Non-Newtonian magnetohydrodynamic flow over a stretching surface with heat and mass transfer

An analysis is carried out to study the momentum, mass and heat transfer characteristics on the flow of visco-elastic fluid (Walter's liquid-B model) past a stretching sheet in the presence of a transverse magnetic field.In heat transfer, two cases are considered:

1.

The sheet with prescribed surface temperature (PST case); and

2.

The sheet with prescribed wall heat flux (PHF case).

The solution of equations of momentum, mass and heat transfer are obtained analytically. Emphasis has been laid to study the effects of various parameters like magnetic parameter Mn, visco-elastic parameter k₁, Schmidt number Sc, and Prandtl number Pr on flow, heat and mass transfer characteristics.     

Hydrodymagnetic three-dimensional flow over a stretching surface with heat and mass transfer

A general analysis has been developed to study the combined effect of the free convective heat and mass transfer on the steady three-dimensional laminar boundary layer flow over a stretching surface. The flow is subject to a transverse magnetic field normal to the plate. The governing three-dimensional partial differential equations for the present case are transformed into ordinary differential equation using three-dimensional similarity variables. The resulting equations, are solved numerically by applying a fifth order Runge-Kutta-Fehlberg scheme with the shooting technique. The effects of the Magnetic field Parameter M, buoyancy parameter N, Prandtl number Pr and Schmidt number Sc are examined on the velocity, temperature and concentration distributions. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various parametric conditions. The results are compared with known from the literature.     

Two-equation turbulence models for prediction of heat transfer on a transonic turbine blade

Two versions of the two-equation k–ω model and a shear stress transport (SST) model are used in a three-dimensional, multi-block, Navier–Stokes code to compare the detailed heat transfer measurements on a transonic turbine blade. It is found that the SST model resolves the passage vortex better on the suction side of the blade, thus yielding a better comparison with the experimental data than either of the k–ω models. However, the comparison is still deficient on the suction side of the blade. Use of the SST model does require the computation of distance from a wall, which for a multi-block grid, such as in the present case, can be complicated. However, a relatively easy fix for this problem was devised. Also addressed are issues such as (1) computation of the production term in the turbulence equations for aerodynamic applications, and (2) the relation between the computational and experimental values for the turbulence length scale, and its influence on the passage vortex on the suction side of the turbine blade.     

Purge flow and interface gap geometry influence on the aero-thermal performance of a rotor blade cascade

This paper is focused on the influence of the geometry of an interface seal gap on the aerodynamic and thermal performance of a rotor blade cascade. Tests are performed in a seven-blade cascade of a gas turbine high-pressure subsonic rotor at low Mach number (Ma_2is = 0.3). To simulate some of the effects of rotation on the seal flow exiting the gap on a linear cascade environment, a number of fins are installed inside the slot, providing the coolant flow with an injection angle in the tangential direction. Tests are carried out at variable blowing conditions and different gap widths. Moreover, the influence of a radial misalignment between stator and rotor platforms is also investigated for variable injection conditions. The 3D flow field is surveyed by traversing a 5-hole miniaturized pressure probe in a downstream plane. Secondary flows velocities, loss coefficient and vorticity distributions are presented for the most relevant test conditions. Film cooling effectiveness distributions on the platform are obtained by Thermochromic Liquid Crystals technique. Results show that engine purge flow injection conditions have to be reproduced in the wind tunnel as close as possible, in order to get the correct blade aero-thermal performance.     

Slip effects on unsteady stagnation-point flow and heat transfer over a shrinking sheet

This paper investigates the unsteady boundary layer stagnation-point flow and heat transfer over a linearly shrinking sheet in the presence of velocity and thermal slips. Similarity solutions for the transformed governing equations are obtained and the reduced equations are then solved numerically using fourth order Runge-Kutta method with shooting technique. The numerical results show that multiple solutions exist for certain range of the ratio of shrinking velocity to the free stream velocity (i.e., α) which again depend on the unsteadiness parameter β and the velocity slip parameter (i.e., δ). An enhancement of the velocity slip parameter δ causes more increment in the existence range of similarity solution. Fluid velocity at a point increases increases with the increase in the value of the velocity slip parameter δ, resulting in a decrease in the temperature field. The effects of the velocity and thermal slip parameters, unsteadiness parameter (β) and the velocity ratio parameter (α) on the velocity and temperature distributions are computed, analyzed and discussed. The reported results are in good agreement with the available published results in the literature.     

