Local Thermal Non-equilibrium Model Research Articles

Conjugated heat transfer analysis of a foam filled double-pipe heat exchanger for high-temperature application

A numerical investigation is performed to analyze the high-temperature heat transfer behavior in a double-pipe heat exchanger filled with open-cell porous foam. The Forchheimer-extended Darcy equation and the local thermal non-equilibrium model are utilized to simulate the flow and thermal transport inside the foam regions, considering the coupling effects between the inner and annular spaces. The effect of solid wall thickness is incorporated in the modelling process, following the continuity conditions of temperature and heat flux at the porous-solid interface. Simulations are conducted for a counter-flow heat exchanger while the thermal radiation transfer is solved using the P1 approximation. The cold fluid flows in the inner pipe, whereas the hot fluid in the annular gap. The temperature distribution, pressure drop, heat exchanger effectiveness and the overall performance are predicted. Effects of thermal radiation, foam structural parameters and the heat exchanger size are examined. The results indicate that thermal radiation promotes the thermal exchange between the two fluid sides. The heat exchanger effectiveness is improved by decreasing the porosity or increasing the pore density, exchanger length and annulus dimension, however, the potential increase in the total pressure drop should be seriously considered. Besides, the overall performance is slightly improved by further increasing the exchanger length when the dimensionless length is greater than 35.

Numerical Simulation and Optimization of Waste Heat Recovery in a Sinter Vertical Tank

In this paper, a two-dimensional steady model is established to investigate the gas-solid heat transfer in a sinter vertical tank based on the porous media theory and the local thermal non-equilibrium model. The influences of the air flow rate, sinter flow rate, and sinter particle diameter on the gas-solid heat transfer process are investigated numerically. In addition, exergy destruction minimization is used as a new principle for heat transfer enhancement. Furthermore, a multi-objective genetic algorithm based on a Back Propagation (BP) neural network is applied to obtain a combination of each parameter for a more comprehensive performance, with the exergy destruction caused by heat transfer and the one caused by fluid flow as the two objectives. The results show that the heat dissipation and power consumption both gradually increase with an increase of the air mass flow rate. Additionally, the increase of the sinter flow rate results in a decrease of the heat dissipation and an increase of the power consumption. In addition, both heat dissipation and power consumption gradually decrease with an increase of the sinter particle diameter. For the given structure of the vertical tank, the optimal operating parameters are 2.99 kg/s, 0.61 kg/s, and 32.8 mm for the air flow rate, sinter flow rate, and sinter diameter, respectively.

Effect of thickness and thermal conductivity of metal foams filled in a vertical channel – a numerical study

PurposeThis paper aims to discuss about the two-dimensional numerical simulations of fluid flow and heat transfer through high thermal conductivity metal foams filled in a vertical channel using the commercial software ANSYS FLUENT.Design/methodology/approachThe Darcy Extended Forchheirmer model is considered for the metal foam region to evaluate the flow characteristics and the local thermal non-equilibrium heat transfer model is considered for the heat transfer analysis; thus the resulting problem becomes conjugate heat transfer.FindingsResults obtained based on the present simulations are validated with the experimental results available in literature and the agreement was found to be good. Parametric studies reveal that the Nusselt number increases in the presence of porous medium with increasing thickness but the effect because of the change in thermal conductivity was found to be insignificant. The results of heat transfer for the metal foams filled in the vertical channel are compared with the clear channel in terms of Colburn j factor and performance factor.Practical implicationsThis paper serves as the current relevance in electronic cooling so as to open up more parametric and optimization studies to develop new class of materials for the enhancement of heat transfer.Originality/valueThe novelty of the present study is to quantify the effect of metal foam thermal conductivity and thickness on the performance of heat transfer and hydrodynamics of the vertical channel for an inlet velocity range of 0.03-3 m/s.

