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Accurate prediction of temperature distribution during thermotherapy is a significant factor in the thermotherapy process. Thermotherapy equipment produces a different distribution spatial and time-dependent heat fluxes in the thermotherapy processes. This paper presents an exact analytical solution of steady and unsteady Pennes and porous bioheat equations in a cylindrical coordinate system for multi-layer skin with different spatial and time-dependent heat fluxes on the surface. The proposed analytical solutions are useful to make accurate temperature distribution in multi-layer skin tissue with various properties. The results show that the unsteady temperature distributions in both Pennes and porous models are the same in the initial times of process. When the temperature rises, the cooling effect of blood perfusion in the Pennes model increases the difference in temperature distribution for these two models. The skin surface temperature is linear versus time in constant and linear fluxes, and skin temperature increment has a second-degree trend versus time in the quadratic flux. The magnitude of the flux coefficient and the time of applying flux to the tissue are effective in increasing the temperature of the tissue and the skin surface.

An image-based numerical algorithm is presented for simulating blood flow through the liver tissue. First, a geometric model is constructed by applying image processing techniques on a real microscopic image of a liver tissue. Then, incompressible blood flow through liver lobules is simulated. Effects of tissue heterogeneity and deformity, presence/absence of the second central vein in a particular lobule, and apparent sinusoids density in the liver cross section on the blood flow are investigated. Numerical results indicate that the existence of thick low permeability vascular septum, high permeability sinusoids, and lobule tissue heterogeneity can considerably affect interlobular and intralobular blood flow.

Two dimensional, steady state, and incompressible blood and bile flows through the liver lobules are numerically simulated. Two different geometric models A and B are proposed to study the effects of lobule structure on the fluid flow behaviour. In Model A, the lobule tissue is represented as a hexagonal shape porous medium with a set of flow channels at its vertices accounting for the hepatic artery, portal and central veins along with bile ductules. Model B is a channelized porous medium constructed by adding a set of flow channels, representing the bile canaliculies and lobule sinusoids, to Model A. The bile and blood flow through the lobule is simulated by the finite element approach, based on the Darcy/Brinkman equations in the lobule tissue and the Navier-Stokes (or Stokes) equations in the flow channels. In Model B, a transmission factor on the boundaries of the bile canaliculies is introduced to connect the bile and blood flows. First, a single regular lobule is utilized to exhibit the fluid flow pattern through the liver lobule represented by proposed geometric models. Then, the model is extended to a group of liver lobules to demonstrate the flow through a liver slice represented by irregular lobules. Numerical results indicate that the Darcy and Brinkman equations provide nearly the same solutions for Model A and similar solutions with a little difference for Model B. It is shown that the existence of sinusoids and bile canaliculies inside the liver lobules has noticeable effects on its fluid flow pattern, in terms of pressure and velocity fields.

Proper analysis of the temperature distribution during heat therapy in the target tissue and around it will prevent damage to other adjacent healthy cells. In this study, the exact solution of steady and unsteady of the hyperbolic bioheat equations is performed for multilayer skin with tumor at different heat fluxes on its surface and the generation of internal heat in the tumor. By determining the temperature distribution in three modes of constant heat flux, parabolic heat flux and internal heat generation in tumor tissue, the amount of burn in all three modes is evaluated. The results indicated that the Fourier or non-Fourier behavior of tissue has no role in the rate of burns in thermotherapy processes. At equal powers applied to the tissue, the internal heat generation in the tumor, constant flux and parabolic flux on the skin surface have the most uniform and most non-uniform temperature distribution, respectively and cause the least and the most thermal damage in the tissue.

