Semi-implicit Method For Pressure-linked Equations Research Articles

Semi-submersible Offshore Coupled Motion in Irregular Waves

In order to predict the hydrodynamic performance of semi-submersible offshore platform accurately, based on CFD theory, continuous equation and N-S equation as the control equation, RNG type k-ε model as turbulence model, using the finite difference method to discretize the control equation，using the Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm to solve the control equation，using the VOF method to capture the free surface. The numerical wave tank of irregular wave is established, and the wave force and motion response of the semi-submersible platform under irregular wave are studied. Based on the Jonswap spectrum density function, for a certain area of two irregular waves (South China sea, a-ten-year return period, a-hundred-year return period) sea condition, five wave direction Angle (0 °, 30 °, 45 °, 60 °, 90 °), a total of 10 kinds of conditions of the motion response of semi-submersible platform are simulated, through analysis and comparison of simulation results, the influence law of wave angle, wave period and wave height on platform motion is obtained. Compared with the experimental values, the results of heave and pitch are close to the experimental data under the sea condition of 2, 0 degree wave angles. The research results in this paper can provide reference for the design and motion response prediction of practical semi-submersible offshore platforms.

Natural Convection of Dusty Hybrid Nanofluids in Diverging–Converging Cavities Including Volumetric Heat Sources

Abstract Two Semi-Implicit-Method for Pressure-Linked-Equations (SIMPLE) techniques have been performed to solve the dimensionless equations governing a dusty hybrid nanofluid flow in wavy enclosures contain a volumetric heat source. These techniques are applied to evaluate the pressure terms for both the hybrid nanofluid and the dusty particles based on the control volume solver. Two systems of equations are proposed to simulate the hybrid nanofluid phase and the dusty particles phase. In addition, a body-fitted method is applied to map the irregular domain into a rectangular domain, and an inverse map technique is used to present the obtained data inside the given wavy domain. The hybrid mixture, here, is consisting of water as a base fluid, and the nanoparticles are Al2O3 and Cu. The controlling parameters are the Rayleigh numbers RaE and Ral, the ratio of the densities of the mixture Ds, the dusty parameter αs, and the total nanoparticles volume fraction. The results revealed that the absolute values of the stream function are reduced by 54.5% when the heating modes are switched from (Ral/RaE) < 1 to (Ral /RaE) > 1. Also, the average Nusselt is enhanced by 5.2% at a = 0.9, 6.74% at a = 0.95, and 11.36% at a = 1.1 when the nanoparticles volume fraction is increased from 1% to 5%.

A segregated spectral element method for the 2D transient incompressible Navier-Stokes equations

In this paper, a spectral element method for the solution of the two-dimensional transient incompressible Navier-Stokes equations is introduced, which combines the segregated velocity-pressure equal-order formulation originated from the SIMPLE (semi-implicit method for pressure linked equations) algorithm. In contrast to previous segregated finite element method based on the SIMPLE algorithm, the pressure equation is derived from the momentum and continuity equations using the element matrices to ensure the convergence of the pressure. High-order element basis functions are adopted to construct the discrete form that presents arbitrary order or accuracy. The validation test with analytical solution verifies the high accuracy of the method. The flow in a lid-driven cavity with different inclination angles and the flow over a backward-facing step are investigated to further illustrate the property of the scheme. The computed results are in excellent agreement with the benchmark solutions, even if fewer grid points are used. The almost periodic solution for the flow of Re=10000 in a lid-driven square cavity is also captured by the present scheme. The numerical results indicate that the proposed high-order method can significantly reduce the number of grid points used in the calculation.

Experimental and Numerical Investigations of Subcooled Boiling Heat Transfer in a Small-Diameter Tube