Investigation on Heat Extraction Performance of Fractured Geothermal Reservoir Using Coupled Thermal-Hydraulic-Mechanical Model Based on Equivalent Continuum Method

Natural fractures and artificial fractures in a tight rock matrix of an enhanced geothermal system make flow and heat transfer become seriously anisotropic. In this paper, a field-scale fractured heterogeneous geothermal reservoir model is built to study the heat transfer process. Based on an equivalent continuum method and local thermal non-equilibrium model, an equivalent permeability tensor is mapped from discrete fractures and a coupled thermal-hydraulic-mechanical mathematical model is adopted in which logarithmic stress sensitivity model is used to couple effective stress and permeability. From numerical simulation results at different injection rates, the contour results show the heterogeneity of flow, heat transfer and stress sensitivity are dominated by fractures distribution. Temperature contours reveal that the heat convection between water and rock in a fracture is more intense than the heat conduction between rock under different temperatures. The predicted power generation of a geothermal plant reveals the adverse effect on heat conversion efficiency, which is caused by the temperature drop at high injection rates.

A Synergistic Combination of Thermal Models for Optimal Temperature Distribution of Discrete Sources Through Metal Foams in a Vertical Channel

This paper discusses about the numerical prediction of forced convection heat transfer through high-porosity metal foams with discrete heat sources in a vertical channel. The physical geometry consists of a discrete heat source assembly placed at the center of the channel along with high thermal conductivity porous metal foams in order to enhance the heat transfer. The novelty of the present work is the use of combination of local thermal equilibrium (LTE) model and local thermal nonequilibrium (LTNE) model for the metal foam region to investigate the temperature distribution of the heat sources and to obtain an optimal heat distribution so as to achieve isothermal condition. Aluminum and copper metal foams of 10 PPI having a thickness of 20 mm are considered for the numerical simulations. The metal foam region is considered as homogeneous porous media and numerically modeled using Darcy Extended Forchheimer model. The proposed methodology is validated using the experimental results available in literature. The results of the present numerical solution indicate that the excess temperature of the bottom heat source reduces by 100 °C with the use of aluminum metal foam. The overall temperature of the vertical channel reduces based on the combination of LTE and LTNE models compared to only LTNE model. The results of excess temperature for both the empty and the metal foam filled vertical channels are presented in this work.

Unsteady natural convection in a partially porous cavity having a heat-generating source using local thermal non-equilibrium model

PurposeThe purpose of this study is a numerical analysis of transient natural convection in a square partially porous cavity with a heat-generating and heat-conducting element using the local thermal non-equilibrium model under the effect of cooling from the vertical walls. It should be noted that this research deals with a development of passive cooling system for the electronic devices.Design/methodology/approachThe domain of interest is a square cavity with a porous layer and a heat-generating element. The vertical walls of the cavity are kept at constant cooling temperature, while the horizontal walls are adiabatic. The heat-generating solid element is located on the bottom wall. A porous layer is placed under the clear fluid layer. The governing equations, formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions, are solved using implicit finite difference schemes of the second order accuracy. The governing parameters are the Darcy number, viscosity variation parameter, porous layer height and dimensionless time. The effects of varying these parameters on the average total Nusselt number along the heat source surface, the average temperature of the heater, the fluid flow rate inside the cavity and on the streamlines and isotherms are analyzed.FindingsThe results show that in the case of local thermal non-equilibrium the total average Nusselt number is an increasing function of the interphase heat transfer coefficient and the porous layer thickness, while the average heat source temperature decreases with the Darcy number and viscosity variation parameter.Originality/valueAn efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady natural convection within a partially porous cavity using the local thermal non-equilibrium model in the presence of a local heat-generating solid element. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer in enclosures with local heat-generating heaters and porous layers, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

Experimental and numerical investigation of forced convection heat transfer in porous lattice structures produced by selective laser melting

