In this paper, the steady-state natural convection in a square cavity filled with water–Al2O3 nanofluid in the presence of magnetic fields with variable inclination angles is investigated numerically. The enclosure is subjected to different side-wall temperatures while the top and bottom walls are assumed to be adiabatic. The thermal behavior of enclosure is assessed using a finite volume-based computer program. In order to ensure the accuracy of results, comparisons are also made with a previous published work. In this research, at constant magnetic field strengths, the effect of magnetic field inclination angle on the rate of heat transfer in the square cavity is investigated at the Rayleigh numbers of Ra = 103, 104, 105 and 106. In this work, the Hartmann number ranges from Ha = 0 to 120 and the solid volume fraction varies from φ = 0 to 0.06. Numerical results show that depending on the Rayleigh and Hartmann numbers, the maximum heat transfer rate may occur at magnetic field inclination angles of 45°, 60° or 90° and the effect of magnetic field inclination angle is significant at high values of Rayleigh and Hartmann numbers. It is found that addition of nano-sized solid particles causes higher heat transfer rate when Ra = 103, whereas at Rayleigh number of Ra = 106, a reverse behavior is observed. Results show that at Rayleigh numbers of Ra = 104 and 105, the effect of solid particles addition on the thermal performance of the enclosure depends on the Hartmann number. It is also shown that an increase in the inclination angle causes higher velocity within the enclosure and addition of solid particles leads to suppression of flow field.
SUMMARYIn this research, an efficient methodology for calculation of pitching moment coefficient at low Mach number transonic flows by using the perturbed nonlinear reduced frequency approach is presented. The proposed approach uses the perturbation technique in the nonlinear frequency domain (NLFD) method to estimate the solution at high harmonics. In this approach, the density and velocity fields at high harmonics are perturbed about those at low harmonics. Perturbing the density and velocity fields, the semi-linear form of the governing equations is obtained. The resulting solution vector and spatial operator are then approximated by discrete form of Fourier transformation and governing equations are solved by using the pseudo-spectral approach. Numerical results show that the proposed approach predicts good pitching moment coefficient at low Mach number transonic flows with up to 50% savings in computational time.
Purpose – The objective of present research is to characterize the unsteady thermal behavior of a square enclosure filled with water-Al2O3 nanofluids in the presence of oriented magnetic fields. The purpose this paper is to study the effect of pertinent parameters on the transient natural convection in the enclosure. Design/methodology/approach – In this research, an in-house implicit finite volume code based on the SIMPLE algorithm is utilized for numerical calculations. To ensure the accuracy of results, comparisons are also made with previous works in literature. In this study, a constant strength magnetic field is concerned and for Rayleigh numbers of Ra=103, 104 and 105 the effect of magnetic field orientation with respect to the case of zero inclination on the thermal performance of cavity is investigated at Hartmann number range of Ha=15-90. In the present work, the nano-particle volume fractions range from φ=0-0.06. Findings – Results show that when Rayleigh number is Ra=103, the inclination angle, solid particles and Hartmann number has no effect on the transient behavior. It is shown that during the time advancement to steady condition, the heat transfer rate relative to zero inclination angle, may reach to a maximum value. This relative maximum heat transfer increases as the inclination angle increases and decreases as the solid volume fraction increases. The effect of increase in Hartmann number is to decrease this maximum value at Rayleigh number of Ra=104 and at Rayleigh number of Ra=105, depending on the Hartmann number, this value may increase or decrease. It is also found that an increase in Hartmann number leads to delay the appearance of the relative maximum value of heat transfer. Results show that this maximum value is of more significance at zero solid volume fraction when inclination angle is 90 degrees and Hartmann number is Ha=60. Originality/value – Limited works could be found in the literature regarding the idea of using nanofluids as the working fluid in an enclosure in the presence of magnetic field. In these works, the steady state thermal behavior of enclosures subjected to fixed magnetic fields is concerned. In the present work, the unsteady thermal behavior is concerned and the effect of magnetic field orientation angles on transient heat transfer performance of the enclosure at different Rayleigh and Hartmann numbers and solid volume fractions is explored.
Purpose -The purpose of this paper is to discuss the capability of nonlinear frequency domain (NLFD) method in predicting surface pressure coefficient presented in the time domain in unsteady transonic flows. Design/methodology/approach -In this research, the solution and spatial operator are approximated by discrete form of Fourier transformation and resulting nonlinear equations are solved by use of pseudo-spectral approach. Considered transonic flows involve different flow pattern on the airfoil surfaces. One of the test cases involves moving shocks on both lower and upper airfoil surfaces and in the two other test cases a moving shock occurs only on the upper surface. Findings -Pressure distributions presented in the time domain using NLFD are compared with three test cases. Results show that NLFD predicts reasonable pressure distributions in time domain except in vicinity of shock positions. Although this method may predict unfair results near shock positions, however gives good estimates for global properties such as lift coefficient. Originality/value -In the previous works on NLFD method, the flow field results have been limited to representing the pressure in the frequency domain or global coefficients such as lift coefficients. No details of pressure distributions in the time domain have been provided in such investigations. In this research, by presenting the pressure in the time domain, the conditions on which good pressure distributions are obtained are demonstrated. IntroductionThe calculation of unsteady flows continues to challenge computational fluid dynamists (CFD). This challenge comes from the fact that in addition to preserving the accurate spatial discretization for steady-state solutions, unsteady codes should also accurately resolve the time history of the solution. The challenge to CFD lies in this added dimension and its associated computational cost.The time accurate methods are common ones in solving unsteady flows. These methods include explicit and implicit time stepping schemes and factored ADI. Although these methods are applicable to a wide range of unsteady flows, they consume more computational time than steady-state solvers. In these methods, the semi-discrete form of governing equations is constructed by discretizing the space while leaving the time term. Finally, advancing in time leads to the solution.An alternative to the time accurate methods is to assume a periodic solution over a time interval regarding the fact that transient portion of solution is of less importance. Examples of such solutions are among unsteady flows in turbomachinery cascades. Given the assumption of periodicity, some special methods can be used to calculate the solution. It is evident that the transient decay of the solution using these methods cannot be admitted as a part of the solution.
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