Three-dimensional flow structures and associated turbulence in the tip region of a waterjet pump rotor blade

Stereo particle image velocimetry measurements focus on the flow structure and turbulence within the tip leakage vortex (TLV) of an axial waterjet pump rotor. Unobstructed optical access to the sample area is achieved by matching the optical refractive index of the transparent pump with that of the fluid. Data obtained in closely spaced planes enable us to reconstruct the 3D TLV structure, including all components of the mean vorticity and strain-rate tensor along with the Reynolds stresses and associated turbulence production rates. The flow in the tip region is highly three-dimensional, and the characteristics of the TLV and leakage flow vary significantly along the blade tip chordwise direction. The TLV starts to roll up along the suction side tip corner of the blade, and it propagates within the passage toward the pressure side of the neighboring blade. A shear layer with increasing length connects the TLV to the blade tip and initially feeds vorticity into it. During initial rollup, the TLV involves entrainment of a few vortex filaments with predominantly circumferential vorticity from the blade tip. Being shed from the blade, these filaments also have high circumferential velocity and appear as swirling jets. The circumferential velocity in the TLV core is also substantially higher than that in the surrounding passage flow, but the velocity peak does not coincide with the point of maximum vorticity. When entrainment of filaments stops in the aft part of the passage, newly forming filaments wrap around the core in helical trajectories. In ensemble-averaged data, these filaments generate a vortical region that surrounds the TLV with vorticity that is perpendicular to that in the vortex core. Turbulence within the TLV is highly anisotropic and spatially non-uniform. Trends can be traced to high turbulent kinetic energy and turbulent shear stresses, e.g., in the shear layer containing the vortex filaments and the contraction region situated along the line where the leakage backflow meets the throughflow, causing separation of the boundary layer at the pump casing. Upon exposure to adverse pressure gradients in the aft part of the passage, at 0.65–0.7 chord fraction in the present conditions, the TLV bursts into a broad turbulent array of widely distributed vortex filaments.     

Some characteristics of heat and mass transfer in a turbulent air flow over a surface

It is shown that, for a certain proportion between the rib height (2–15 mm) installed at the test-section entrance and the turbulence level of the main flow (1–26%), there are extrema of parameters that describe mass transfer on the surface of an evaporating liquid fuel. In tests with and without combustion, discrete changes in the rates of heat and mass transfer are observed. Conditions for their manifestation are analyzed. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskava Fizika, Vol. 41, No.4, pp. 124–130, July–August, 2000.     

A note on heat transfer in laminar flow through a gap

Summary The problem of heat transfer in laminar flow through a gap between two semi-infinite parallel plates at constant temperature was recently studied by Agrawal¹⁾. He solved this problem with the use of infinite Fourier sine series and derived an expression for the local temperature profile and the local Nusselt number as a function of the distance along the gap. A detailed solution for Péclèt number Pe=1 is given. Far enough from the entrance of the gap the local temperature profile of the fluid is almost independent of it's initial temperature. In this paper this limit temperature profile is expressed with the confluent hypergeometric function and the corresponding Nusselt number as a function of Pe is calculated.     

Transient growth mechanisms of low Reynolds number flow over a low-pressure turbine blade

A direct transient growth analysis for three-dimensional perturbations to flow past a periodic array of T-106/300 low-pressure turbine fan blades is presented. The methodology is based on a singular value decomposition of the flow evolution operator, linearised about a steady or periodic base flow. This analysis yields the optimal growth modes. Previous work on global mode stability analysis of this flow geometry showed the flow is asymptotically stable, indicating a non-modal explanation of transition may be more appropriate. The present work extends previous investigations into the transient growth around a steady base flow, to higher Reynolds numbers and periodic base flows. It is found that the notable transient growth of the optimal modes suggests a plausible route to transition in comparison to modal growth for this configuration. The spatial extent and localisation of the optimal modes is examined and possible physical triggering mechanisms are discussed. It is found that for longer times and longer spanwise wavelengths, a separation in the shear layer excites the wake mode. For shorter times and spanwise wavelengths, smaller growth associated with excitation of the near wake are observed.     

Viscous dissipation effects on heat transfer in flow over an inclined plate

The effects of viscous dissipation are considered for natural convection flow past a semi-infinite inclined plate with variable surface temperature. Velocity and temperature profiles, skin friction, and rate of heat transfer are obtained. The effects of Grashof and Prandtl numbers, inclination angle, exponent in the wall temperature variation law, and viscous dissipation parameter on the flow are discussed. It is shown that the time required to reach steady states increases with increasing Prandtl number of the fluid. In addition, an increase in the plate temperature due to viscous dissipation was found to lead to a rise in the average skin friction and a decrease in the average Nusselt number.     

Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour effects

In this paper, we study the unsteady coupled heat and mass transfer of two-dimensional MHD fluid over a moving oscillatory stretching surface with Soret and Dufour effects. Viscous dissipation effects are adopted in the energy equation. A uniform magnetic field is applied vertically to the flow direction. The governing equations are reduced to non-linear coupled partial differential equations and solved by means of homotopy analysis method （HAM）. The effects of some physical parameters such as magnetic parameter, Dufour number, Soret number, the Prandtl num- ber and the ratio of the oscillation frequency of the sheet to its stretching rate on the flow and heat transfer characteristics are illustrated and analyzed.     

Experimental investigation to study flow and heat transfer characteristics over a NACA0018 aerofoil for different height ratios

Experiments are carried out to study flow and heat transfer characteristics over NACA0018 aerofoil when the body approaches the wall of a wind tunnel. Investigations have been done to study the effect of wall proximity due to flow separation around the body at Reynolds number 2.5 × 10⁵, different height ratios and various angles of attack. The static pressure distribution has been measured on upper and lower surfaces of the aerofoil. The results have been presented in the form of pressure coefficient, drag coefficient for different height ratios. Pressure coefficient values are decreased and then increased on the lower surface of the aerofoil and decreased on the upper surface of the aerofoil at all angles of attack. The negative pressure coefficient and drag coefficient decreases as the body approaches the upper wall of wind tunnel. The maximum value of drag coefficient has been observed at an angle of attack 30° for the aerofoil at all height ratios. The Heat transfer experiments have been carried out under constant heat flux condition. Heat transfer coefficients are determined from the measured wall temperature and ambient temperature and presented in the form of Nusselt number. The variation of local as well as average Nusselt number has been shown with non dimensional distance for different angles of attack and for various height ratios. The local as well as average Nusselt number decreases as the height ratio decreases for all non-dimensional distance and angles of attack respectively. Maximum value of average Nusselt number has been observed at an angle of attack 40°.     

Intensity of convective mass/heat transfer in a rotary regenerator rotor with the transverse needle-fins

A forced convective mass transfer coefficient was electrochemically measured for a cylindrical bundle of transverse needle-fins ?1 × 10.9, applied as the rotor porous matrix of a rotary heat regenerator. The baffle inside the rotor was present. The technique based on the ferricyanide–ferrocyanide redox reaction controlled at the cathode, in the presence of a sodium hydroxide based electrolyte, was used in this experiment. A set of the six neighbouring fins, connected in parallel, was the cathode. The distribution of the mass transfer coefficient according to different static rotor angle position and the mean mass transfer Chilton–Colburn coefficient correlation j _M  = j _M (Re) for rotation numbers, Ro: 0, 0.8, 1.6 and 2.0 were stated in the mean Reynolds number, Re, range 180–985. The comparison was made between the convective heat fluxes of the pin-fins and the sheet rotor, for Ro = 0.     

Boundary layer flow and heat transfer of a dusty fluid flow over a stretching sheet with non-uniform heat source/sink

The present paper deals with the analysis of boundary layer flow and heat transfer of a dusty fluid over a stretching sheet with the effect of non-uniform heat source/sink. Here we consider two types of heating processes namely (i) prescribed surface temperature and (ii) prescribed surface heat flux. The momentum and thermal boundary layer equations of motion are solved numerically using Runge Kutta Fehlberg fourth–fifth order method (RKF45 Method). The effects of fluid particle interaction parameter, Eckert number, Prandtl number, Number of dust particle and non-uniform heat generation/absorption parameter on temperature distribution are analyzed and also the effect of wall temperature gradient function and wall temperature function are tabulated and discussed.     

Laminar flow and heat transfer over a two-dimensional triangular step

The velocity correction algorithm is used in the finite element method to solve forced convection problems between parallel plates with a triangular step, for Reynolds numbers up to 1000. Equal-order interpolation functions for velocity, pressure and temperature are used. The solutions show a smooth variation of pressure. The streamfunction, isotherms, isobars and velocity profiles are presented for a typical Reynolds number of 500. The skin friction and heat transfer results are presented for Reynolds numbers up to 1000.     

The effects of transpiration on the boundary layer flow and heat transfer over a vertical slender cylinder

This paper deals with a theoretical (numerical) analysis of the effects that blowing/injection and suction have on the steady mixed convection or combined forced and free convection boundary layer flows over a vertical slender cylinder with a mainstream velocity and a wall surface temperature proportional to the axial distance along the surface of the cylinder. Both cases of buoyancy forces aid and oppose the development of the boundary layer are considered. Similarity equations are derived and their solutions are dependent upon the mixed convection parameter, the non-dimensional transpiration parameter and the curvature parameter, as well as of the Prandtl number. Dual solutions for the previously studied mixed convection boundary layer flows over an impermeable surface of the cylinder are shown to exist also in the present problem for aiding and opposing flow situations.