Magnetogasdynamic flow past an infinite porous flat plate in slip flow regime

This paper presents an exact solution for the flow of a rarefied ionized gas over an infinite porous plate in the presence of a transverse magnetic field, by using the well known continuum approach. An attempt is made to bring out the salient features of the interaction between the applied magnetic field and the flow of a rarefied conducting gas. The analysis reveals that the skin friction, and the heat transfer into the plate are reduced due to gas rarefaction.     

Hypersonic flow past a plate of finite length

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 66–73, September–October, 1991.     

Hall effects on convective hydromagnetic flow past a flat plate

Hydromagnetic free convective flow past an infinite vertical, porous plate in the presence of a uniform transverse magnetic field has been considered taking Hall effects into account. Approximate solutions for the mean velocity, mean temperature and their related quantities are obtained. The influence of various dimensionless parameters is discussed     

A new approach on MHD natural convection boundary layer flow past a flat plate of finite dimensions

A new approach on MHD natural convection boundary layer flow from a finite flat plate of arbitrary inclination in a rotating environment, is presented. This problem plays a significant role on boundary layer flow control. It is shown that taking into account the pressure rise region at the leading edge of the plate leads to avoid separation and the back flow is reduced by the strong magnetic field. It is also shown that the frictional drag at the leading edge of the plate is reduced when the inclination angle α=π/4. In the case of isothermal flat plate, the bulk temperature becomes identical for any value of Gr (Grashof number) when the value of M ² (Hartmann number) and K ² (rotation parameter) are kept fixed.     

Simulations of the unsteady separated flow past a normal flat plate

Well-resolved two-dimensional numerical simulations of the unsteady separated flow past a normal flat plate at low Reynolds numbers have been performed using a fractional step procedure with high-order spatial discretization. A fifth-order upwind-biased scheme is used for the convective terms and the diffusive terms are represented by a fourth-order central difference scheme. The pressure Poisson equation is solved using a direct method based on eigenvalue decomposition of the coefficient matrix. A systematic study of the flow has been conducted with high temporal and spatial resolutions for a series of Reynolds numbers. The interactions of the vortices shed form the shear layers in the near-and far-wake regions are studied. For Reynolds numbers less than 250 the vortices are observed to convect parallel to the freestream. However, at higher Reynolds numbers (500 and 1000), complex interactions including vortex pairing, tearing and deformations are seen to occur in the far-wake region. Values of the drag coefficient and the wake closure length are presented and compared with previous experimental and numerical studies.     

Generation of coherent structures in supersonic flow past a finite-span flat plate

The formation of coherent structures on a flat plate in a supersonic flow is numerically investigated both in the case of strong shock incidence on the plate and in the problem of oncoming harmonic waves having an intensity of 1–5% of the freestream pressure P ₀. The same mechanism of the coherent structure formation is noticed in both nonstationary problems; it is due to the manifestation of the secondary instability generated in the gas flow owing to the influence of the vortices formed at the lateral edges of the plate. An analysis of the incident wave enhancement at the rear of the plate is made for different wave intensities and wavelength to plate width ratios. The flow patterns in the plate wake indicate the generation of an intense expansion wave in this region, which accelerates the gas flow to the freestream velocity.     

On hydromagnetic fluctuating flow past an infinite porous plate in slip flow regime

