in Heat and Mass Transfer, Mar 1, 2022

Research paper thumbnail of Numerical analysis of vacuum drying of a porous body in the integrated domain

Journal of Food Process Engineering, 2022

Research paper thumbnail of Numerical Investigation Of The Effect Of Geometrical Shape Of Plate Heat Exchangers On Heat Transfer Efficiency

Optimizations of Plate Heat Exchangers (PHS) have received great attention in the past decade. In... more Optimizations of Plate Heat Exchangers (PHS) have received great attention in the past decade. In this study, heat transfer and pressure drop coefficients are compared for rectangular and circular PHS employing numerical simulations. Plates are designed to have equivalent areas. Simulations were implemented to investigate the efficiency of PHSs considering heat transfer, friction factor and pressure drop. Amount of heat transfer and pressure drop was obtained for different range of Reynolds numbers. These two parameters were compared with aim of <em>F</em> "weighting factor correlation". In this comparison, the minimum amount of F indicates higher efficiency. Results reveal that the <em>F</em> value for rectangular shape is less than circular plate, and hence using rectangular shape of PHS is more efficient than circular one. It was observed that, the amount of friction factor is correlated to the Reynolds numbers, such that friction factor decrease...

Research paper thumbnail of A Numerical Simulation of Cure Process Using General Coordinates Method

Research paper thumbnail of Computational Modeling of Flow inside High Pressure Swirl Injectors By Considering Air-Cavity

In this paper the computational fluid dynamic (CFD) method was used to simulate two-phase flow wi... more In this paper the computational fluid dynamic (CFD) method was used to simulate two-phase flow within high pressure swirl injectors. The two-dimensional axisymmetric swirl Navier-Stokes equations coupled with the Volume-of-Fluid (VOF) method was employed for accounting the formation mechanism of the liquid film inside the swirl chamber and the orifice hole of the high pressure swirl injector. The VOF method was used to identify the liquid-gas interface developing inside the injector. Numerical simulations were carried out under MPa 7

Research paper thumbnail of Integral Method Solution for Flow and Heat Transfer Over a Permeable Surface with Convective Boundary Condition

A classical problem of hydrodynamic and thermal boundary layers over a permeable plate in a unifo... more A classical problem of hydrodynamic and thermal boundary layers over a permeable plate in a uniform laminar flow is considered in this paper. It is well known that the similarity and integral solutions for the flow and energy equations are possible for the boundary condition of constant surface temperature and constant heat flux but only a few similarity solutions has been attempted for convective surface boundary condition. It is implied in this paper that an integral solution is available if the mass transpiration and the convective heat transfer coefficient associated with the hot lower sided fluid vary like �� −1 2 ⁄ . Where x is the distance from the leading edge of the solid surface. The governing partial differential equations are first described and then transformed into integral form, before being solved numerically. At the end, the effect of some parameters on the flow and thermal fields are examined and discussed.

Research paper thumbnail of بررسی و مطالعه عددی انتقال حرارت در سیل های مکانیکی

Research paper thumbnail of Estimation of Time-dependent Surface Heat Flux in a Nonlinear Inverse Bio-heat Transfer Problem

This study deals with the solution of an inverse pr oblem in a living tissue to estimate the time... more This study deals with the solution of an inverse pr oblem in a living tissue to estimate the time-depen dent heat flux. The thermal properties such as thermal conductivity, blood perf usion and metabolic heat generation are considered t mperature dependent. The Pennes bioheat model is applied to simulate thermal behavior. The Sequential Function Specification Me thod (SFSM) and Conjugate Gradient Method (CGM) with adjoint problem are appl ied to obtain the unknown surface heat flux. Two ex amples are considered to examine the accuracy and ability of the inverse ana lysis. A comparison of two methods in the solution of the nonlinear inverse bioheat transfer problem is done. Results confirm the accuracy of both methods in estimating unknown surf ace heat flux for exact data. The effects of measurement error, initial guess and measurement location upon the precision of the est imated results are evaluated. Results demonstrate that the accuracy of conjugate gr dient method is more than ...

