A numerical study on heat transfer enhancement and design of a heat exchanger with porous media in continuous hydrothermal flow synthesis system

The aim of this study is to use a new configuration of porous media in a heat exchanger in continuous hydrothermal flow synthesis(CHFS)system to enhance the heat transfer and minimize the required length of the heat exchanger.For this purpose,numerous numerical simulations are performed to investigate performance of the system with porous media.First,the numerical simulation for the heat exchanger in CHFS system is validated by experimental data.Then,porous media is added to the system and six different thicknesses for the porous media are examined to obtain the optimum thickness,based on the minimum required length of the heat exchanger.Finally,by changing the flow rate and inlet temperature of the product as well as the cooling water flow rate,the minimum required length of the heat exchanger with porous media for various inlet conditions is assessed.The investigations indicate that using porous media with the proper thickness in the heat exchanger increases the cooling rate of the product by almost 40% and reduces the required length of the heat exchanger by approximately 35%.The results also illustrate that the most proper thickness of the porous media is approximately equal to 90% of the product tube's thickness.Results of this study lead to design a porous heat exchanger in CHFS system for various inlet conditions.

NUMERICAL STUDY ON NATURAL CONVECTION HEAT TRANSFER INSIDE RECTANGULAR ENCLOSURE FILLED WITH ANISOTROPIC POROUS MEDIA

Natural convection heat transfer inside horizontal rectangular enclosure filled with the anisotropic porous media, with isothermally heated bottom and cooled top while the vertical walls are adiabatic, is analyzed numerically by applying the Brinkman model-a modified form of Darcy model giving consideration to the viscous effect. The results show that: (1)the permeability ratio (K*=Ky/Kx) is an important factor affecting natural convection heat transfer in the porous media. As K' decreases, the circulation intensity of the natural convectioncells increase significantly, resulting in an enhancement of heat transfer coefficient; (2)the increase of Darcy number (aa=Ky/H2) implies that the viscous effect is more significant. As Da≥10-, there exists a certain difference between the Darcy model and the Brinkman model. It is more significant at a lower permeability ratio. In particalar, with K*≤0. 25, the Nusselt number for Da=10-3 would differ form that of Darcy model up to an amount of 30K. The Darcy flow as depicted by Darcy model is no longer existing and an analysis neglecting the viscous effect will inevitably be of considerable error.

Cooling of Superheated Refrigerants Flowing inside Tubes Filled with Porous Media： Study of Heat Transfer and Pressure Drop, Carbon Dioxide Case Study

In this work an experimental study combined with an analytical investigation for cooling superheated Carbon Dioxide （CO2） gas were carried out. This work is intended to be part of the super critical Gustav Lorentzen refrigeration cycle of CO2. Experimental and analytical works concentrated on heat transfer and pressure drop for single phase flow during gas cooling inside tubes filled with porous media. Analytical empirical correlations were formulated for the coefficient of convectional heat transfer and for the pressure drop. A comparison between experimental results and that obtained by developed correlations were carried out, and a comparison between these results and literature published ones were carried out too. The results of this research showed that for cooling process the proposed correlations were proved to be acceptably accurate for pressure drop with difference from experimental results of 2%, while for convective heat transfer the difference from experimental results reached about 3%. More than 90% agreement with literature results was obtained. This work can enhance the calculations of heat flux and pressure drop of gases flow inside porous media filled tubes, and can help in the design procedure of heat exchangers and cooling processes.

Molecular dynamics simulation of decomposition and thermal conductivity of methane hydrate in porous media

The hydrate has characteristics of low thermal conductivity and temperature sensitivity. To further analysis the mechanism of thermal conductivity and provide method for the exploitation, transportation and utilization of hydrate, the effect of decomposition and thermal conductivity of methane hydrate in porous media has been studied by using the molecular dynamics simulation. In this study, the simulation is carried out under the condition of temperature 253.15 K-273.15 K and pressure 1 MPa. The results show that the thermal conductivity of methane hydrate increases with the increase of temperature and has a faster growth near freezing. With the addition of porous media, the thermal conductivity of the methane hydrate improves significantly. The methane hydrate-porous media system also has the characteristics of vitreous body.With the decrease of the pore size of the porous media, thermal conductivity of the system increases gradually at the same temperature. It can be ascertained that the porous media of different pore sizes have strengthened the role of the thermal conductivity of hydrates.