The effect of a uniform external magnetic field on the laminar, incompressible rarefied gas flow along an infinite porous flat plate is studied under the following conditions: 1) there is uniform suction, 2) the external flow velocity varies periodically with time in magnitude but not in direction, 3) the magnetic Reynolds number is small and 4) the current occurs under slip flow boundary conditions. Expressions for the velocity and temperature fields in the boundary layer are obtained. The response of skin friction, and heat transfer to the fluctuating stream is studied for variations in the rarefaction parameter h ₁, the magnetic field parameter M, and the frequency of the fluctuating stream.Nomenclature c _p specific heat of the gas - f ₁ Maxwells reflection coefficient - f ₂ thermal accommodation coefficient - G as defined in (36) - h ₁ rarefaction parameter (L ₁ v ₀/) - h ₂ nondimensional temperature jump coefficient (L ₂ v ₀/) - H amplitude of the skin friction - k thermal conductivity - K _n Knudsen number - L mean free path - L ₁ (2–f ₁/f ₁) L - L ₂ - M magnetic field parameter ( ₀ B ₀ ² /v ₀ ² ) - m 1/2[1+(1+4M+4i)^1/2], m _r+im _i - n ₁ 1/2[1+(1+4M)^1/2] - q heat flux - R suction Reynolds number - T temperature - x, y coordinates along and perpendicular to the plates - u, v velocity components along x, y-directions - density - kinematic viscosity - ₀ electrical conductivity - Prandtl number - frequency of the fluctuating stream - nondimensional frequency parameter (/v ₀ ² ) - nondimensional distance from wall (v ₀ y/) - phase lead - U _{0 0} mean velocity in the boundary layer - U _{0 1}, U _{0 2} amplitude of the velocity fluctuation in the boundary layer - specific heat ratio     

Velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium

In this paper the velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium are obtained for the governing equations (Kaviany [7]) following the technique adopted by Chandrashekara [2] which are concerned with the interesting situations of the existence of transverse, velocity and thermal boundary layers. Here the pressure gradient is just balanced by the first and second order solid matrix resistances for small permeability and observed that by increasing of the flow resistance the asymptotic value for the heat transfer rate increases. Further we concluded that the transverse boundary layers are thicker than that of axial boundary layers. Hence we evaluated the expressions for the boundary layer thickness, the shear stress at the semi-infinite plate and _T (the ratio of the thicknesses of the thermal boundary layer and momentum boundary layer). The variations of these quantities for different values of the porous parameterB and the flow resistanceF have been discussed in detail with the help of tables. The curves for velocity and temperature distributions have been plotted for different values ofB andF.Lastly we have evaluated the heat fluxq(x) and found that it depends entirely upon the Reynolds numberRe, Prandtl numberPr,B andF.     

Numerical solution of natural convection flow past a non-isothermal vertical flat plate

The problem of natural convection over a semi-infinite flat plate with non-uniform wall temperature is studied by using a numerical method. The local rates of heat transfer as a function of the distance along the plate are tabulated for a range of Prandtl numbers (0.01 to 100) and for a few cases of wall temperature distributions. Such tabulations serve as a reference against which other approximate solutions can be compared in the future.     

Heat transfer in a flow past a semi-in-finite plate with oscillating temperature

The response of laminar boundary layer flow past a semi-infinite flat plate to harmonic oscillations in the plate temperature in the form of a travelling wave convected in the direction of the free-stream has been studied here. Series solutions in terms of the small amplitude and the small oscillations to the non-linear system have been derived and the resulting nonlinear ordinary equations due to usual similarity transformations are solved numerically. The function affecting the temperature is shown on a graph. Due to greater viscous dissipative heat the function K ₁, increases and it decreases with increasing Prandtl number. Also the time averaged heat flux function K ₁(0) increases with Prandtl number and decreases due to greater viscous dissipative heat.     

Heat transfer in flow past a continuously moving porous flat plate with heat flux

The analysis of the heat transfer in flow past a continuously moving semi-infinite plate in the presence of suction/ injection with heat flux has been presented. Similarity solutions have been derived and the resulting equations are integrated numerically. It has been observed that an increase in suction value leads to an increase in temperature whereas it is opposite in the case of injection.

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Wärmeübergang in einer Strömung hinter einer wärmeabgebenden, kontinuierlich bewegten, porösen Platte

Zusammenfassung Es wird eine Analyse des Wärmeübergangs in einer Strömung hinter einer bewegten, halbunendlichen Platte bei gleichzeitiger Absaugung bzw. Ausströmung präsentiert. Mit Hilfe von Ähnlichkeitsbetrachtungen wurden Lösungen erarbeitet und die daraus resultierenden Gleichungen wurden numerisch integriert. Als Ergebnis zeigte sich, daß zunehmende Absaugung zu einer Erhöhung der Temperatur führt, während bei der Ausströmung das Gegenteil der Fall ist.