Forced convection heat transfer in four structured porous materials produced by selective laser melting (SLM) was experimentally and numerically studied. The porous materials are lattice structures consisting of periodic arrangements of Rhombi-Octet unit cells. The lattice structures have similar porosity (ε) but are of different unit cell sizes of 5 mm, 7 mm, 10 mm and 12 mm. This investigation aims to characterize and evaluate the thermo-hydraulic properties of this new class of lattice structures. The hydrodynamic and heat transfer characteristics of the lattices structures such as the permeability (K), inertia coefficient (CE) and Nusselt number (Nu) were determined experimentally in an air flow channel in which the Reynolds number (Re) can be varied between 1300 and 7000. Using a linear heat conduction setup, the stagnant effective thermal conductivities (keff) of the various lattice structures were determined and a relationship between keff and the ligament width (d) of the lattice structure was obtained. Based on the local thermal non-equilibrium model, numerical simulations were performed to determine the interfacial heat transfer coefficients (hsf) of the lattice structures. Our results showed that the pressure drop (ΔP) and Nusselt number (Nu) of the lattice structures increase with decreasing d and the highest Nu of 906 was obtained with the L1 lattice structure which has the smallest ligament width. The lattice structures also exhibited high keff values which were up to 5.5 times higher than that of the aluminum foams. Due to the orderly arrangements of the lattice structures, their permeability-based friction factors (f⋅Da1/2) were found to be lower than the metallic foams. However, their hsf values were also lower. The Colburn j-factor and thermal efficiency index (η) of the lattice structures were determined and found to be higher than those of the commercial metallic foams and conventional pin fin heat sinks. In summary, this investigation demonstrates the promising use of a new class of lattice structures (Rhombi-Octet) for enhancing single-phase forced convection cooling.

A solid-liquid local thermal non-equilibrium lattice Boltzmann model for heat transfer in nanofluids. Part II: Natural convection of nanofluids in a square enclosure

The novel solid-liquid local thermal non-equilibrium lattice Boltzmann model, developed in Part I of this paper series [1], is applied to the classical problem of natural convection of nanofluids in a square enclosure with vertical walls at differential temperatures. Effects of Rayleigh numbers, nanoparticles random motion, nanoparticles volume fraction and nanoparticles non-uniform distribution in natural convection of nanofluids are studied. Because random motions of nanoparticles are intensified with temperature, vertical velocity and temperature profiles in the nanofluid are asymmetric with respect to the hot and cold vertical walls. Distribution of nanoparticles in the nanofluid inside the enclosure is affected by both the Rayleigh number and random motion of nanoparticles, and nanoparticles’ distribution become relatively non-uniform at relatively high Rayleigh numbers. The non-uniform distribution of nanoparticles also affect local vertical velocity distribution, local temperature distribution, and the average Nusselt numbers. The effect of random motion of nanoparticles is shown to be responsible for enhanced convection at small Rayleigh numbers, the increasing viscosity of nanofluids is shown to be responsible for the deteriorating effects on heat transfer at intermediate Rayleigh numbers and non-uniform distribution of nanoparticles is shown to be responsible for ascending trend of Nusselt numbers at high Rayleigh numbers. The non-monotonous variation of the Nusselt number with respect to the Rayleigh number are in qualitative agreement with existing experimental data.

A solid-liquid local thermal non-equilibrium lattice Boltzmann model for heat transfer in nanofluids. Part I: Model development, shear flow and heat conduction in a nanofluid

A solid-liquid local thermal non-equilibrium lattice Boltzmann model for hydrodynamics and heat transfer in a nanofluid is developed in this paper. In this proposed model, interactions between fluid and solid nanoparticles, random motion of nanoparticles as well as heat transfer between nanoparticles and the base fluid are taken into consideration. This novel model is applied to two simple nanofluids problems: isothermal shear flow between two parallel plates moving at different velocities, and heat conduction between two parallel plates at different temperatures. For the problem of shear flow, it is found that nanoparticles random motion causes the instantaneous velocity distribution of a nanofluid to become non-linear in the shear flow between two parallel plates at microscopic level. At macroscopic level, it is found that as nanoparticles volume fraction increases, effects of nanoparticles random motion are enlarged and the time-average velocity distribution of a nanofluid deviates more from a linear distribution in a shear flow. For the problem of heat conduction between parallel plates at different temperatures, it is found that random motion of nanoparticles together with their high thermal diffusivity and thermal conductivity, causing the instantaneous temperature distribution in the nanofluid to become non-linear between two parallel plates at different temperatures. Temperature inside a nanoparticle is shown to be non-uniform, and temperature gradients in the fluid near a nanoparticles are elevated, thus heat transfer rate is enhanced near a nanoparticle. Time-average temperature gradients of a nanofluid at hot/cooled wall are higher than those of a pure fluid in heat conduction between parallel plates at different temperatures. Comparisons of calculated dynamic viscosity and thermal conductivity based on this novel model are found in good agreement with existing correlation equations. Thus, the accuracy of this novel solid–liquid local thermal non-equilibrium model for a nanofluid is validated.