There is no doubt that density is one of the most crucial thermophysical properties of hybrid nanofluids in thermal energy applications. Various research papers have been devoted to thermophysical properties of various hybrid nanofluids. However, a few of them focused on the simultaneous effects of nanoparticles, base fluids, and other factors on the density of hybrid nanofluids. In this research, a comparative study was conducted on non-parametric and evolutionary machine learning paradigms, namely, Multivariate Adaptive Regression Spline (MARS) and Evolutionary Polynomial Regression (EPR) models to accurately predict the density of a wide variety type of nanofluids in thermal energy applications. Here, for providing the predictive models, 501 data points were collected from the reliable recent literature. Besides, the Gene Expression Programming (GEP) and Multivariate Linear Regression (MLR) models were examined for validating the outcomes of MARS and EPR models. The comprehensive assessment demonstrated that the MARS outperformed the other models.

Purpose The purpose of this paper is to present detailed algorithms for simulation of individual and group control of production wells in hydrocarbon reservoirs which are implemented in a finite volume-based reservoir simulator. Design/methodology/approach The algorithm for individual control is described for the multi-lateral multi-connection ones based on the multi-segment model considering cross-flow. Moreover, a general group control algorithm is proposed which can be coupled with any well model that can handle a constraint and returns the flow rates. The performance of oil production process based on the group control criteria is investigated and compared for various cases. Findings The proposed algorithm for group control of production wells is a non-optimization iterative scheme converging within a few number of iterations. The numerical results of many computer runs indicate that the nominal power of the production wells, in general, is the best group control criterion for the proposed algorithm. The production well group control with a proper criterion can generally improve the oil recovery process at negligible computational costs when compared with individual control of production wells. Research/limitations/implications Although the group control algorithm is implemented for both production and injection wells in the developed simulator, the numerical algorithm is here described only for production wells to provide more details. Practical/implications The proposed algorithm can be coupled with any well model providing the fluid flow rates and can be efficiently used for group control of production wells. In addition, the calculated flow rates of the production wells based on the group control algorithm can be used as candidate solutions for the optimizer in the simulation-optimization models. It may reduce the total number of iterations and consequently the computational cost of the simulation-optimization models for the well control problem. Originality/value A complete and detailed description of ingredients of an efficient well group control algorithm for the hydrocarbon reservoir is presented. Five group control criteria are extracted from the physical, geometrical and operating conditions of the wells/reservoir. These are the target rate, weighted potential, ultimate rate and introduced nominal power of the production wells. The performance of the group control of production wells with different group control criteria is compared in three different oil production scenarios from a black-oil and highly heterogeneous reservoir.

This paper presents the numerical analysis of a novel thermal energy storage (TES) system using phase change material (PCM) for direct steam solar power plants. The energy storage system consists a preheater, steam generator and superheater in a cascade arrangement. The performance of the integrated system that constitutes a novel concept of thermal storage system is analyzed, numerically. The numerical model is verified against experimental data and the realistic effects of the operating conditions on the energy storage system performance are considered. The effects of different design parameters on the performance of the system are investigated. The effects of thermal conductivity of PCM, heat transfer fluid (HTF) flow rate and the diameter of heat exchanger tubes are analyzed during the entire thermal cycling of the evaporator. The effects of HTF flow rate and temperature on the exergy efficiency of TES system are analyzed. The results indicate that thermal conductivity of PCM is the most effective parameter, and increase of this parameter from 0.5 to 5 W K−1 m−1 leads to decrease of charging time from 25 to 4.5 h and increase of output steam quality from 0.2 to 0.5 during the discharging process. It is observed that cascade arrangement in preheater and superheater heat exchangers results in lower temperature gradient of the output HTF.

Different families of the Discrete Vapour Cavity Model (DVCM) are developed, including the frictionless, steady and quasi-steady friction models. A relaxation-dissipation approach is proposed to improve the timing of pressure pulses predicted by the classic DVCM. In this approach, a friction correction factor is introduced into the steady/quasi-steady friction term to reduce the local value of the dissipation term in regions facing with cavitation. The proposed approach is completely consistent with the classical water-hammer framework. The importance of the steady/quasi-steady friction term is investigated by comparing numerical results of different DVCMs with the experimental data for various cavitation problems. Based on a frictionless study, it is shown that there exists an unrealistic attenuation in pressure pulses of the classic DVCM. For problems with high-intensity cavitation, it is shown that the frictionless, steady and quasi-steady friction models generally produce different results, especially in terms of the pressure pulses timing. Within the range described in the manuscript, the timing of the classic DVCM pressure pulses can generally be improved by applying the proposed relaxation-dissipation approach on the steady/quasi-steady friction term.