     

Heat transfer in flow past a continuous moving plate with variable temperature

A study of thermal boundary layer on a continuously moving semi-infinite flat plate, whose temperature varies as Axⁿ, where A is a constant and x is measured from the leading edge of the plate, has been presented. Similarity solutions have been derived and the resulting equations are integrated numerically. It has been observed that the value of the Nusselt number increases with increasing n.

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Wärmeübertragung in einer Strömung längs einer kontinuierlich bewegten Platte mit variabler Temperatur

Zusammenfassung Es wird die thermische Grenzschicht an einer gleichförmig bewegten halbunendlichen Platte, deren Temperatur sich nach der Gleichung Axⁿ ändert, betrachtet. A ist eine Konstante und x ist der Abstand von der Vorderkante. Ähnlichkeitslösungen wurden abgeleitet und die entstehenden Gleichungen numerisch integriert. Aus den Ergebnissen ergibt sich ein Anstieg der Nusselt-Zahlen mit steigendem Exponenten n.

     

Supersonic flow past a wedge on a flat plate. Laminar boundary layer separation and reattachment

Supersonic laminar flow past a two-dimensional “flat-plate/wedge“ configuration is numerically investigated. The pressures at the boundary layer separation and reattachment points are calculated over wide Mach and Reynolds number ranges. The minimum angles of the wedge surface inclination at which a return flow occurs are determined. The results are presented in the form of generalized Mach-number-dependences of the theoretical pressure on the wedge surface initiating boundary layer separation and the pressure at the boundary layer reattachment point.     

Effects of viscous dissipation on heat transfer in an oscillating flow past a flat plate

Theoretical investigation has been carried out of laminar thermal boundary layer response to harmonic oscillations in velocity associated with a progressive wave imposed on a steady free stream velocity and convected in the free stream direction. Series solutions are derived both to velocity and temperature field and the resulting equations are solved numerically. The functions affecting the temperature field are shown graphically for different values of Prandtl number. It is observed that there is more reduction in the rate of heat transfer for P _r<1 and a rise in the rate of heat transfer for P _r>1 due to the presence of oscillatory free-stream.Nomenclature u, v velocity components in the x and y direction - x, y Cartesian coordinate axes - t time - U, U ₀ instantaneous value of and mean free stream velocity - density of fluid - kinematic viscosity - T, T _w, T temperature of the fluid, wall and free stream fluid - c _p specific heat at constant pressure - thermal diffusivity - amplitude of free stream velocity - frequency - _p non-dimensional temperature (T–T /T _w–T ) - P _r Prandtl number (c _p/K) - E _c Eckert number (U ₀ ² /c _p(T _w–T )) - a parameter ( ) - ₀ boundary layer thickness of the oscillation of a harmonic oscillation of frequency ( ) - ordinary boundary layer thickness ( ) - time-averaged, time-independent external velocity - A, B, C, D, E, K, L, M, N, P functions used in expansion for u and - Nu Nusselt number (hx/k) - T _w–% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8V4rqqrFfpeea0Jc9yq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepGe9fr-xfr-x% frpeWZqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaacIcadaGcaa% qaaiaadAhacaWG4bGaai4laiqadwfagaqeaaWcbeaakiaacMcaaaa!3CA6!\[(\sqrt {vx/\bar U} )\] - k thermal conductivity     

Effects of suction or blowing on the velocity and temperature distribution in the flow past a porous flat plate of a power-law fluid

An analysis is made of the steady flow of a non-Newtonian fluid past an infinite porous flat plate subject to suction or blowing. The incompressible fluid obeys Ostwald-de Waele power-law model. It is shown that steady solutions for velocity distribution exist only for a pseudoplastic (shear-thinning) fluid for which the power-law index n satisfies 0<n<1 provided that there is suction at the plate. Velocity at a point is found to increase with increase in n. No steady solution for velocity distribution exists when there is blowing at the plate. The solution of the energy equation governing temperature distribution in the flow of a pseudoplastic fluid past an infinite porous plate subject to uniform suction reveals that temperature at a given point near the plate increases with n but further away, temperature decreases with increase in n. A novel result of the analysis is that both the skin-friction and the heat flux at the plate are independent of n.