Abstract The boiling heat transfer for subcooled water flowing in a small-diameter tube was investigated experimentally and numerically. In the experiment, a platinum tube was used as an experimental tube (d = 1.0–2.0 mm) to conduct joule heating by direct current. The heat generation rate of the tube was controlled with an exponential function. The numerical simulation of boiling heat transfer for subcooled water flowing in the small-diameter tube was conducted using the commercial computational fluid dynamics (CFD) code, phoenics ver. 2013. The small-diameter tube was modeled in the simulation. As the boundary condition, the measured heat flux was given at the inner wall. The inlet temperature ranged from 302 to 312 K. The flow velocities of d = 1.0 mm and d = 2.0 mm were 9.29 m/s and 2.34 m/s, respectively. The three-dimensional analysis was carried out from non-boiling to the critical heat flux (CHF). Governing equations were discretized using the finite volume method in the phoenics. The semi-implicit method for pressure linked equation (SIMPLE) method was applied in the numerical simulation. For modeling boiling phenomena in the tube, the Eulerian–Eulerian two-fluid model was adopted using the interphase slip algorithm of phoenics. The surface temperature difference increased as the heat flux increased in the experiment. The numerical simulation predicted the experimental data well. When the heat flux of the experiment reached the CHF point, the predicted value of the heat transfer coefficient was approximately 3.5% lower than that of the experiment.

Fluid Flow and Heat Transfer in an Annulus With Ribs on the Rotating Inner Cylinder Surface

Abstract Numerical studies on heat transfer in Taylor-Couette-Poiseuille flow in a cylindrical annulus with ribs mounted on the rotating inner cylinder are presented. The present study focuses on two different types of ribs, namely, longitudinal ribs and helical ribs. Three-dimensional, steady, incompressible, turbulent fluid flow is solved using a semi-implicit method for pressure linked equations (SIMPLE) algorithm based finite volume method. The numerical solution method is validated using two sets of benchmark experimental data. Extensive numerical computations are carried out at various Reynolds numbers (2100 < Re < 2400) and modified Taylor numbers (30,000 < Tam < 90,000) for annulus with and without ribs. Ribs enhance the transport of heat and momentum by inducing more vorticity and turbulence in the flow. The overall performance is presented in terms of thermal performance factor (TPF), which takes in to account the heat transfer as well as pressure drop in the ribbed annulus. Helical ribs are found to offer superior thermal performance than its longitudinal counterpart.

Modeling and assessment of two-phase transonic steam flow with condensation through the convergent-divergent nozzle

In the Fukushima accident, it was found that the Reactor Core Isolation Cooling (RCIC) system played a crucial role in delaying core meltdown by almost three days in Fukushima Daiichi Unit 2, because of self-regulated operation of the steam driven RCIC turbine-pump injection system. Steam flow in the convergent-divergent nozzles of the RCIC Terry turbine is two-phase non-equilibrium transonic flow with homogenous nucleation condensation. To more accurately predict the dynamic process and behavior of the transonic compressible steam flow, a one-dimensional transient two-phase analytical model is presented. A simplified four-fluid model was employed in the present work with the consideration of four separate fluid fields: vapor, liquid film, entrained droplets and condensed droplets. The mass, momentum and energy interactions between the fluids were considered and modeled. An extended seven-equation non-equilibrium critical flow model was developed to obtain the critical pressure and velocities of each phase at the nozzle throat. To predict the wetness in the divergent section, a mechanistic nucleation condensation model was integrated in the nozzle analysis model, considering the generation and consequent growth of droplets. The governing differential equations on a staggered grid were discretized using the second-order Lax-Wendroff scheme with a flux limiter, and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm was employed to solve the discrete linear system. To demonstrate the predictability and reliability of the physical models and the numerical method proposed in the present work, three representative nozzles were modeled and simulated. The results show good agreement with the available experimental data, even for condensation shock.

Simulation on Vortex Induced Vibration of Circular Cylinder

In order to study the vortical flow field and the vibration caused by fluid-structure interaction (FSI), an efficient simulation setup was established. The simulation made use of the built-in Deforming Mesh function, Semi-Implicit Method for Pressure Linked Equations (SIMPLE) Algorithm and SST-kw Turbulence Model of Ansys Fluent to generate the flow field. A User Defined Function (UDF) was written to calculate the displacement of the cylinder based on the simulated flow field information. A range of Reduced Velocity was scanned through in order to find the “locked-in” region, which is the resonance occurring region. The present study focused on the forces acting on the cylinder and the resultant trajectory of different cylinder natural frequencies. The simulation needs further fine tuning to improve the accuracy.

