Effect of heat flux on boundary layer flow under rotating conditions

The boundary layer flow behaviour in a smooth rotating channel with heated walls is measured by particle image velocimetry (PIV). To simulate the real operation environment of an internal coolant channel in a turbine blade, airflow is analysed in a rotating channel, whose four walls are uniformly heated by Indium Tin Oxide (ITO) glass. The flow is measured in the middle plane of the rotating channel with a Reynolds number equal to 10000 and rotation numbers ranging from 0 to 0.52. The results are presented for the boundary layer flow behaviour with and without heated thermal boundary conditions. The buoyancy force generated by the heated walls influences the flow behaviour under rotating conditions. Separated flow occurs, which substantially influences the turbulent flow behaviours. Sometimes, this buoyancy force can determine the flow behaviours. The results also showed that the displacement thickness and the momentum loss thickness present new changes at different radius positions due to the heated thermal boundary conditions. The displacement thicknesses of both the leading and trailing sides with heated walls are both thicker than those of the leading and trailing sides without heated walls. Then, the difference of the boundary layer thickness between these two cases increases with the increase of rotation number. For momentum loss thickness, a sharp drop happens when the rotation number increases to a certain value. At the large radius position, the drop in momentum loss thickness is much greater than that in the small radius position.     

Determining the form of a body resulting in minimum heat flux,with laminar flow in the boundary layer

The exact solution of the problem of determining the optimal body shape for which the total thermal flux will be minimal for high supersonic flow about the body involves both computational and theoretical difficulties. Therefore, at the present time wide use is made of the inverse method, based on comparing the thermal fluxes for bodies of various specified form [1, 2]. The results of such calculations cannot always replace the solution of the direct variational problem. Therefore it is advisable to consider the direct variational problem of determining the form of a body with minimal thermal flux by using the approximate Newton formula for finding the gasdynamic parameters at the edge of the boundary layer. This approach has been used in finding the form of the body of minimal drag in an ideal fluid [3–5] arid with account for friction [6], and also for determining the form of a thin two-dimensional profile with minimal thermal flux for given aerodynamic characteristics [7].     

Non-fourier heat conduction in a plane slab with prescribed boundary heat flux

The non-stationary heat conduction in an infinitely wide plane slab with a prescribed boundary heat flux is studied. An arbitrary time dependent boundary heat flux is considered and a non-vanishing thermal relaxation time is assumed. The temperature and the heat flux density distributions are determined analytically by employing Cattaneo-Vernotte's constitutive equation for the heat flux density. It is proved that the temperature and the heat flux density distributions can be incompatible with the hypothesis of local thermodynamic equilibrium. A comparison with the solution which would be obtained by means of Fourier's law is performed by considering the limit of a vanishing thermal relaxation time.     

Transient free convective flow in a vertical channel with constant temperature and constant heat flux on walls

This note presents transient motion of a viscous and incompressible fluid in a vertical channel due to free convective currents occuring as a result of application of constant heat flux at one wall and constant temperature on other wall. The method of Laplace transform is used to solve the problem. The transient behaviour of flow on velocity and temperature fields are shown on the graphs.     

Similarity conditions for heat transfer in incompressible two-dimensional laminar boundary layer flow

Summary Similarity conditions are presented for the solution of some problems of heat transfer in incompressible two-dimensional boundary layer flow. The treatment holds for forced convection as well as for free convection. For free convection no a priori restriction is made with respect to geometry or temperature distribution of the solid surface. For forced convection the treatment is restricted to uniform bulk flow parallel to a flat surface of non-uniform temperature or heat flux. The results are summarized in some tables that facilitate comparison with older work.     

On the longitudinal heat flux in a Couette flow

The problem of shear motion of a gas (Couette flow) is studied. Two infinite parallel plates with temperatures T₁ and T₂ separated by the distance L each move in their own plane with velocities u₀ and -u₀, respectively. It is assumed that there is a monatomic gas between the plates. In such a formulation, the Couette problem has been considered earlier by many authors. A difference in the present paper is that it investigates the behavior of the heat flux directed along the plates. It has been found that the presence of this heat flux has a strong influence on the direction of energy transfer that is established in a Couette flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–166, May–June, 1980.We are grateful to O. S. Ryzhov and A. T. Onufriev for discussions which led to the writing of the present paper.     