Research paper thumbnail of A novel approach in integral solution of laminar natural convection induced by a line heat

Linan and Kurdymov [6] studied numerically the laminar free convection induced by a line heat sou... more Linan and Kurdymov [6] studied numerically the laminar free convection induced by a line heat source at small Grashof numbers, using the Boussinesq equations, in stream function-vorticity (ω − ψ) variables. Wang et al. [7] studied the transient laminar natural convection from horizontal cylinders, and they used the (ω − ψ) equations. Ayani et al. [8] investigate the effect of radiation on laminar natural convection induced by a line heat source and concluded a considerable departure from the Boussinesq-based solution and from the boundary layer results. All the additional equations applied in the analytical solutions are strongly dependent to experimental data and some simplifying assumptions. In this paper, the additional equation is based on the physics of the flow obtained using the governing equations of the phenomena. In addition, no more simplifying assumptions are applied. Governing Equations Laminar natural convection flow from a horizontal line heat source, figure 1, assuming the end effects of the source, is negligible, is governed by continuity equation, the two-dimensional Navier-Stocks equations using Boussinesq approximation and the energy equation [3]. Figure 1. Problem under consideration Based on the physical configuration shown in Figure 1, the governing equations in the Cartesian coordinate system take the following form :

Research paper thumbnail of Applying response surface method to optimize the performance of a divergent-chimney solar power plant

Sustainable Energy Technologies and Assessments, 2021

One of the effective tools to generate electricity from solar energy is Divergent-chimney solar p... more One of the effective tools to generate electricity from solar energy is Divergent-chimney solar power plant (DSPP). Divergent and cylindrical chimneys of solar power plants have different performances considering turbine pressure drop ratio (ft). For the first time, the divergent angle (DA) and solar radiation (SR) interaction effects on 〖ft〗_opt are discussed through applying the Computational Fluid Dynamics (CFD) and Response Surface Method (RSM). FLUENT software is employed to perform 2D axisymmetric numerical stimulation for the Manzanares prototype. The DA, SR, and ft with ranges of 0°-3°, 200-800 W/m2, and 0.2-0.9 are considered, respectively, in the RSM optimization. The outcomes denote that the amount of 〖ft〗_optvaries from 0.71 to 0.89 continuously, and it is related inversely to the DA and directly to the SR. The maximum efficiency 〖(η〗_max) is obtained at 〖ft〗_opt, for different SRs and DAs. It is concluded that the η_max is enhanced from 0.42% to 0.50%, achieved by increasing the DA and SR values. Furthermore, the quadratic correlation of the 〖ft〗_opt and η_max in terms of DA and SR parameters are provided. Therefore, the consequences of this research would be a suitable resource for designing optimum turbines for the DSPPs.

Research paper thumbnail of Sudden contraction effects in nanochannel cross section on the rarefied gas flow characteristics: LBM analysis

The European Physical Journal Plus, 2020

This mesoscopic investigation aims to study the rarefied gas flow inside a contracting nanochanne... more This mesoscopic investigation aims to study the rarefied gas flow inside a contracting nanochannel in the slip and transitional regimes by two relaxation time lattice Boltzmann method. Bosanquet-type effective viscosity and distribution functions correction at the corner points are used to enhance the precision of slippage velocity on the walls. The boundary conditions at the entrance and exit sections of the nanochannel are assumed nonequilibrium-equilibrium distribution functions. The bounce back-specular reflection boundary conditions are considered for the wall exteriors. It is found that both momentum and rarefaction play essential roles concerning the separation phenomena in nanochannel flow. The higher outlet Knudsen number possesses the higher effective viscosity and shear stress, while the vortices become smaller and tend to disappear at higher Knudsen numbers. The results of the direct simulation Monte Carlo method have been utilized to validate the present numerical prediction, and an outstanding agreement between the results is shown.

Research paper thumbnail of Melting process of paraffin wax inside plate heat exchanger: experimental and numerical study

Journal of Thermal Analysis and Calorimetry, 2020

In this paper, an experimental and numerical study has been performed on melting process of comme... more In this paper, an experimental and numerical study has been performed on melting process of commercial Iranian paraffin wax, with melting temperature of about 60 °C, inside a plate heat exchanger. A 500 × 100 mm plate thermal storage system and 22 mm thick phase change material has been designed. Experimental and numerical results are compared with each other in three different inlet temperatures of heat transfer fluid (HTF), which are 343, 348, and 353 K, and three different volume flow rates, which are 15, 30, are 45 L min −1. The temperature contours of paraffin wax at various time steps are presented to investigate the conduction and convection effects of melting process with respect to time. It has been shown that the melting rate of paraffin wax is higher at the upper part of the system due to the presence of natural convection. Results showed that increasing HTF temperature enhances the amount of heat transfer and reduces the melting time up to 37%. Also, by increasing volume flow rate of HTF, the melting time reduced up to 0.9%.

