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In this article, we have discussed two-dimensional steady, incompressible, and laminar hydromagnetic flow along with the transfer of heat above a plane plate that contains water and ethylene glycol-based nanofluids with multi- and single-wall CNTs. The velocity slip boundary condition is included in this research article to evaluate the nature of flow. The plate surface is subjected to variable wall temperature. The transfer of heat has been contemplated in the company of suspended CNTs above a flat plate. Navier–Stokes and the concept of the Prandtl boundary layer have been used to determine the governing equations of heat transfer and flow. Since the attained governing equations representing energy and flow are nonlinear PDEs, they are altered into nonlinear ODEs accompanied by analogous boundary limitations by applying some appropriate similarity transformations. Hence the "RK45" function is used to solve them numerically. The influence of governing parameters on the dimensionless flow and heat transfer profiles are studied and discussed thorough graphical plots. [ABSTRACT FROM AUTHOR]

Modelling of transition from the laminar to turbulent flow became a hot topic due to recent developments in renewable energy, UAV technologies and similar aerospace applications. The transition from laminar flow to turbulence is challenging to model in CFD analysis. The drag is overestimated if the transition is neglected in CFD solutions by assuming the flow is fully turbulent. This results in missing the fundamental characteristics of the flow and inaccurate predictions of the flow field. The most popular transition models are Menter's models applied to the SST turbulence model and the Baş-Çakmakçıoğlu (BC) transition model applied to the Spalart-Almaras model. We have focused on Menter's simpler but more popular γ model and Baş Çakmakçıoğlu models. The γ model relies on the local turbulence intensity, which makes applying the model challenging in external flows. This difficulty stems from the complex relationship between turbulence decay and transition onset. BC transition model utilizes the free stream turbulence intensity. Both models are verified using the Klebanoff and ERCOFTAC flat plate cases and several 2D external flow cases. Skin friction coefficient results are compared to experimental data. Results show that both models predict transition very similarly. BC model is computationally cheaper and easier to implement than the γ model. Also, γ model suffers from boundary conditions ambiguity. [ABSTRACT FROM AUTHOR]

In this paper, the new semi-analytical correlation for displacement thickness of laminar fluid flow along an arbitrary-angle corner formed by the intersection of two plates has been proposed because of the discrepancy in displacement thickness for strong interference corner between the present computational fluid dynamics simulation and previous analytical correlation. [ABSTRACT FROM AUTHOR]

Heat transfer is one of the most fundamental engineering subjects and is found in every moment of life. Heat transfer problems, such as heating and cooling, where the transfer of heat between regions is calculated, are problems that can give exact solutions with parametric equations, many of which were obtained by solving differential equations in the past. Today, the fact that heat transfer problems have a more complex structure has led to the emergence of multivariate models, and problems that are very difficult to solve with differential equations have emerged. Optimization techniques, which are also the subject of computer science, are frequently used to solve complex problems. In this study, laminar thermal boundary layers in flow over a flat plate, a sub-problem of heat transfer, is solved with recent metaheuristic algorithms. Teaching learning-based optimization (TLBO), sine cosine optimization (SCO), gray wolf optimization (GWO), whale optimization (WO), salp swarm optimization (SSO), and Harris hawk optimization (HHO) algorithms are used in the study. In the optimization problem, the laminar boundary layer thickness, heat flow, and distance from the leading edge are determined. These three models' minimum, maximum, and target values are found under the specified design variables and constraints. In the study, 540 optimization models are run, and it is seen that HHO is the most suitable optimization technique for heat transfer problems. Additionally, SSO and WO algorithms gave results close to HHO. Other algorithms also set model targets with an average of less than 0.07% and acceptable error rates. In addition, the average problem solution time of all optimization algorithms and all models was 0.9 s. To conclude, the recent metaheuristic algorithms are found to be powerful and fast in solving heat transfer problems. [ABSTRACT FROM AUTHOR]