Analysis of the Influence of Viscosity and Thermal Conductivity on Heat Transfer by Al2O3-Water Nanofluid

The addition of nanoparticles into liquid,even at low concentrations,leads to an increase in both,dynamic viscosity and thermal conductivity.Furthermore,the increase in temperature causes an increase in thermal conductivity and a decrease in the nanofluid viscosity.In this context,a numerical investigation of the competition between viscosity and thermal conductivity about their effects on heat transfer by Al_(2)O_(3)-water nanofluid was conducted.A numerical study of heat transfer in a square cavity,filled with Al_(2)O_(3)-water nanofluid and heated from the left side,was presented in this paper.Continuity,momentum,and thermal energy equations are solved by the finite volume method.Regarding the pressure-velocity coupling,the SIMPLER algorithm was used.The working conditions,allowing the increase of heat transfer,are established.In addition,two correlations for viscosity and thermal conductivity of Al_(2)O_(3)-water nanofluid as functions of the concentration and diameter size based on experimental measurement are proposed.These correlations were more precisely compared to those given by the theoretical models.Moreover,other models for viscosity and conductivity depending on temperature are used and discussed.The results reveal that heat transfer by Al_(2)O_(3)-water nanofluid is enhanced only when the temperature exceeds 40℃ and the diameter size does not exceed a certain limit of the order of 45-50 nm depending on temperature.

Analysis of the Influence of Viscosity and Thermal Conductivity on Heat Transfer By Al_(2)O_(3)-Water Nanofluid

The addition of nanoparticles into liquid,even at low concentrations,leads to an increase in both,dynamic viscosity and thermal conductivity.Furthermore,the increase in temperature causes an increase in thermal conductivity and a decrease in the nanofluid viscosity.In this context,a numerical investigation of the competition between viscosity and thermal conductivity about their effects on heat transfer by Al_(2)O_(3)-water nanofluid was conducted.A numerical study of heat transfer in a square cavity,filled with Al_(2)O_(3)-water nanofluid and heated from the left side,was presented in this paper.Continuity,momentum,and thermal energy equations are solved by the finite volume method.Regarding the pressure-velocity coupling,the SIMPLER algorithm was used.The working conditions,allowing the increase of heat transfer,are established.In addition,two correlations for viscosity and thermal conductivity of Al_(2)O_(3)-water nanofluid as functions of the concentration and diameter size based on experimental measurement are proposed.These correlations were more precisely compared to those given by the theoretical models.Moreover,other models for viscosity and conductivity depending on temperature are used and discussed.The results reveal that heat transfer by Al_(2)O_(3)-water nanofluid is enhanced only when the temperature exceeds 40℃ and the diameter size does not exceed a certain limit of the order of 45-50 nm depending on temperature.

Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters

The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.

Radiative heat transfer analysis of a concave porous fin under the local thermal non-equilibrium condition:application of the clique polynomial method and physics-informed neural networks

The heat transfer through a concave permeable fin is analyzed by the local thermal non-equilibrium(LTNE)model.The governing dimensional temperature equations for the solid and fluid phases of the porous extended surface are modeled,and then are nondimensionalized by suitable dimensionless terms.Further,the obtained nondimensional equations are solved by the clique polynomial method(CPM).The effects of several dimensionless parameters on the fin's thermal profiles are shown by graphical illustrations.Additionally,the current study implements deep neural structures to solve physics-governed coupled equations,and the best-suited hyperparameters are attained by comparison with various network combinations.The results of the CPM and physicsinformed neural network(PINN)exhibit good agreement,signifying that both methods effectively solve the thermal modeling problem.

Heat transfer analysis in peristaltic flow of MHD Jeffrey fluid with variable thermal conductivity

The effect of an inclined magnetic field in the peristaltic flow of a Jeffrey fluid with variable thermal conductivity is discussed. The temperature dependent thermal conductivity of fluid in an asymmetric channel is taken into account. A dimensionless nonlinear system subject to a long wavelength and a low Reynolds number is solved. The explicit expressions of the stream function, the axial velocity, the pressure gradient, and the temperature are obtained. The effects of all physical parameters on peristaltic transport and heat transfer characteristics are observed from graphical illustrations. The behaviors of θ∈ [0, π/2] and θ∈ [π/2, π] on fluid flow and heat transfer are found to be opposite. Further, the size of trapped bolus is greater for the case of the inclined magnetic field （θ≠ π/2） than that for the case of the transverse magnetic field （θ = π/2）. The heat transfer coefficient decreases when the constant thermal conductivity （Newtonian） fluid is changed to the variable thermal conductivity （Jeffrey） fluid.

Thermal Conductivity and Heat Transfer Coefficient of Concrete

A very simple model for predicting thermal conductivity based on its definiensis was presented. The thermal conductivity obtained using the model provided a good coincidence to the investigations performed by other authors. The heat transfer coefficient was determined by inverse analysis using the temperature measurements. From experimental results, it is noted that heat transfer coefficient increases with the increase of wind velocity and relative humidity, a prediction equation on heat transfer coefficient about wind velocity and relative humidity is given.