Research paper thumbnail of Lattice Boltzmann simulation of diluted gas flow inside irregular shape microchannel by two relaxation times on the basis of wall function approach

Vacuum, Mar 1, 2020

Abstract The rarefied gas flow through a long microchannel with multi throats is studied in both ... more Abstract The rarefied gas flow through a long microchannel with multi throats is studied in both slip and transition flow regimes by the lattice Boltzmann method with Two Relaxation Times (TRT). The power-law analytical function is applied to improve the slippage velocity on the microchannel surfaces. The slip velocity correction at the corner point of microchannel is used. Therefore, a slip coefficient basis on the kinetic theory is considered. The Zou-He and Bounce back-Specular Reflection boundary conditions are used at the inlet-outlet of the geometry and on the microchannel wall surfaces, respectively. The present model results coincide with the Direct Simulation Monte Carlo and the Information Preservation values. The present model predicts the slippage velocity with higher accuracy as compared with the single relaxation time one. Moreover, this model has low cost and running time in comparison with the mention models.

Research paper thumbnail of Simulation of rarefied gas flow in a microchannel with backward facing step by two relaxation times using Lattice Boltzmann method – Slip and transient flow regimes

International Journal of Mechanical Sciences, Jul 1, 2019

Simulation of rarefied gas flow in a microchannel with backward facing step by two relaxation tim... more Simulation of rarefied gas flow in a microchannel with backward facing step by two relaxation times using lattice Boltzmann method-Slip and transient flow regimes, International

Research paper thumbnail of Heat transfer and deposition analysis of CuO-Water nanofluid inside a baffled channel: Two-phase Eulerian–Lagrangian method

Journal of The Taiwan Institute of Chemical Engineers, Jul 1, 2023

Research paper thumbnail of The Developed Conservation Element and Solution Element Method in Two-Dimensional Spherical Coordinate and Its Application to the Analysis of Non-Fourier Heat Conduction

Arabian journal for science and engineering, Mar 29, 2023

Research paper thumbnail of The Developed Conservation Element and Solution Element Method in Two-Dimensional Spherical Coordinate and Its Application to the Analysis of Non-Fourier Heat Conduction

Arabian Journal for Science and Engineering

Research paper thumbnail of Optimisation of plate thermal energy storage during the charging process: A numerical and experimental study

THE 6TH INTERNATIONAL CONFERENCE ON ENERGY, ENVIRONMENT, EPIDEMIOLOGY AND INFORMATION SYSTEM (ICENIS) 2021: Topic of Energy, Environment, Epidemiology, and Information System

Research paper thumbnail of Numerical study of non-Fourier heat conduction in a biolayer spherical living tissue during hyperthermia

Journal of Thermal Biology, 2016

Laser interstitial thermal therapy is one of the best methods for tumor treatment. Quality of tre... more Laser interstitial thermal therapy is one of the best methods for tumor treatment. Quality of treatment is highly influenced by the way of temperature control that depends strongly upon the living tissue thermal properties. One-dimensional dual-phase-lag (DPL) in spherical coordinate system numerically has been investigated for bioheat transfer during laser treatment in living biological tissues, which contain tumoral and normal layers. Various behaviors of heat transfer models such as wave, wavelike and diffusion are studied by adjusting the relaxation parameters. Effect of different phase lags values of the heat flux and the temperature gradient and thermal diffusivity on the behavior of heat transfer overshooting phenomenon is also investigated as well. Results indicate variation of the time lag and the thermal diffusivity of the normal and tumoral tissues. Also it has cleared that the geometrical conditions have significant effects upon the thermal response and overshooting phenomenon in biological tissue.