This numerical study investigates the wake-induced vibration of single or parallel flat plates mounted in the wake of a circular cylinder in laminar flow. The results highlight the critical role of flat plate positioning, as it influences their ability to act as control mechanisms or experience significant vibrations. For a single plate, mounting outside the critical position initiates large amplitude vibrations, gradually decreasing as the plate moves away from the horizontal axis. Additionally, vibrations with moderate amplitudes are observed at specific short horizontal positions due to variations in the near-wake structure. In the case of parallel plates constrained to vibrate independently, vibrations only occur when there is sufficient space for shear-layer interaction. Different vortex suppression and plate vibration mechanisms are identified by adjusting the vertical gap, where increasing the gap reduces the non-vibrating zone. The study also examines a range of reduced velocities, revealing that although the plate(s) follow the upstream cylinder's shedding frequency in all configurations, this frequency may be affected and altered in short gaps. Comparing single and parallel plates demonstrates their potential for designing energy harvesting systems. However, parallel plates offer a slight advantage due to using independent objects within a relatively identical area. • A single plate may vibrate considerably even in near wake under certain circumstances due to the vortex formation mechanisms. • Unlike a single plate, the parallel plates show a distinct boundary separating the vibrating and non-vibrating zones. • The parallel plates show different vibration mechanisms depending on their vertical gap. • While the single plate shows better mean vibration amplitude, the parallel ones have higher amplitude per swept area. [ABSTRACT FROM AUTHOR]

In the present study, new drag reduction techniques applied to aerodynamic structures have been developed. The test cases have been numerically performed using three simplified models. Simulations have been performed by using the CFD software Ansys fluent. The first case deals with a laminar flow over a flat plate. Drag reduction is obtained by corrugating the shape of the plate. The second case treats a laminar flow over a NACA 0012 airfoil. By the addition of a device fixed on the flow separation point, the drag could be reduced. The last case concerns a turbulent flow over the Ahmed body. Drag reduction is obtained by the perforation of a conduit leading a part of the flow from the front to be injected at the rear of the body. [ABSTRACT FROM AUTHOR]

Heat transfer is one of the most fundamental engineering subjects and is found in every moment of life. Heat transfer problems, such as heating and cooling, where the transfer of heat between regions is calculated, are problems that can give exact solutions with parametric equations, many of which were obtained by solving differential equations in the past. Today, the fact that heat transfer problems have a more complex structure has led to the emergence of multivariate models, and problems that are very difficult to solve with differential equations have emerged. Optimization techniques, which are also the subject of computer science, are frequently used to solve complex problems. In this study, laminar thermal boundary layers in flow over a flat plate, a sub-problem of heat transfer, is solved with recent metaheuristic algorithms. Teaching learning-based optimization (TLBO), sine cosine optimization (SCO), gray wolf optimization (GWO), whale optimization (WO), salp swarm optimization (SSO), and Harris hawk optimization (HHO) algorithms are used in the study. In the optimization problem, the laminar boundary layer thickness, heat flow, and distance from the leading edge are determined. These three models’ minimum, maximum, and target values are found under the specified design variables and constraints. In the study, 540 optimization models are run, and it is seen that HHO is the most suitable optimization technique for heat transfer problems. Additionally, SSO and WO algorithms gave results close to HHO. Other algorithms also set model targets with an average of less than 0.07% and acceptable error rates. In addition, the average problem solution time of all optimization algorithms and all models was 0.9 s. To conclude, the recent metaheuristic algorithms are found to be powerful and fast in solving heat transfer problems.

This study investigates the heat transfer capability between the near-wall water and a heating flat surface under the low frequency ultrasonic waves. The experiment was conducted at the main stream velocities of 0.12, 0.14, and 0.17 m/s, corresponding with the local Reynolds number between 60,000 and 200,000. The ultrasound, having a frequency of 25, 33, and 40 kHz was released from a 60 W flat transducer in a downward direction to disturb a near-wall flow over the flat surface having a constant heat flux of 1875 W/m 2 . The temperature decrease due to the disturbance of ultrasound, detected by 7 thin-leaf thermocouples, led to the increase in the Nusselt number by up to 10%, 16.5%, and 20.8%, at the wave frequency of 25, 33, and 40 kHz, respectively. The use of the thermochromic liquid crystals on the heating surface, disturbed by the 40 kHz wave, revealed that the bound of the wave incident region was shaped like a spiky structure that alternately occurs following with time. This incident region moved further downstream when the mainstream velocity increased and caused a retardation of the near wall flow, leading to a worse heat transfer in the upstream region. Therefore, the inclination of the acoustic beam, occurring as a variation of mainstream velocity, must be considered in order to use the ultrasound to enhance the heat transfer. Finally, the predictive formulas for the local Nusselt number under the 25–40 kHz waves are also provided and the mechanism of heat transfer is discussed. [ABSTRACT FROM AUTHOR]