Thermal Non-equilibrium Double Diffusive Convection in a Maxwell Fluid with Internal Heat Source

In this study, double-diffusive natural convection in a Maxwell fluid saturated porous layer with internal heat under local thermal non-equilibrium model (LTNM) is studied analytically. The study has been carried out based on using linear stability analysis. The linear stability analysis is based on normal mode technique. The modified Darcy model for the viscoelastic fluid of the Maxwell type is used to govern the momentum equation. A two-field model for energy equation has been applied for fluid and solid phases. The onset criterion for stationary convection has been derived analytically. The effects of inter-phase heat transfer coefficient and internal heat parameter on the stability of the system are investigated.

Numerical investigation on transpiration cooling with coolant phase change under hypersonic conditions

Owing to the huge phase-change latent heat, transpiration cooling using liquid coolant has been widely recognized as an effective thermal protection approach for hypersonic vehicles. This paper presents a modified local thermal non-equilibrium two-phase mixture model (LTNE-TPMM), and develops a multi-region numerical strategy to solve the coupled problems of internal heat and mass transfer in a porous cone with the external aerodynamic heat/force. The modified LTNE-TPMM and numerical strategy are validated by the experimental data obtained under a supersonic condition. Using the validated model and numerical strategy, numerical simulations are carried out under the condition of flight Mach number 7.0 and altitude 26.5 km, to study the mechanisms and analyze the performances of the transpiration cooling with liquid phase-change in a porous wedge-shaped nose cone. The numerical results revealed some interesting, valuable phenomena generated in liquid phase-change process, including the coolant movement and the distributions of temperature, pressure, saturation within the porous cone. The coolant mass flux along the radial direction of the cone decreases gradually in the vapor region, and then decreases rapidly at the beginning of two-phase region, but increases in the liquid region. Another important discovery is that the relation between coolant injection pressure and mass flow rate is not one-to-one. One injection pressure may correspond to multiple mass flow rates.

Analytical solutions of fluid flow and heat transfer in a partial porous channel with stress jump and continuity interface conditions using LTNE model

Forced convection heat transfer is analytically performed in a channel partially filled with porous media located at two inner walls under local thermal non-equilibrium (LTNE) condition. A constant heat flux is imposed at the channel walls. The Brinkman extended Darcy model is applied in the porous region and the stress jump and continuity conditions are employed at the interface. Exact solutions are obtained for velocity, pressure drop, the fluid and solid temperatures and Nusselt number. The effects of pertinent parameters on the fluid flow and heat transfer are conducted. Furthermore, the solution for the Nusselt number is compared to that by applying the local thermal equilibrium (LTE) assumption and the validity of the LTE is examined. It is shown that by applying LTNE model for different solid to fluid effective thermal conductivity ratios (K) and Biot numbers (Bi), the variations of Nusselt number with hollow ratio include three types of curves, which are: a maximized Nusselt number occurs at a small optimum hollow ratio, Nusselt number monotonically decreases by increasing hollow ratio and a minimized Nusselt number occurs at a small hollow ratio, respectively. For high K, a small critical value of S at which the Nusselt number reaches to LTE Nusselt number occurs and it lowers with the increase of Bi number and the decrease of Darcy number; while for low K, the LTNE Nu number versus hollow ratio is almost the same with LTE Nu number and therefore the LTE is valid. The stress jump at the interface is found to have negligible effect on the Nusselt number and the pressure drop, except in a high Darcy number with a low stress jump coefficient where the calculation of pressure drop need to account for the stress jump effect at the interface and the Nusselt numbers for both LTE and LTNE models slightly differs from the case of stress continuity interface condition.