Research paper thumbnail of بررسی و مطالعه عددی انتقال حرارت در سیل های مکانیکی

Research paper thumbnail of Analyses of non-Fourier heat conduction in 1-D spherical biological tissue based on dual-phase-lag bio-heat model using the conservation element/solution element (CE/SE) method: A numerical study

International Communications in Heat and Mass Transfer, Mar 1, 2022

Research paper thumbnail of Numerical analysis of vacuum drying of a porous body in the integrated domain

Journal of Food Process Engineering, 2022

Research paper thumbnail of Numerical Investigation Of The Effect Of Geometrical Shape Of Plate Heat Exchangers On Heat Transfer Efficiency

Optimizations of Plate Heat Exchangers (PHS) have received great attention in the past decade. In... more Optimizations of Plate Heat Exchangers (PHS) have received great attention in the past decade. In this study, heat transfer and pressure drop coefficients are compared for rectangular and circular PHS employing numerical simulations. Plates are designed to have equivalent areas. Simulations were implemented to investigate the efficiency of PHSs considering heat transfer, friction factor and pressure drop. Amount of heat transfer and pressure drop was obtained for different range of Reynolds numbers. These two parameters were compared with aim of <em>F</em> "weighting factor correlation". In this comparison, the minimum amount of F indicates higher efficiency. Results reveal that the <em>F</em> value for rectangular shape is less than circular plate, and hence using rectangular shape of PHS is more efficient than circular one. It was observed that, the amount of friction factor is correlated to the Reynolds numbers, such that friction factor decrease...

Research paper thumbnail of A Numerical Simulation of Cure Process Using General Coordinates Method

Research paper thumbnail of Computational Modeling of Flow inside High Pressure Swirl Injectors By Considering Air-Cavity

In this paper the computational fluid dynamic (CFD) method was used to simulate two-phase flow wi... more In this paper the computational fluid dynamic (CFD) method was used to simulate two-phase flow within high pressure swirl injectors. The two-dimensional axisymmetric swirl Navier-Stokes equations coupled with the Volume-of-Fluid (VOF) method was employed for accounting the formation mechanism of the liquid film inside the swirl chamber and the orifice hole of the high pressure swirl injector. The VOF method was used to identify the liquid-gas interface developing inside the injector. Numerical simulations were carried out under MPa 7

Research paper thumbnail of Integral Method Solution for Flow and Heat Transfer Over a Permeable Surface with Convective Boundary Condition

A classical problem of hydrodynamic and thermal boundary layers over a permeable plate in a unifo... more A classical problem of hydrodynamic and thermal boundary layers over a permeable plate in a uniform laminar flow is considered in this paper. It is well known that the similarity and integral solutions for the flow and energy equations are possible for the boundary condition of constant surface temperature and constant heat flux but only a few similarity solutions has been attempted for convective surface boundary condition. It is implied in this paper that an integral solution is available if the mass transpiration and the convective heat transfer coefficient associated with the hot lower sided fluid vary like �� −1 2 ⁄ . Where x is the distance from the leading edge of the solid surface. The governing partial differential equations are first described and then transformed into integral form, before being solved numerically. At the end, the effect of some parameters on the flow and thermal fields are examined and discussed.

Research paper thumbnail of بررسی و مطالعه عددی انتقال حرارت در سیل های مکانیکی

Research paper thumbnail of Estimation of Time-dependent Surface Heat Flux in a Nonlinear Inverse Bio-heat Transfer Problem

This study deals with the solution of an inverse pr oblem in a living tissue to estimate the time... more This study deals with the solution of an inverse pr oblem in a living tissue to estimate the time-depen dent heat flux. The thermal properties such as thermal conductivity, blood perf usion and metabolic heat generation are considered t mperature dependent. The Pennes bioheat model is applied to simulate thermal behavior. The Sequential Function Specification Me thod (SFSM) and Conjugate Gradient Method (CGM) with adjoint problem are appl ied to obtain the unknown surface heat flux. Two ex amples are considered to examine the accuracy and ability of the inverse ana lysis. A comparison of two methods in the solution of the nonlinear inverse bioheat transfer problem is done. Results confirm the accuracy of both methods in estimating unknown surf ace heat flux for exact data. The effects of measurement error, initial guess and measurement location upon the precision of the est imated results are evaluated. Results demonstrate that the accuracy of conjugate gr dient method is more than ...