CFD simulation and experimental verification of the spatial and temporal distributions of the downwash airflow of a quad-rotor agricultural UAV in hover

The plant protection effect of an agricultural unmanned aerial vehicle (UAV) with multiple rotors is closely related to its speed and direction and the spatial and temporal distributions of the effective coverage of the downwash airflow. By combining compressible Reynolds-averaged Navier-Stokes (RANS) equations, the shear stress transport (SST) k-ω turbulence model, sliding grid technology and the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm, this paper establishes a computational fluid dynamics (CFD) model of the downwash airflow of the quad-rotor agricultural UAV in hover and discusses the distribution of the downwash airflow in the spatial and temporal dimensions. The simulation results show that most areas of the downwash airflow tend to be stable within 4.5 s, and due to the downward flow characteristics after the stabilization, the z-direction (perpendicular to the ground) velocity of the downwash airflow directly under the rotor is the highest with a maximum value of −8.96 m/s, which accounts for the main part of the downwash flow. The rotor downwash airflow flows downward in spiral form and the phenomenon of “contraction and expansion” is obvious during the downwash flow. Closer to the ground, the coverage area of the z-direction velocity is larger, the pressure distribution is more uniform, and the airflow exhibits an “upwash” phenomenon due to the “ground effect”. The test and simulation values at test points from 1 m to 2.5 m and 0.75 m exhibit the same variation trend with maximum relative errors of 10% and 15%, and the numerical simulation is accurate.

A heterogeneous parallel Red–Black SOR technique and the numerical study on SIMPLE

A basic heterogeneous parallel Red–Black successive over-relaxation (SOR) implement, the mono-color floating-point scheme, was developed on graphics processing units (GPU) with OpenCL platform. Designed in fine granularity, compact data structure, and stencil function, a concise mapping relationship was created to implicitly describe the complex rules for searching neighbor elements, which could avoid low utilization of GPU in the traditional scheme of Red–Black SOR. The new mono-color floating-point scheme was applied to build fast Semi-Implicit Method for Pressure Linked Equations (SIMPLE) solver with OpenCL and OpenMP on the heterogeneous parallel computing device. Compared with SIMPLE solver in the traditional Red–Black SOR scheme, the new scheme can achieve 1.7 to 1.8 faster accelerative performance on the same GPU. And this scheme can eliminate the complex searching module in mono-color logical scheme and behave better than the mono-color logical scheme by 20–30% acceleration. Numerical cases in double precision showed that SIMPLE solver on GPU with new scheme of Red–Black SOR could save up to 92% computing time compared with the serial solver on CPU.

Offshore Wind Turbine Coupled Motion in Regular Waves

AbstractThis study aims to accurately predict the hydrodynamic performance and motion responses of offshore wind turbines on the basis of computational fluid dynamics (CFD) theory. Continuous and Navier-Stokes (N-S) equations are employed as control equations, and the k-ε model is used as a turbulence model. The finite difference method is utilized to discretize the equation. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm is applied to solve the control equation, and the volume-of-fluid (VOF) method is used to capture the free surface. The numerical wave tank of irregular wave is also established. The hydrodynamic performances and motion responses of the offshore wind turbines under regular waves are studied. First, we assume a floating foundation without the influence of a rotational fan and examine its motion responses and wave force in three typical sea conditions, namely, Levels 5, 6, and 7. Thereafter, we use a series of force and torque acting on the rotating center of the offshore to substitute for the influence of the rotational fan on the floating foundation. Then, we study the hydrodynamic performance influenced by blade rotation of the floating foundation in various sea conditions and three wind speeds, namely, 5, 8, and 11 m/s. Research results can provide usable theoretical principle and technical support for the investigation of the hydrodynamic performance and motion responses of similar offshore wind turbines.

An Efficient Parallel Implementation of the SIMPLE Algorithm Based on a Multigrid Method

This paper deals with a parallel implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm to numerically solve the Navier–Stokes system of equations for viscous incompressible flows. A mechanism of interprocess communication using a mesh decomposition with virtual cells and an algebraic multigrid method is proposed. A method of distributed matrix storage and an algorithm for matrix-vector operations reducing the number of interprocess communications are presented. The results of a series of numerical experiments on structured and unstructured grids (including a problem of external aerodynamics) are presented. Based on the results obtained, an analysis of the influence of multigrid solver settings on the overall efficiency of the algorithm is made. It is shown that the parallel algorithm based on an algebraic multigrid technique proposed for the SIMPLE method makes it possible to efficiently calculate problems on hundreds of processors.