Inhalation gas humidification is a kind of major matter for patients using mechanical ventilation systems due to the necessity of keeping mucus layer at the suitable thickness and wetness. The performance of membrane humidifier with partially blocked gas channels, is investigated in this study. Three types of membrane humidifier channel arrangement, including a normal, wet channel with obstacles, and similar ones in both channels (wet and dry) are studied under various mass flow rates and temperatures. Flanged obstacles improve the thermal efficiency of the humidifier so that in this case the outlet dry air temperature can be increased about 4°by using 10 obstacles in both channels but they increase the pressure drop noticeably. PEC is calculated as a dimensionless parameter to compare the performance enhancement with pressure drop increment, simultaneously. Higher water recovery rate (WRR) and dew point temperatures at the dry side channel outlet, indicate the higher humidifier performance. At all mass flow rates, presence of obstacles improves the performance of the humidifier by increasing the dew point temperature and water recovery rate (WRR). Overall, the presence of obstacles on both channels amplifies the overall performance of the membrane humidifier in almost all cases.

The quantitative determination of specific heat capacity (SHC) of molten (nitrate) salt-based nanofluids helps to control the start-up heat and prevent overheating when deployed as a working heat transfer fluid in a wide range of solar thermal applications. Thus, accurate measurement of the SHC and capturing the melting point is of paramount importance in the molten salt-based nanofluids’ characterization analyses applied in solar collectors. In this research, two modern ensemble machine learning models, Extra Tree Regression (ETR) and AdaBoost Regression (ABR), were developed based on 2,384 datasets, including solid mass fraction (w), temperature (T), SHC of base fluid ( C P Base ), mean diameter (Dp), and density ( ρ p ) of nanoparticle as all independent input variables and the SHC of molten salt-based nanofluids ( C P MS - n f ) as the target. Herein, the stepwise forward method and mutual information were addressed to determine the best input combination and sensitivity analysis. The provided models were validated using Random Forest (RF) and Boosted Regression Tree (BRT) as two powerful other ensemble models. The results demonstrated that ETR model in terms of (R = 0.9964, RMSE = 0.1566, and U95%=3.6062) outperformed the ABR (R = 0.9949, RMSE = 0.1855, and U95%=3.6009), RF (R = 0.9922, RMSE = 0.2326, and U95%=3.5904), and BRT (R = 0.9907, RMSE = 0.2508, and U95%=3.5857). The SHC of molten salt base fluid was identified as the most significant factor in estimating the SHC of molten salt-based nanofluids.

This paper concerns with numerical modeling of fluid flow through a zigzag-shaped channel to be used as the cooling plate for polymer electrolyte membrane fuel cells. In general, large scale PEM fuel cells are cooled by liquid water flows through coolant flow channels, and the shape of these channels has a key role in the cooling performance. We perform a three-dimensional numerical simulation to obtain the flow field and heat transfer rate in square area cooling plates. The performance of zigzag flow channels is evaluated in terms of maximum surface temperature, temperature uniformity and pressure drop. The results indicate that in the zigzag channels model, maximum surface temperature, surface temperature difference and temperature uniformity index, respectively, reduce about 5%, 23%, and 8% with respect to straight channels model. Hence, the cooling performance of fuel cells can be improved by implementing the zigzag channels model as the coolant fluid distributors, although the coolant pressure drop is higher than straight channels in this model.