Research paper thumbnail of A novel approach in integral solution of laminar natural convection induced by a line heat

Linan and Kurdymov [6] studied numerically the laminar free convection induced by a line heat sou... more Linan and Kurdymov [6] studied numerically the laminar free convection induced by a line heat source at small Grashof numbers, using the Boussinesq equations, in stream function-vorticity (ω − ψ) variables. Wang et al. [7] studied the transient laminar natural convection from horizontal cylinders, and they used the (ω − ψ) equations. Ayani et al. [8] investigate the effect of radiation on laminar natural convection induced by a line heat source and concluded a considerable departure from the Boussinesq-based solution and from the boundary layer results. All the additional equations applied in the analytical solutions are strongly dependent to experimental data and some simplifying assumptions. In this paper, the additional equation is based on the physics of the flow obtained using the governing equations of the phenomena. In addition, no more simplifying assumptions are applied. Governing Equations Laminar natural convection flow from a horizontal line heat source, figure 1, assuming the end effects of the source, is negligible, is governed by continuity equation, the two-dimensional Navier-Stocks equations using Boussinesq approximation and the energy equation [3]. Figure 1. Problem under consideration Based on the physical configuration shown in Figure 1, the governing equations in the Cartesian coordinate system take the following form :

Research paper thumbnail of Applying response surface method to optimize the performance of a divergent-chimney solar power plant

Sustainable Energy Technologies and Assessments, 2021

One of the effective tools to generate electricity from solar energy is Divergent-chimney solar p... more One of the effective tools to generate electricity from solar energy is Divergent-chimney solar power plant (DSPP). Divergent and cylindrical chimneys of solar power plants have different performances considering turbine pressure drop ratio (ft). For the first time, the divergent angle (DA) and solar radiation (SR) interaction effects on 〖ft〗_opt are discussed through applying the Computational Fluid Dynamics (CFD) and Response Surface Method (RSM). FLUENT software is employed to perform 2D axisymmetric numerical stimulation for the Manzanares prototype. The DA, SR, and ft with ranges of 0°-3°, 200-800 W/m2, and 0.2-0.9 are considered, respectively, in the RSM optimization. The outcomes denote that the amount of 〖ft〗_optvaries from 0.71 to 0.89 continuously, and it is related inversely to the DA and directly to the SR. The maximum efficiency 〖(η〗_max) is obtained at 〖ft〗_opt, for different SRs and DAs. It is concluded that the η_max is enhanced from 0.42% to 0.50%, achieved by increasing the DA and SR values. Furthermore, the quadratic correlation of the 〖ft〗_opt and η_max in terms of DA and SR parameters are provided. Therefore, the consequences of this research would be a suitable resource for designing optimum turbines for the DSPPs.

Research paper thumbnail of Sudden contraction effects in nanochannel cross section on the rarefied gas flow characteristics: LBM analysis

The European Physical Journal Plus, 2020

This mesoscopic investigation aims to study the rarefied gas flow inside a contracting nanochanne... more This mesoscopic investigation aims to study the rarefied gas flow inside a contracting nanochannel in the slip and transitional regimes by two relaxation time lattice Boltzmann method. Bosanquet-type effective viscosity and distribution functions correction at the corner points are used to enhance the precision of slippage velocity on the walls. The boundary conditions at the entrance and exit sections of the nanochannel are assumed nonequilibrium-equilibrium distribution functions. The bounce back-specular reflection boundary conditions are considered for the wall exteriors. It is found that both momentum and rarefaction play essential roles concerning the separation phenomena in nanochannel flow. The higher outlet Knudsen number possesses the higher effective viscosity and shear stress, while the vortices become smaller and tend to disappear at higher Knudsen numbers. The results of the direct simulation Monte Carlo method have been utilized to validate the present numerical prediction, and an outstanding agreement between the results is shown.

Research paper thumbnail of Melting process of paraffin wax inside plate heat exchanger: experimental and numerical study

Journal of Thermal Analysis and Calorimetry, 2020

In this paper, an experimental and numerical study has been performed on melting process of comme... more In this paper, an experimental and numerical study has been performed on melting process of commercial Iranian paraffin wax, with melting temperature of about 60 °C, inside a plate heat exchanger. A 500 × 100 mm plate thermal storage system and 22 mm thick phase change material has been designed. Experimental and numerical results are compared with each other in three different inlet temperatures of heat transfer fluid (HTF), which are 343, 348, and 353 K, and three different volume flow rates, which are 15, 30, are 45 L min −1. The temperature contours of paraffin wax at various time steps are presented to investigate the conduction and convection effects of melting process with respect to time. It has been shown that the melting rate of paraffin wax is higher at the upper part of the system due to the presence of natural convection. Results showed that increasing HTF temperature enhances the amount of heat transfer and reduces the melting time up to 37%. Also, by increasing volume flow rate of HTF, the melting time reduced up to 0.9%.