Investigation of the three-dimensional structure, pressure drop, and heat transfer characteristics of the thermohydraulic flow in a circular pipe with different twisted-tape geometrical configurations

The effect of inserting twisted tapes with various configurations and parameters inside a circular pipe on the flow field is studied. The pressure drop and turbulent heat transfer are investigated using the computational fluid dynamics (CFD) technique. Ten cases of heat exchanger pipes are considered numerically. The 3D Navier–Stokes, continuity, momentum, and energy equations are solved using Fluent software. To study the impact of the turbulent flow on the heat transfer performance, a scheme with the semi-implicit method for pressure-linked equations (SIMPLE) algorithm is adopted. Water is applied as the working liquid, with constant heat flux boundary conditions. The results show that insertion of a twisted tape has a strong effect on all the flow properties inside the pipe, such as the pressure, velocity, vorticity, and temperature. Moreover, the turning induced by the twisted tape can provide more effective mixing of the fluid and enhance the turbulent intensity, leading to a thermal boundary layer. It is reported that the maximum dynamic pressure occurs midway between the surface of the twisted tape and the pipe outlet. Such use of a twisted tape could lead to a greater pressure drop and make the flow in the pipe more unstable, due to influences of the stronger swirling flow and vortex flow as well as the effect of the increased turbulent intensity. The resulting strong swirling flow leads to an improvement in the heat transfer performance. The numerical results reveal that the introduction of a twisted tape efficiently increases the pressure drop and heat transfer, as well as improving the heat transfer performance by about 46.0%. Furthermore, the results indicate that insertion of a twisted tape can improve the thermal performance of the system.

Combined Heat and Mass Transfer of Fluid Flowing through Horizontal Channel by Turbulent Forced Convection

In the present paper, we report a numerical study of dynamic and thermal behavior of the incompressible turbulent air flow by forced convection in a two-dimensional horizontal channel. This one contains the complicated form of the deflector which has been studied by varying the inclination angle from φ = 40°, φ = 55° to φ = 65°. The baffles are mounted on lower and upper walls of the channel. The walls are maintained at a constant temperature (375 K), the inlet velocity of air is Uint = 7.8 m/s, and the Reynolds number Re = 8.73 × 104. A specifically developed numerical model was based on the finite-volume method to solve the coupled governing equations and the SIMPLE (Semi Implicit Method for Pressure Linked Equation) algorithm for the treatment of velocity-pressure coupling. For Pr = 0.71, the results obtained show that (i) the streamlines and isotherms are strongly affected by the inclinations angles at Re = 8.73 × 104, (ii) the friction coefficient near the baffles increases under the angle exchange effect, and (iii) for a constant Re, the local Nusselt number at the walls of the channel varies with increasing the inclination angle of the deflector. Furthermore, the deflectors are generally used to change the direction of the structure of flow and also to increase the turbulence levels. We can conclude that the contribution of inclined baffles improves the increase of heat and mass transfer in which the Nusselt number at a certain angle increases noticeably.

Transient numerical analysis of thermophoresis and particle dynamics in a nanofluid – pool boiling conditions

This paper attempts to apply two different equations of thermophoresis (applicable to micro-fluids) to nanofluids. Three significant parameters namely thermophoretic diffusion coefficient, thermophoretic velocity and thermophoretic mobility are used to analyse thermophoresis in a nanofluid. Both experiments and CFD simulations (ANSYS Fluent) are performed for water-alumina nanofluid under transient pool boiling conditions. A hollow stainless steel/glass chamber with a brass heater is used to boil water-alumina nanofluid under sub-cooled conditions. Three different heater surface temperatures (60, 70 and 80°C) are investigated to realize thermophoresis phenomena of the nanofluid. Random variation of temperature measurements in experiments is justified using an uncertainty analysis. Although, volume fraction of nanoparticles (diameter 46 nm) dispersed in the fluid is only 2% by volume, they are featured to exist in every frame of the numerical model for better understanding. 2-D transient implicit pressure based Navier-Stokes solver with SIMPLE (Semi-implicit Method for Pressure Linked Equation) pressure correction technique is used to discretize the numerical grid. Gauss-Seidel iterative procedure is used to solve the discretized equations. Simulation results are validated using a sequence of investigation (thermal property variation of water-alumina nanofluid with respect to pure water under steady-state/transient conditions, thumb rule from literature and experiments). A thin line of differentiation is found to exist between viscosity induced particle migration and thermophoresis induced particle migration for the nanofluid. Implications of equations and parameters used for estimating thermophoresis of nanofluid are discussed.

