Study on MHD Flow over a Stretching Surface with Convective Boundary Condition by Numerical Method

The thermal and mass diffusive MHD flow through a stretching sheet has been inspected in the presence of a chemically reactive solute under convective boundary conditions in the present paper. The non-linear PDEs of the system concerning the flow, temperature, and species are recasted into a set of non-linear ODEs using ST. The consequential system of the differential equations is numerically resolved by using an implicit FDS in combination with the QL technique. The velocity ratio factor plays an important role in reducing the thickness of the velocity boundary layer, whereas the presence of magnetic parameters decreases the thickness of the velocity boundary layer profile. The study reveals that the fluid moves away from the surface during injection, resulting in a fall of the velocity gradient, whereas the opposite effect is observed in suction. The thermal and concentration boundary layer thicknesses are influenced by non-dimensional numbers, namely Prandtl and Schmidt numbers. The reaction rate parameter acts as a decelerating agent, and it thins the solute boundary layer formed in the neighborhood of the sheet. An increase in the convective parameter leads to an increase in the plate surface temperature. The present results of the paper are compared with the existing one, and good agreement is found between them.

Numerical Investigation of Multiple Solutions for Caputo Fractional-Order-Two Dimensional Magnetohydrodynamic Unsteady Flow of Generalized Viscous Fluid over a Shrinking Sheet Using the Adams-Type Predictor-Corrector Method

In this paper, magnetohydrodynamic (MHD) flow over a shrinking sheet and heat transfer with viscous dissipation has been studied. The governing equations of the considered problem are transformed into ordinary differential equations using similarity transformation. The resultant equations are converted into a system of fractional differential boundary layer equations by employing a Caputo derivative which is then solved numerically using the Adams-type predictor-corrector method (APCM). The results show the existence of two ranges of solutions, namely, dual solutions and no solution. Moreover, the results indicate that dual solutions exist for a certain range of specific parameters which are in line with the results of some previously published work. It is also observed that the velocity boundary layer decreases as the suction and magnetic parameters increase.

Experimental Study of a Boundary Layer on a Heated Flat Plate

Boundary layer on a uniformly heated flat plate was studied experimentally. Both, the velocity boundary layer and the temperature boundary layer, was investigated by means of hot-wire anemometry. A probe with parallel wires was used for velocity-temperature measurement. Experiment was performed in the closed-circuit wind tunnel with several levels of heat flux at the wall. The wall temperature was set up in the interval from 20 ºC to 200 ºC.

Exponentially Decaying Heat Source on MHD Tangent Hyperbolic Two-Phase Flows over a Flat Surface with Convective Conditions

The present framework addresses Darcy-Forchheimer steady incompressible magneto hydrodynamic hyperbolic tangent fluid with deferment of dust particles over a stretching surface along with exponentially decaying heat source. To control the thermal boundary layer Convective conditions are considered. Appropriate transformations were utilized to convert partial differential equations (PDEs) into nonlinear ordinary differential equations (NODEs). To present numerical approximations Runge-Kutta Fehlberg integration is implemented. Computational results of the flow and energy transport are interpreted for both fluid and dust phase with the support of graph and table illustrations. It is found that non-uniform inertia coefficient of porous medium decreases velocity boundary layer thickness and enhances thermal boundary layer. Improvement in Weissenberg number improves the velocity boundary layer and declines the thermal boundary layer.

Fractional Boundary Layer Flow and Heat Transfer Over a Stretching Sheet With Variable Thickness

The paper gives a comprehensive study on the space fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness, and the variable magnetic field is applied. Novel governing equations with left and right Riemann–Liouville fractional derivatives subject to irregular region are formulated. By introducing new variables, the boundary conditions change as the traditional ones. Solutions of the governing equations are obtained numerically where the shifted Grünwald formulae are applied. Good agreement is obtained between the numerical solutions and exact solutions which are constructed by introducing new source items. Dynamic characteristics with the effects of involved parameters on the velocity and temperature distributions are shown and discussed by graphical illustrations. Results show that the velocity boundary layer is thicker for a larger fractional parameter or a smaller magnetic parameter, while the temperature boundary layer is thicker for a larger fractional parameter, a smaller exponent parameter, or a larger magnetic parameter. Moreover, it is thicker at a smaller y and thinner at a larger y for the velocity boundary layer with a larger exponent parameter while for the velocity and temperature boundary layers with a smaller weight coefficient.

A Numerical Proof of Concept for Thermal Flow Control

In this paper computational fluid dynamics is used to provide a proof of concept for controlled flow separation using thermal wall interactions with the velocity boundary layer. A 3D case study is presented, using a transition modeling Shear Stress Transport turbulence model. The highly loaded single slot flap airfoil was chosen to be representative for a light aircraft and the flow conditions were modeled after a typical landing speed. In the baseline case, adiabatic walls were considered while in the separation control case, the top surface of the flaps was heated to 500 K. This heating lead to flow separation on the flaps and a significant alteration of the flow pattern across all the elements of the wing. The findings indicate that this control method has potential, with implications in both aeronautical as well as sports and civil engineering applications.

Global and local statistics in turbulent convection at low Prandtl numbers

Statistical properties of turbulent Rayleigh–Bénard convection at low Prandtl numbers $Pr$, which are typical for liquid metals such as mercury or gallium ($Pr\simeq 0.021$) or liquid sodium ($Pr\simeq 0.005$), are investigated in high-resolution three-dimensional spectral element simulations in a closed cylindrical cell with an aspect ratio of one and are compared to previous turbulent convection simulations in air for $Pr=0.7$. We compare the scaling of global momentum and heat transfer. The scaling exponent $\unicode[STIX]{x1D6FD}$ of the power law $Nu=\unicode[STIX]{x1D6FC}Ra^{\unicode[STIX]{x1D6FD}}$ is $\unicode[STIX]{x1D6FD}=0.265\pm 0.01$ for $Pr=0.005$ and $\unicode[STIX]{x1D6FD}=0.26\pm 0.01$ for $Pr=0.021$, which are smaller than that for convection in air ($Pr=0.7$, $\unicode[STIX]{x1D6FD}=0.29\pm 0.01$). These exponents are in agreement with experiments. Mean profiles of the root-mean-square velocity as well as the thermal and kinetic energy dissipation rates have growing amplitudes with decreasing Prandtl number, which underlies a more vigorous bulk turbulence in the low-$Pr$ regime. The skin-friction coefficient displays a Reynolds number dependence that is close to that of an isothermal, intermittently turbulent velocity boundary layer. The thermal boundary layer thicknesses are larger as $Pr$ decreases and conversely the velocity boundary layer thicknesses become smaller. We investigate the scaling exponents and find a slight decrease in exponent magnitude for the thermal boundary layer thickness as $Pr$ decreases, but find the opposite case for the velocity boundary layer thickness scaling. A growing area fraction of turbulent patches close to the heating and cooling plates can be detected by exceeding a locally defined shear Reynolds number threshold. This area fraction is larger for lower $Pr$ at the same $Ra$, but the scaling exponent of its growth with Rayleigh number is reduced. Our analysis of the kurtosis of the locally defined shear Reynolds number demonstrates that the intermittency in the boundary layer is significantly increased for the lower Prandtl number and for sufficiently high Rayleigh number compared to convection in air. This complements our previous findings of enhanced bulk intermittency in low-Prandtl-number convection.