A simulation-optimization model is proposed for identifying the characteristics of local immiscible NAPL contaminant sources inside aquifers. This model employs the UTCHEM 9.0 software as its simulator for solving the governing equations associated with the multi-phase flow in porous media. As the optimization model, a novel two-level saturation based Imperialist Competitive Algorithm (ICA) is proposed to estimate the parameters of contaminant sources. The first level consists of three parallel independent ICAs and plays as a pre-conditioner for the second level which is a single modified ICA. The ICA in the second level is modified by dividing each country into a number of provinces (smaller parts). Similar to countries in the classical ICA, these provinces are optimized by the assimilation, competition, and revolution steps in the ICA. To increase the diversity of populations, a new approach named knock the base method is proposed. The performance and accuracy of the simulation-optimization model is assessed by solving a set of two and three-dimensional problems considering the effects of different parameters such as the grid size, rock heterogeneity and designated monitoring networks. The obtained numerical results indicate that using this simulation-optimization model provides accurate results at a less number of iterations when compared with the model employing the classical one-level ICA.

Regarding their ability to enhance conventional thermal oils' thermophysical properties, oil-based hybrid nanofluids have recently been widely investigated by researchers, especially on lubrication and cooling application in the automotive industry. Thermal conductivity is one of the most crucial thermophysical properties of oil-based hybrid nanofluids, which has been studied in a minimal case of studies on the specific types of them. In this research, for the first time, a comprehensive data-intelligence analysis performed on 400 gathered data points of various types of oil-based hybrid nanofluids using a novel hybrid machine learning approach; the Extended Kalman Filter-Neural network (EKF-ANN). The genetic programming (GP) and response surface methodology (RSM) approaches were examined to appraise the main paradigm. In this research, the best subset regression analysis, as a novel feature selection scheme, was provided for finding the best input parameter among all existing predictive variables (the volume fraction, temperature, thermal conductivity of the base fluid, mean diameter, and bulk density of nanoparticles). The provided models were examined using several statistical metrics, graphical tools and trends, and sensitivity analysis. The results assessment indicated that the EKF-ANN in terms of (R = 0.9738, RMSE = 0.0071 W/m.K, and KGE = 0.9630) validation phase outperformed the RSM (R = 0.9671, RMSE = 0.0079 W/m.K, and KGE = 0.9593) and GP (R = 0.9465, RMSE = 0.010 W/m.K, and KGE = 0.9273), for accurate estimation of the thermal conductivity of oil-based hybrid nanofluids.

Two-phase incompressible fluid flow through highly heterogeneous porous media is simulated by using the Multiscale Finite Volume (MsFV) method. Effects of the localization assumption on the accuracy of the MsFV are investigated by comparing the results associated with different boundary conditions of local problems producing the basis functions. The total number of six boundary conditions of two general types, including Dirichlet and Dirichlet-Neumann types, are compared. For the former, the linear, variable (reduced), and step-type boundary conditions are considered and a modified variable boundary condition is proposed. For the latter, a basic and a step-type Neumann-Dirichlet boundary condition are suggested. To estimate the errors in the MsFV solutions for continuous problems, a heterogeneous two-dimensional problem with continuous permeability field is designed and solved analytically. Synthetic two-scale permeability fields as well as highly heterogeneous random fields are used to assess the accuracy of the MsFV solutions with different localization schemes, in comparison with the fine-scale reference solution. Numerical results indicate that the modified variable boundary condition, with a proper value of its weighting factor, can generally produce the most accurate results, when compared with the other localization schemes.

In the present work, the performance of proton exchange membrane fuel cells is studied for three cases; A fuel cell with two parallel flow channels (model A), locally baffle restricted flow channels (model B), and metal foam as a flow distributor (model C). The fully coupled thermal-electrochemical equations are numerically solved in three dimensions, based on the macroscopic, single-domain, and finite-volume approaches. While having no significant effect on temperature distribution, the existence of baffles inside flow channels results in more oxygen penetration into gas diffusion and catalyst layers at the cathode side of the cell. This improves the chemical reaction rate, current density and cell performance. Using metal foam increases oxygen concentration and current density at the cathode catalyst surface, and improves the uniformity of their distributions. Furthermore, a more uniform temperature distribution is achieved, when compared with the other cases. For the considered dimensions, it is observed that decreasing the flow channel depth results to an increase in current density and also in pressure drop along channels (models A and C). Moreover, increasing metal foam porosity can increase the current density value and decrease pressure drop in model C, while it has nearly no effects on temperature distribution.