PARAMETRIC STUDY, MODELING, AND NUMERICAL SOLUTION OF AN INCLINED SOLAR STILL

This work numerically studies the heat transfer and fluid flow of an inclined solar still cavity. These devices convert saline or low-quality water into potable transporting water vapor from a warmer surface to a cooler one. The phenomenon of double-diffusion natural convection is considered. The solar still cavity has top and bottom sides inclined and subjected to temperature and concentration gradients, while the vertical walls are adiabatic. Water vapor is considered to be at the saturated state. The governing equations are conservation of mass, energy, momentum, and concentration. The conservation equations are coupled, and their solutions are based on the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. Velocity, temperature, and concentration fields are obtained for a Rayleigh number range in which laminar flow prevails, and for different cavity inclination angles and aspect ratios. The results show that for high Rayleigh numbers an increase in cavity inclination causes the Nusselt and Sherwood numbers and the solar still condensation rate to increase. When the aspect ratio is decreased, the Nusselt and Sherwood numbers also decrease; however, the condensation rate increases due to the increment of the condensable area. A solar still cavity of good thermal performance presented an inclination angle of 45° and an aspect ratio of 1/12 when the thermal Rayleigh number was 106.

How a conductive baffle improves melting characteristic and heat transfer in a rectangular cavity filled with gallium

The configuration of a latent heat thermal energy storage (LHTES) is an important factor considered by manufacturers of heat storage systems. In this study, an applicable and low-cost way of improving melting behavior in a rectangular cavity was remarked. There was a preconceived idea that with a single conductive baffle, embedded on the upper wall of the cavity, the melting rate and the amount of heat storage could improve. Therefore, for different locations as well as lengths of a baffle, the heat transfer and melting characteristic of gallium as a phase change material (PCM) in a rectangular cavity were investigated numerically. The cavity has the insulated upper and bottom walls. The sidewalls are regarded to have constant temperatures one higher and another lower than the melting point of gallium. The phase change process is modeled with the fixed grid-based enthalpy-porosity method coupled with the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. The isotherm lines and streamlines, as well as the liquid fraction and Nusselt number on the hot wall, are considered to present the results at a constant Rayleigh number equal to 106. The results show the baffle imposes noticeable improvement on the melting process of gallium in a rectangular cavity by influencing the feature of convective heat transfer. Investigating the different baffle’s locations (LX/L = 0.2 to 0.9) revealed that when the baffle located at the right half of the cavity, melting initiates from the left side, the more amount of PCM melts in comparison with the other cases. Ultimately, the dimensionless location of LX/L = 0.8 demonstrates the best melting characteristic and the most final liquid fraction. The more liquid-fraction, the more energy storing concluded. It also observed a dimensionless height of LY/L = 0.4 represents the most liquid-fraction compared to the heights of LY/L = 0.2, 0.3, and 0.4.

A segregated spectral finite element method for the 2D transient incompressible Navier–Stokes equations

In this paper, the spectral element approximation and the velocity–pressuredecoupling method implementing the SIMPLE (semi-implicit method for pressure linked equations) algorithm are first combined to form a high-order segregated scheme for the solution of the two-dimensional transient incompressible Navier–Stokes equations. In contrast to previous segregated finite element methods based on the SIMPLE algorithm, the pressure equation is derived from the continuity equation using the element matrices to ensure convergence. High-order element basis functions are adopted, which greatly reduces the number of nodal points used in the calculation. The validation test that has an analytical solution demonstrates the high accuracy and convergence rate of the method. The flow in a lid-driven cavity with different inclination angles and the flow over a backward-facing step are investigated to further illustrate the performance of the scheme. The computed results are in excellent agreement with the benchmark solutions. The almost periodic solution for the flow of Re=10000 in a lid-driven square cavity is also captured by the present scheme.