A numerical simulation is carried out to study flow-induced vibration of an elliptical cylinder equipped with a wake-mounted flat plate in a laminar flow regime at Re = 100. The objects are constrained to vibrate independently in the cross-flow direction. The Vortex-induced vibration of an upstream cylinder with four different aspect ratios (AR = 0.25, 0.5, 0.75, 1) is investigated in the presence of a plate mounted in different horizontal spacing of G = 0.5–3. Simulations are performed for a fixed mass ratio of 10 and negligible damping ratio across a range of reduced velocities (U r = 2–12). The results demonstrate that the presence of the flat plate can amplify the vibration amplitude of the cylinder by altering the shear layers' structure, particularly at short horizontal distances. Moreover, the phase difference of the objects shows a correlation with both the horizontal distance and the AR. Furthermore, the presence of the plate results in broader lock-in regimes across all aspect ratios by delaying its end to larger reduced velocities. While reducing the AR leads to a higher maximum vibration amplitude of the cylinder, it results to a considerably lower amplitude for the plate due to different wake structures and reduced interaction between the shear layers and the flat plate. • FIV of an elliptical cylinder with a wake-mounted flat plate is studied for different aspect ratios and horizontal spacing. • While lowering the gap amplifies the cylinder's vibration amplitude in all ARs; it is limited to AR = 0.25, 1 for the plate. • Vibration phase difference is correlated with the AR and horizontal spacing simultaneously. • Change in the shear layers structure results in higher vibration amplitude and a broader lock-in regime. • A larger maximum vibration amplitude for the cylinder and a lower one for the plate is found by reducing the AR. [ABSTRACT FROM AUTHOR]

A numerical investigation is carried out to demonstrate a proof of concept, magnetohydrodynamics-based active flow control, for mitigation of laminar flow separation over a flat plate due to shock wave-boundary layer interaction. The CERANS-MHD code has been used to solve the governing resistive magnetohydrodynamic equations discretized in finite-volume framework. The AUSM-PW+ flux function is used in modelling the advection terms and central differencing is used in modelling the resistive terms. Powell's source term method is used for divergence cleaning of the magnetic field. The Hartmann number is varied from 0 to 12,000 to effectuate mitigation of flow separation, with the magnetic field applied at the wall and oriented transverse to the flat plate flow direction. Due to the Hartmann effect, flow separation is observed to be suppressed with increase in Hartmann number beyond 6000. However, the overall magnitude of skin friction distribution increases drastically, resulting in large increase in skin friction drag as compared with the non-magnetic case, and is a cause of concern. [ABSTRACT FROM AUTHOR]

The multiple solutions of a conjugate heat transfer problem modeling laminar forced convection on one side of a flat plate and multi-boiling cooling on the other side has been numerically studied. The hydrodynamic and thermal boundary layers are treated by means of an integral technique coupled with axial conduction along the plate. The boiling process is modeled by a simple and generalized heat transfer coefficient valid for all three boiling regimes. Two problems with different boundary conditions have been considered and up to five solutions have been numerically calculated. The analysis reveals that the longitudinal conduction along the plate together with the nonlinear boiling curve, are the key processes responsible for the multiplicity features of the problem whereas the modified Brun number and the conduction-convection parameter significantly affect the solution. The boundary conditions have a profound effect on the bifurcation structure but they do not affect the stability properties since for both problems out of the five solutions three are stable and two unstable. Stability analysis shows that there exists a temperature distribution where all boiling modes may be present simultaneously along the plate. [ABSTRACT FROM AUTHOR]