Horizontal wells have gained considerable interest among petroleum engineers and hydrologists in the last decades. Many attempts were made to reach a better understanding of fluid flow behaviour inside the reservoir/aquifer, especially in the near-wellbore regions. In most of the previous studies on horizontal wells, each well is treated as a volumetric source term in governing equations describing the fluid flow in the main reservoir/aquifer. Many important features affecting the fluid flow, such as the realistic wellbore geometry, have been ignored for mathematical convenience. In the present study, the three-dimensional single-phase fluid flow through a large size reservoir block is coupled to wellbore flow through imposing the pressure and flux continuity at the reservoir-well interface. As the momentum equations, the Darcy and turbulent Navier–Stokes equations are used in the reservoir block and wellbore, respectively. The governing equations are discretized on unstructured grids and solved by using the finite volume method. Using the computed pressure and velocity distributions, the horizontal well characteristics are numerically estimated and compared with available analytic data for various cases. It is shown that the calculated well index, a coefficient in reflecting the geometric features of the well-reservoir system, deviates from its analytic value, as a result of reservoir block boundary condition, the pattern of the wellbore open intervals, the horizontal well drilling path, and its vertical eccentricity. In addition, the proposed approach is used to improve Economides model, an analytical model for horizontal well index, by estimating its pseudo-skin factor in various cases of the well vertical eccentricity, horizontal orientation, and reservoir block conditions.

Purpose – The purpose of this paper is to present a detailed algorithm for simulating three-dimensional hydrocarbon reservoirs using the blackoil model. Design/methodology/approach – The numerical algorithm uses a cell-centred structured grid finite volume method. The blackoil formulation is written in a way that an Implicit Pressure Explicit Saturation approach can be used. The flow field is obtained by solving a general gas pressure equation derived by manipulating the governing equations. All possible variations of the pressure equation coefficients are given for different reservoir conditions. Key computational details including treatment of non-linear terms, expansion of accumulation terms, transitions from under-saturated to saturated states and vice versa, high gas injection rates, evolution of gas in the oil production wells and adaptive time-stepping procedures are elaborated. Findings – It was shown that using a proper linearization method, less computational difficulties occur especially when free gas is released with high rates. The computational performance of the proposed algorithm is assessed by solving the first SPE comparative study problem with both constant and variable bubble point conditions. Research limitations/implications – While discretization is performed and implemented for unstructured grids, the numerical results are presented only for structured grids, as expected, the accuracy of numerical results are best for structured grids. Also, the reservoir is assumed to be non-fractured. Practical implications – The proposed algorithm can be efficiently used for simulating a wide range of practical problems wherever blackoil model is applicable. Originality/value – A complete and detailed description of ingredients of an efficient finite volume-based algorithm for simulating blackoil flows in hydrocarbon reservoirs is presented.

In the present work, the multiscale finite volume (MsFV) method is implemented on a new coarse grids arrangement. Like grids used in the MsFV methods, the new grid arrangement consists of both coarse and dual coarse grids but here each coarse block in the MsFV method is a dual coarse block and vice versa. Due to using the altered coarse grids, implementation, computational cost, and the reconstruction step differ from the original version of MsFV method. Two reconstruction procedures are proposed and their performances are compared with each other. For a wide range of 2-D and 3-D problem sizes and coarsening ratios, the computational costs of the MsFV methods are investigated. Furthermore, a matrix (operator) formulation is presented. Several 2-D test cases, including homogeneous and heterogeneous permeability fields extracted from different layers of the tenth SPE comparative study problem are solved. The results are compared with the fine-scale reference and basic MsFV solutions.