Theoretical study on the effective thermal conductivity of silica aerogels based on a cross-aligned and cubic pore model

Aerogel nanoporous materials possess high porosity, high specific surface area, and extremely low density due to their unique nanoscale network structure. Moreover, their effective thermal conductivity is very low, making them a new type of lightweight and highly efficient nanoscale super-insulating material. However, prediction of their effective thermal conductivity is challenging due to their uneven pore size distribution. To investigate the internal heat transfer mechanism of aerogel nanoporous materials, this study constructed a cross-aligned and cubic pore model(CACPM) based on the actual pore arrangement of SiO_(2) aerogel. Based on the established CACPM, the effective thermal conductivity expression for the aerogel was derived by simultaneously considering gas-phase heat conduction, solid-phase heat conduction, and radiative heat transfer. The derived expression was then compared with available experimental data and the Wei structure model. The results indicate that, according to the model established in this study for the derived thermal conductivity formula of silica aerogel, for powdery silica aerogel under the conditions of T = 298 K, a_(2)= 0.85, D_(1)= 90 μm, ρ = 128 kg/m^(3), within the pressure range of 0–10^(5)Pa, the average deviation between the calculated values and experimental values is 10.51%. In the pressure range of 10^(3)–10^(4)Pa, the deviation between calculated values and experimental values is within 4%. Under these conditions, the model has certain reference value in engineering verification. This study also makes a certain contribution to the research of aerogel thermal conductivity heat transfer models and calculation formulae.

Numerical investigation of flow and heat transfer behind a two-dimensional backward-facing step equipped with a semi-porous baffle

The backward-facing step is a critical problem existing in many engineering and industrial applications.In this study,a semi-porous baffle(the root of the baffle is a porous medium and the tip is solid) is placed behind the step.The effects of the length of the porous part,and the baffle location on the energy transfer and pressure drop are studied in different Reynolds numbers(Re=100,200,300,400,500).The effect of the Darcy number of the porous medium on the aforementioned parameters is also investigated.Both the local maximum and average relative Nusselt numbers(divided by the Nusselt of the base case with no baffle at the same Reynolds) and relative pressure drop(calculated as the relative Nusselt number) are reported.The results show that by adoption of the proper length of the porous medium,the average relative and maximum local Nusselt numbers could be enhanced by 20% and 90%,respectively.Low permeable porous media give better energy transfer.For example,porous media with Da=10^(-5) give 30% better maximum local Nusselt number and about 7% higher average Nusselt number with respect to the same case with Da=10^(-2).

Thermal stretching in two-phase porous media: Physical basis for Maxwell model

An alternate yet general form of the classical effective thermal conductivity model （Maxwell model） for two-phase porous materials is presented, serving an explicit thermo-physicM basis. It is demonstrated that the reduced effective thermal conductivity of the porous media due to non-conducting pore inclusions is caused by the mechanism of thermal stretching, which is a combi- nation of reduced effective heat flow area and elongated heat transfer distance （thermal tortuosity）.

Experiments and Analyses on Heat Transfer Characteristics from a Solid Wall to a Strip-ShapedWick Structure

Centered or striped wick structures have been used to develop ultrathin heat pipes.Differing from traditional heat pipes,the centered or striped wick structures leave noncontact container surfaces with the wick structure.In this study,experiments andnumerical analyseswere conductedtoinvestigate the influenceof thesenoncontact surfaces.In the experiments,a strip-shaped wick structure was placed vertically,the top was sandwiched between wider rods and the bottom was immersed in a working fluid.The rod width was greater than the wick width;thus,noncontact surfaces were left between the rod and the wick structure.The heat was applied from the rod to the wick structure,and the evaporation heat transfer characteristics of the working fluid from the wick structure were evaluated.Water was used as the working fluid.The experiments were conducted by varying the rod and wick widths.The experimental results were obtained when the wick structures were placed separately.In the numerical analyses,the temperature and heat flux distributions in the rod were obtained.From the experimental and numerical results,it was confirmed that the noncontact surfaces caused the heat flux in the rod near both surfaces of the wick structure to concentrate,which increased the evaporation thermal resistance of the wick structure.A reduction in the noncontact surface area by increasing the wick width was found to be effective in decreasing the evaporation thermal resistance and increasing themaximumheat transfer rate of the wick structure.The separation of the wick structure increased the evaporation surface area.However,its effectiveness was limited when the heat transfer rate was small.