Nonhomogeneous Model for the Mixed Convection and Entropy Generation of a Nanofluid in a Lid-Driven Inclined Enclosure With Discrete Heat Source

Abstract A numerical study on the mixed convection of Al2O3–water nanofluid in a lid-driven inclined square enclosure partially heated from below is performed based on Buongiorno's two phase model. The velocity of the nanoparticles relative to the base fluid is considered due to thermophoresis and Brownian diffusion. The thermophysical properties of the nanofluid are assumed to be dependent on temperature as well as the nanoparticle volume fraction. A control volume method over a staggered grid arrangement is used to discretize the governing equations. The discretized equations of two-dimensional continuity, momentum, energy, and volume fraction are solved through a pressure-correction-based semi-implicit method for pressure linked equations (SIMPLE) algorithm. The effects of relevant parameters such as nanoparticle diameter (25 nm ≤ dp ≤ 90 nm), Richardson number (0.1≤Ri≤5), nanoparticle bulk volume fraction (0 ≤φb≤ 0.05) on the mixed convection of the nanofluid is studied by considering the inclination angle of the enclosure to vary between 0 deg and 60 deg. The entropy generation as well as the Bejan number is evaluated to illustrate the thermodynamic optimization of the mixed convection. Both the heat transfer and entropy generation are higher in the nanofluid compared to the clear fluid and the rate of increment in entropy generation remains lower than the rate by which the heat transfer is augmented in the nanofluid. We find that due to the presence of the Brownian diffusion and thermophoresis in the nonhomogeneous model, a higher heat transfer is yielded as compared to the homogeneous model. The discrepancy between the homogeneous and nonhomogeneous models is significant when the mixed convection is dominated by the shear force. When the mixed convection is dominated by the thermal buoyancy, an increase in positive inclination angle of the enclosure creates a significant increment in the heat transfer.

Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier–Stokes equations. The key feature of this approach is the seamless integration of a reduced order model (ROM) in the framework of an industrially validated computational fluid dynamics software. This is of special importance in an industrial environment because in the online phase of the PGD ROM the description of the flow for a specific set of parameters is obtained simply via interpolation of the generalised solution, without the need of any extra solution step. On the one hand, the spatial problems arising from the PGD separation of the unknowns are treated using the classical solution strategies of OpenFOAM, namely the semi-implicit method for pressure linked equations (SIMPLE) algorithm. On the other hand, the parametric iteration is solved via a collocation approach. The resulting ROM is applied to several benchmark tests of laminar incompressible Navier–Stokes flows, in two and three dimensions, with different parameters affecting the flow features. Eventually, the capability of the proposed strategy to treat industrial problems is verified by applying the methodology to a parametrised flow control in a realistic geometry of interest for the automotive industry.

Numerical simulation of forced convection in a bi-disperse porous medium channel by creating new porous micro-channels inside the porous macro-blocks

PurposePorous medium has always been introduced as an environment for increasing heat transfer in cooling systems. However, increase in heat transfer and resolving pressure drop in the fluid flow have been focused on by researchers.The purpose of this paper is to study the effects of creating porous micro-channels inside porous macro-blocks to optimize system performance in channels.Design/methodology/approachTo simulate flow field, a developed numerical code that solves Navier–Stokes equations by finite volume method and semi-implicit method for pressure linked equations (SIMPLE) algorithm will be used together with bi-disperse porous medium (BDPM) method. Working fluid is air with Pr = 0.7 in laminar state. Influence of permeability changes by creation of micro-channels containing porous medium in vertical, horizontal and cross-shape patterns will be investigated.FindingsBy creating porous micro-channels inside macro-blocks, not only does the heat transfer increase significantly but the pressure also drops remarkably. Increase in performance evaluation criteria (PEC) is more evident in lower Reynolds numbers that can increase the PEC to 75 per cent by creating cross-shape micro-channels. By changing the permeability of micro-channels, PEC will increase by reducing the pressure drop but it has minor changes in Nu.Research limitations/implicationsThe current work is applicable to optimizing system performance by decreasing the pressure drop and increasing the heat transfer.Practical implicationsThe developed patterns are useful in increasing the system performance including the increase in heat transfer and decrease in pressure drop in systems such as air coolers required in electrical circuits.Originality/valueDevelopment and optimization of system performance by new patterns using BDPM in comparison to the previous patterns.