A synthetic optimization is presented for the Pareto layouts of discrete heat sources (with uniform heat flux) flush mounted on a flat plate over which laminar flow serves for cooling purpose. The peak temperatures and the flow drag loss are minimizing simultaneously provided that the total heat dissipation rate and the plate length are held constant. The impact of the manufacturing limit, i.e. the minimum length of the heated or the adiabatic patch, on the optimum layout is discussed. The results in general comply with analytical deduction based on the constructal theory. However in a finite length scenario, geometric constraints on the adiabatic spacing differ from that fits the situation in which maximum heat transfer performance alone is to be achieved. [ABSTRACT FROM AUTHOR]

Flow-induced vibration of bluff bodies and especially circular cylinders have been always of great interest and flat plates are known as useful means for altering flow structure to the desired condition. This work aims to investigate the effect of two parallel downstream flat plates which are mounted in the wake of a circular cylinder. Different configurations including eight horizontal (0.5≤G ≤ 4) and two vertical gaps (H = 0.5, 1) are numerically simulated to focus on the near wake structure and FIV of objects. The results show that the response of parallel plates in the wake of a stationary cylinder depends on both their horizontal and vertical locations. Change in the vertical distance alters the vortex shedding suppression mechanism. While a smaller vertical distance leads to a larger horizontal non-oscillating range, it comes with a higher maximum vibration amplitude. In the case of simultaneous oscillation, all three objects vibrate in all horizontal distances for the smaller vertical gap. The vibration disappears for the larger gap due to weaker interaction between the plates and the shear layers for a range of horizontal distances. The higher vibration amplitude in simultaneous vibration shows the considerable potential of the current concept for developing an improved energy harvesting system. • The FIV of a circular cylinder and two wake parallel flat plates are numerically simulated in laminar flow. • The effect of horizontal and vertical spacing of the plates are investigated. • Different vortex shedding suppression methods are found as the vertical spacing changes. • Smaller vertical gap results in a higher vibration amplitude for the plates in the wake of fixed cylinder. • In simultaneous oscillation, small horizontal gap may amplify the vibration and widen the lock-in regime of all objects. [ABSTRACT FROM AUTHOR]

The Flow-Induced vibration around bluff bodies is always of great interest in terms of control and suppressing the motion or amplifying and harvesting energy and the flat plates are known as useful means to make proper changes in flow structure. The objective of this paper is to investigate the effect of a downstream flat plate with one degree of freedom on the wake structure and FIV of an upstream circular cylinder in laminar flow. Numerical simulation is used to simulate the two-dimensional incompressible flow around two rigid objects with identical characteristic lengths and a variable horizontal spacing in a range of 0.5D ≤ G ≤ 4D to focus on the near wake and interaction of two objects. The results show that a free to vibrate flat plate located in the wake of a rigid cylinder not necessarily plays the role of a splitter in the near wake and starts to vibrate in an even small spacing such as G = 1.5D. The Recirculation zone structure and its length are found to be the main reasons for induced vibration in such close configurations. In the case of simultaneous free oscillation, reducing the horizontal gap amplifies the amplitude of both objects. The interaction of the oscillating plate and the shear layers results in vortices with more strength that affect both objects. This amplification in oscillation amplitude shows that the present concept has a considerable potential to be utilized in the design of an improved energy harvesting system by converting fluid dynamic energy into electric energy from independent objects in a small area. • The FIV of a circular cylinder and a downstream flat plate are numerically simulated in laminar flow. • The effect of horizontal spacing of the plate is investigated for individual and simultaneous free vibration. • Different vortex formation mechanisms are found depending on the horizontal spacing for fixed cylinder. • In simultaneous vibration, small gaps amplifies the vibration amplitude of all objects. • Small horizontal gap widens the lock-in regime for both objects which shows the energy harvesting potential. [ABSTRACT FROM AUTHOR]