Exact Analytical Nanofluid Flow and Heat Transfer Involving Asymmetric Wall Heat Fluxes with Nonlinear Velocity Slip

Nanofluid slip flow and heat transfer over the microchannel with asymmetric wall heat fluxes are investigated theoretically. The local thermal nonequilibrium model in which there is a difference between the solid temperature and nanofluid temperature is modified by considering the nonlinear velocity slip and temperature jump. Exact analytical solutions and homotopy series solutions for both velocity and temperature of nanofluid and solid are first obtained. Two groups of solutions agree well with existing references and residual errors are plotted. In addition, the effects of the physical factors on the heat transfer are graphically discussed. The results show that the first velocity slip enhances Nusselt numbers while the second slip coefficient has a reverse effect on them. As expected, the nanoparticle concentration enhances heat transfer on bottom wall.

Analysis of thermally developing forced convection heat transfer in a porous medium under local thermal non-equilibrium condition: A circular tube with asymmetric entrance temperature

Thermally developing forced convective heat transfer in a circular tube filled with a fluid-saturated porous medium is analytically investigated under local thermal non-equilibrium (LTNE) condition. In this study, we assume the forced convection within the porous medium obeys Darcy’s law, the tube has a constant temperature wall and possess an entrance with variable circumferential temperature distribution. Under these conditions, closed-form exact solutions of the fluid and solid phases temperatures are derived by using the method of separation of variables. The finite element (FE) analysis software COMSOL Multiphysics is employed to numerically model the studied problem. The good agreement between the presented analytical solutions and the FE solutions verifies the validity of the analytical solutions presented. Meanwhile, the consistency of the axisymmetric analytical solutions in the case of uniform entrance temperature with the existing analytical solutions in the literature confirms again the correctness and the reliability of the presented analytical solutions. Given the entrance temperature can be an arbitrary well-defined function, the presented analytical solutions are of general applicability. The subsequent parametric studies are carried out based on the presented analytical solutions. It is demonstrated that the temperature fields are non-axisymmetrical with respect to the circumferential coordinate, which is induced by the asymmetric entrance temperature. Besides, the Péclet number and the Biot number play significant roles in heat transfer. The increase of the Péclet number will result in the transition of thermally developing forced convection to the fully developed regime, while the temperature difference between the fluid and solid phases decreases with increasing the Biot number. Moreover, as a limiting case, the LTNE model degenerates to the LTE model when the Biot number approaches infinity. Our findings are of benefit to provide deep insights into the thermal behavior of forced convection in a porous circular tube with asymmetric entrance temperature under LTNE condition.

Analysis of thermal transport and fluid flow in high-temperature porous media solar thermochemical reactor

As a key technical indicator of porous media solar thermochemical reactor, thermal transport and fluid flow characteristics have significant impacts on hydrogen production efficiency. These issues could be achieved more efficiently and at a lower cost by applying computational fluid dynamics (CFD). However, the choice of different thermal transport models might cause the variation of results. In this study, the thermal transport and fluid flow characteristics in high-temperature porous media solar thermochemical reactor were investigated with different thermophysical models using FLUENT software user-defined functions (UDFs). The results indicate that the local thermal non-equilibrium model (LTNE) and radiative transfer model are proved to be indispensable for the thermal performance analysis of high working temperature thermochemical reacting system. Besides, Wu model of momentum source is more suitable for pressure simulation, while Wu model and Vafai model of heat transfer show little difference in temperature distribution.