Thermal instability and heat transfer of viscoelastic fluids in bounded porous media with constant heat flux boundary

A numerical simulation is performed for thermal instability and heat transfer of viscoelastic fluids in bounded porous media under the bottom constant heat flux boundary condition. The results for six different combinations of relaxation and retardation times demonstrate the existence of the thermal instability induced flow bifurcation. It is found that the increase of the relaxation time can enhance the heat transfer efficiency by disturbing the fluid flow and facilitating the bifurcation. The increase of the retardation time can stabilize the flow and postpone the bifurcation, leading to simpler flow pattern and lower heat transfer rate.

Response of saturated porous media subjected to local thermal loading on the surface of semi-infinite space

Heat source function method is adopted in the present paper to derive elementary solutions of coupled thermo-hydro-mechanical consolidation for saturated porous media under conjunct actions of instantaneous point heat source, instantaneous point fluid source and constant volume force. By using the so-called fictitious heat source method and images method, the solutions of a semi-infinite saturated porous medium subjected to a local heat source with time-varied intensity on its free surface are developed from elementary solutions. The numerical integral methods for calculating the unsteady temperature, pore pressure and displacement fields are given. The thermomechanical response are analyzed for the case of a circular planar heat source. Besides, the thermal consolidation characteristics of a saturated porous medium subjected to a harmonic thermal loading are also given, and the fluctuation processes of the field variables located below the center of heat source are analyzed.

Determination of Effective Thermal Conductivity ForReal Porous Media Using Fractal Theory

In this paper, using fractal theory3 the geometric structure of real soil was described with its sectionview and section particle area fractal dimension d of porous media was counted. The volumetric solidcontent and the relation between volumetric solid content and porous media particle arrangementsas well as measure scale were obtainted. A heat conduction model was established and the effectivethermal conductivity of real soil based on the volumetric solid content was calculated.

On the combined heat transfer of natural convection, radiation and conduction in the non-gray semitransparent thermal fibrous insulation

A detailed numerical modeling is performed to investigate heat transfer in high-porous, high-temperature non-gray semitransparent silica insulation materials. Radiation between fibers, conduction within fibers and convection from the fibers to the surrounding fluid are considered. Macroscopic (porous media) modeling is used to determine the velocity, pressure and temperatures fields for fibrous insulation with a random packing geometry under natural convection. Based on a non-gray application of the solution to the radiative transfer equation, the value of the refractive index(n,m)is used to generate macroscopic average radiative properties such as extinction coefficient, scattering albedo and phase function. Key features of the macroscopic model include two-dimensional effects,non-gray radiative exchange, and the relaxation of the local thermodynamic non-equilibrium. The effectiveness of this numerical model is validated by the previous experimental data.

Impact of melting heat transfer in the time-dependent squeezing nanofluid flow containing carbon nanotubes in a Darcy-Forchheimer porous media with Cattaneo-Christov heat flux

This study aims to investigate the time-dependent squeezing of nanofluid flow, comprising carbon nanotubes of dual nature, e.g. single-walled carbon nanotubes, and multi-walled carbon nanotubes,between two parallel disks. Numerical simulations of the proposed novel model are conducted,accompanied by Cattaneo-Christov heat flux in a Darcy-Forchheimer permeable media. Additional impacts of homogeneous–heterogeneous reactions are also noted, including melting heat. A relevant transformation procedure is implemented for the transition of partial differential equations to the ordinary variety. A computer software-based MATLAB function, bvp4c, is implemented to handle the envisioned mathematical model. Sketches portraying impacts on radial velocity, temperature, and concentration of the included parameters are given, and deliberated upon. Skin friction coefficient and local Nusselt number are evaluated via graphical illustrations. It is observed that the local inertia coefficient has an opposite impact on radial velocity and temperature field. It is further perceived that melting and radiation parameters demonstrate a retarding effect on temperature profile.

A Coupled Discrete Unified Gas-Kinetic Scheme for Convection Heat Transfer in Porous Media

In this paper,the discrete unified gas-kinetic scheme(DUGKS)is extended to the convection heat transfer in porous media at representative elementary volume(REV)scale,where the changes of velocity and temperature fields are described by two kinetic equations.The effects from the porous medium are incorporated into the method by including the porosity into the equilibrium distribution function,and adding a resistance force in the kinetic equation for the velocity field.The proposed method is systematically validated by several canonical cases,including the mixed convection in porous channel,the natural convection in porous cavity,and the natural convection in a cavity partially filled with porous media.The numerical results are in good agreement with the benchmark solutions and the available experimental data.It is also shown that the coupled DUGKS yields a second-order accuracy in both temporal and spatial spaces.