Transition control is of great significance in laminar flows since determination of aerodynamics coefficients as well as heat transfer magnitude is strongly affected by accurate prediction and control of this phenomenon. Transition is exceedingly dependent on space and time such that various microscopic and macroscopic scales can convert to each other rapidly. On one side, available uncertainties in RANS turbulence models can lead to inappropriate, or at least expensive, designs. On the other, considering the growing rate of computational resources along with development of more efficient numerical methods in CFD applications, Direct Numerical Simulation, DNS, has found an applicable role even in industrial applications. In the present study, a robust computational code is developed for Direct Numerical Simulation aimed at fundamental purposes. To this end, high-order compact finite-difference for spatial derivatives and high-order Runge-Kutta time integration are used in the present code as well as a low-pass filter to elucidate spurious oscillations. Also, non-reflecting boundary condition is employed to keep the domain size as small as possible and to improve the numerical accuracy at the boundaries. In the present study, Direct Numerical Simulation investigates controlled transition scenarios for flow over a flat plate. Results are in a good agreement with those of previous researches both qualitatively and quantitatively, which verify the various parts of the developed solver. [ABSTRACT FROM AUTHOR]

In this work, the steady flow of a Bingham plastic fluid past a two-dimensional heated flat plate has been investigated to delineate its momentum and heat transfer characteristics. The governing partial differential equations (continuity, momentum and thermal energy) have been solved numerically over the range of conditions as follows: Reynolds number, 0.1 ⩽ Re ⩽ 25, Prandtl number, 1 ⩽ Pr ⩽ 100 and Bingham number, 0 ⩽ Bn ⩽ 1000. Furthermore, the results for the two commonly employed boundary conditions, namely, constant temperature (CWT) and constant heat flux (CHF), prescribed on the plane surface have been contrasted. Detailed structures of the flow and temperature fields near the plane surface have been studied in terms of the streamline and isotherm contours which also help delineate the yield surfaces demarcating the yielded and unyielded regions formed in the vicinity of the heated flat plate depending upon the magnitude of the local stress tensor vis-à-vis the fluid yield stress. Extensive results are reported on the distribution of the local Nusselt number along the surface of the heated plate. The overall behaviour is described in terms of the drag coefficients and the mean Nusselt number which have been correlated in terms of the modified Reynolds number and Prandtl number. The drag coefficients show a positive dependence on the Bingham number. Similarly, the average Nusselt number also shows a positive dependence on the Bingham number for the CWT condition where as for the CHF condition, this trend is modulated by the value of the Reynolds number. In overall terms, it is possible to augment the average heat transfer by up to 35–40% in such fluids under appropriate conditions. [ABSTRACT FROM AUTHOR]

The steady two-dimensional laminar incompressible electrically conducting viscous fluid on a moving flat plate in the presence of a transverse magnetic field is studied. Taking suitable similarity variables, we transform the governing boundary layer equations into ordinary differential equations and solve them numerically by standard techniques. The effects of moving and magnetic parameters, Prandtl number, and Eckert number on the velocity and temperature as well as on the skin-friction coefficient and Nusselt number are studied. [ABSTRACT FROM AUTHOR]

Abstract: Boundary layer transition estimation and modelling is essential for the design of many engineering products across many industries. In this paper, the Reynolds-averaged Navier–Stokes are solved in conjunction with three additional transport equations to model and predict boundary layer transition. The transition model (referred to as the – – model) is based on the – framework with an additional transport equation to incorporate the effects low-frequency flow oscillations in the form of a laminar kinetic energy ( ). Firstly, a number of rectifications are made to the original – – framework in order to ensure an appropriate response to the free-stream turbulence level and to improve near wall predictions. Additionally, the model is extended to incorporate the capability to model transition due to surface irregularities in the form of backward-facing steps with maximum non-dimensional step sizes of approximately 1.5 times the local displacement thickness of the boundary layer where the irregularity is located (i.e ) at upstream turbulence intensities in the range . A novel function is proposed to incorporate transition sensitivity due to aft-facing steps. This paper details the rationale behind the development of this new function and demonstrates its suitability for transition onset estimation on a flat plate at zero pressure gradient. [Copyright &y& Elsevier]