The simulation of thermo-hydro-chemical coupled heat extraction process in fractured geothermal reservoir

Chemical reaction effect is a critical issue in the heat extraction process of a fractured geothermal reservoir. In this study, the thermo-hydro-chemical coupled condition is simulated based on a unified pipe-network method (UPM) by considering interconnected fracture networks embedded in the rock mass. The chemical reaction kinetics of silica precipitation and dissolution is incorporated to capture and examine the effects of the silica-water interaction on the evolution of fracture apertures. The chemical influenced heat transfer between solid and fluid phases in the fractured porous media is characterized by a local thermal non-equilibrium (LTNE) model introduced based on two energy balance equations. A pipe equivalent technique is used to discretize the multiphysical coupled equations and unify the fracture-matrix information at the interface through the superposition principle in the UPM framework. Convergence tests are performed to verify the proposed model with one large fracture embedded in a doublet system for geothermal development. Fracture networks are then introduced in a case study where the influences of different injection temperature, saturation condition, injection pressure differential and initial fracture aperture on the silica reaction related alteration of fracture apertures as well as the heat production are analyzed.

Thermal characteristics analysis with local thermal non-equilibrium model during liquid nitrogen jet fracturing for HDR reservoirs

This paper presents a numerical analysis of thermal characteristics in bottom-hole rock during liquid nitrogen jet fracturing for hot dry rock (HDR) reservoirs. The standard κ-ε and Darcy models are employed to calculate the fluid flow in fluid region and porous-rock region respectively. The heat transfer between flowing fluid and rock matrix is simulated by the local thermal non-equilibrium model. The thermal stresses are evaluated based on thermo-elastic model. Furthermore, a sensitivity study is conducted to investigate the influences of different factors on heat transfer efficiency in porous rock. The results show that the fluid has a relatively high velocity in the rock region impacted by high-speed jet. The flow transport in porous rock can significantly improve the cooling performance of hot rock. The thermal stresses induced by temperature gradient are huge enough to create thermal cracks in formation. The parametric analysis indicates that increasing the values of ambient pressure, rock permeability and convection coefficient can promote the heat transfer in porous rock obviously, while the parameters of pressure drop and rock porosity have a slight impact on the cooling rate. The results in this study would offer guidance for the design of HDR fracturing with liquid nitrogen jet.

Numerical investigation on forced convection of tubes partially filled with composite metal foams under local thermal non-equilibrium condition

In the present study, fully developed forced convection in tubes partially filled with composite metal foams (CMFs) is numerically investigated. In the CMF region, the Brinkman extended Darcy flow model and the local thermal non-equilibrium model are used to predict fluid and thermal transport. At the foam-foam interface in CMF, fluid temperature and solid energy are assumed to be continuous. At the foam-fluid interface, no-slip coupling conditions are used to couple flow and heat transfer of the foam and free regions. Governing equations are solved numerically with SIMPLE algorithm. Momentum and energy equations are discretized using the SGSD finite volume scheme for convective terms. Velocity distribution, temperature profile, the friction factor and Nusselt number in partially-filled CMF tubes are obtained. The results indicate that, porosity gradient has little effect on the friction factor at a low pore density, but the effect increases with increasing pore density. For the fixed pore density gradient, Nusselt number decreases with increasing porosity, and Nusselt number firstly increases sharply and then increases lineally with increasing Reynolds number. For the fixed material gradient, Nusselt number increases lineally with increasing Reynolds number.

Local thermal non-equilibrium analysis of conjugate free convection within a porous enclosure occupied with Ag–MgO hybrid nanofluid

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

Internal heat generation effect on transient natural convection in a nanofluid-saturated local thermal non-equilibrium porous inclined cavity

The aim of the present study is to analyze the convective flow and heat transfer of nanofluid in an inclined cavity filled with heat generating porous medium using the local thermal non-equilibrium model. The horizontal bottom wall of the cavity is maintained at a constant higher temperature while the left and right vertical walls are maintained at a constant lower temperature. The top wall is to be kept as adiabatic. The Darcy model is adopted for flow through the porous medium and the Boussinesq approximation is taken into account. The pores are saturated by a water-based nanofluid consisting of Cu nanoparticles. The governing equations are solved iteratively by finite difference based Alternating Direction Implicit (ADI) method. The results are discussed by various combinations of parameters involved in the study. The average heat transfer rate decreases when increasing the values of nanoparticle volume fraction for the case of high Rayleigh numbers. The heat transfer rate is enhanced by increasing values of the modified conductivity ratio and the porosity of the media. The results have possible applications in the heat-storage nanofluid-saturated porous systems.