Abstract: The flow of a fluid directed normally to a heated flat plate of finite length (two-dimensional flow) is considered in the present paper. Three cases are considered: i. both sides of the plate are heated at the same uniform temperature. ii. The upper side is heated uniformly while the lower side is insulated (upward facing plate). iii. The upper side is insulated while the lower side is uniformly heated (downward facing plate). The problem is investigated numerically with a finite volume method using the commercial code ANSYS FLUENT. The governing parameters are the Reynolds number, the Richardson number and the Prandtl number and the influence of these three parameters on the drag coefficient, the average Nusselt number and the wake length is investigated for all the considered cases. It is found that the drag coefficient, the Nusselt number and the wake length in the downward facing plate is always greater than that in the upward facing plate, for all the examined values of the Richardson, Reynolds and Prandtl number. The vertical centerline velocity above the plate and above the wake increases continuously and finally becomes identical with the velocity of a two-dimensional plume while the vertical velocity below the plate shows a maximum and then goes to zero. At very high Prandtl numbers (Pr → ∞) the buoyancy force near the plate tends to zero and the drag coefficient as well as the wake length approach asymptotically the corresponding values of pure forced convection. [Copyright &y& Elsevier]

Abstract: An experimental study was conducted in order to investigate the influence of upstream conditions with respect to near-wakes evolution by using a two-dimensional flat plate. A position of for the flat plate with a blunt trailing edge was settled upon as an upstream condition point. Three upstream conditions (i.e., natural laminar, bypass transitional, and turbulent boundary layers) were applied by tripping wires that were placed on the upper surface of the plate. The free-stream velocity was 6.0 m/s and the local Reynolds numbers based on momentum thickness at the upstream conditions point were 259, 303, and 331. The boundary layers and the near-wakes were measured by hot-wire anemometry. It was observed that for the symmetric near-wakes, the local similarity profiles of the mean defect velocity matched well with the traditional similarity profile in the center part, whereas some difference in the outer part occurred due to the different trailing edge shape. For the asymmetric upstream conditions, the center of the local similarity profiles moved to one side, and the amplitude of the local similarity profiles over the wakes edge varied according to the momentum thickness of the upstream conditions. Also, the collapse of the normalized Reynolds shear stress depended on turbulent quantities included in the upstream conditions, and these results showed that the evolution of the near-wakes is clearly affected by upstream conditions. [Copyright &y& Elsevier]

Abstract: Analytical solutions for heat and mass transfer to fluids flowing across an isothermal flat plate were obtained. Laminar, inviscid and irrotational flow were assumed in the solution of the energy equation. The derived new relations were comparable with the experimental data and the solutions of other investigators. [Copyright &y& Elsevier]

The flat plate in fluid flow is the paradigm of heat transfer problems. The polynomial approximation of Pohlhausen to the Blasius solution for the flow leads to messy expressions in the integral formulation for the associated heat transfer between plate and flow, together with a continuation of the paradoxical results that the termination in the approximate solution implies. If the distribution is approximated in exponential form, the required integrals are easy– and may safely be attempted by a lecturer at the board or screen– and the anomalies eliminated. The results are perhaps less accurate than the Pohlhausen approximation but in either case would be replaced with exact values of the flow equations, obtained with considerably more difficulty. [ABSTRACT FROM AUTHOR]

In this paper, using the integration method, it is sought to solve the problem for the laminar boundary-layer on a flat plate. At first, a trial function of the velocity profile which satisfies the basical boundary conditions is selected. The coefficients in the trial function awaiting decision are decided by using some numerical results of the boundary-layer differential equations. It is similar to the method proposed by Peng Yichuan, but the former is simpler. According to the method proposed by Peng, when the awaiting decision coefficients of the trial function are decided, it is sought to solve a third power algebraic equation. On the other hand, in this paper, there is only need for solving a linear algebraic equation. Moreover, the accuracy of the results of this paper is higher than that of Peng. [ABSTRACT FROM AUTHOR]

This paper features a mathematical model of the wave function of fully developed nonperturbed laminar flow in the viscous region along an arbitrary-angle corner formed by the intersection of two semi-infinite flat plates. This model is then applied to determine the displacement thickness in the presence of a corner in the flow field. [ABSTRACT FROM AUTHOR]