Transient boundary-layer heat transfer from a flat plate subjected to a sudden change in heat flux

We examine the transient forced convection heat transfer from a fixed, semi-infinite, flat plate situated in a fluid which, at large distances, is moving with a constant velocity parallel to the plate. Both the fluid and the plate are initially at a constant temperature and the transients are initiated when the zero heat flux at the plate is suddenly changed to a constant value. The thermal boundary-layer equations are solved using numerical techniques to extend a series which is valid for small times and describe fully the development from the initial unsteady state solution (small times) to the ultimate steady state solution (large time).     

Transient radiative and conductive heat transfer in non-gray semitransparent two-dimensional media with mixed boundary conditions

This paper is devoted to transient heat transfer involving radiation and conduction. Considering a non-gray purely absorbing media, the radiative heat transfer equation (RTE) is solved iteratively with the Discrete Ordinates Method (DOM) using an exponential differencing scheme. The energy balance equation is used to compute temperature at each time step with the Crank–Nicholson technique. Energy equation is coupled to the RTE through the radiative source term. Both equations are discretized with finite differencing schemes. The energy conservation leads to the sparse system of linear equations A× T=B which is solved with a bi-conjugate stabilized gradient technique (BCSG). Validation of the model with different test cases is achieved and application to transient heating of glass is also studied.     

Mixed convection boundary layer flow along vertical moving thin needles with variable heat flux

The problem of steady laminar mixed convection boundary layer flow of an incompressible viscous fluid along vertical moving thin needles with variable heat flux for both assisting and opposing flow cases is theoretically considered in this paper. The governing boundary layer equations are first transformed into non-dimensional forms. The curvature effects are incorporated into the analysis whereas the pressure variation in the axial direction has been neglected. These equations are then transformed into similarity equations using the similarity variables, which are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for a blunt-nosed needle (m = 0). Numerical calculations are carried out for various values of the dimensionless parameters of the problem, which include the mixed convection parameter λ, the Prandtl number Pr and the parameter a representing the needle size. It is shown from the numerical results that the skin friction coefficient, the surface (wall) temperature and the velocity and temperature profiles are significantly influenced by these parameters. The results are presented in graphical form and are discussed in detail.     

A mechanistic critical heat flux model for subcooled flow boiling based on local bulk flow conditions

The critical heat flux (CHF) mechanisms for subcooled flow boiling are reviewed. Based on experimental observations reported by previous investigators, the authors have developed a new mechanistic CHF model for vertical subcooled flow at high pressure and high mass velocity. This model is based on the dryout of a thin liquid layer (sublayer) beneath an intermittent vapor blanket due to a Helmholtz instability at the sublayer-vapor interface. The parametric trends of CHF have been explored qualitatively and quantitatively with respect to variations in pressure, mass velocity, subcooling and tube diameter. Comparisons of the model predictions with experimental data for water show good agreement in the simulation of subcooled flow conditions of pressurized water reactors (PWRs).     

Effects of heat flux,mass flux,vapor quality,and saturation temperature on flow boiling heat transfer in microchannels

Flow boiling heat transfer with the refrigerants R-134a and R-245fa in copper microchannel cold plate evaporators is investigated. Arrays of microchannels of hydraulic diameter 1.09 and 0.54 mm are considered. The aspect ratio of the rectangular cross section of the channels in both test sections is 2.5. The heat transfer coefficient is measured as a function of local thermodynamic vapor quality in the range −0.2 to 0.9, at saturation temperatures ranging from 8 to 30 °C, mass flux from 20 to 350 kg m⁻² s⁻¹, and heat flux from 0 to 22 W cm⁻². The heat transfer coefficient is found to vary significantly with heat flux and vapor quality, but only slightly with saturation pressure and mass flux for the range of values investigated. It was found that nucleate boiling dominates the heat transfer. In addition to discussing measurement results, several flow boiling heat transfer correlations are also assessed for applicability to the present experiments.     

Characteristics of the critical heat flux for downward flow in a vertical tube at low flow rate and low pressure conditions

The characteristics of the critical heat flux (CHF) for downward flow were studied experimentally with an Inconel 600 circular tube test section in a water test loop at low-flow rate (0 200 kg/m²s) and low-pressure (0.1 0.7 MPa) conditions. The attention was given to the effects of upstream conditions—upper plenum and inlet throttling. Two totally different kinds of CHF behaviors were observed. It seems appropriate to interpret them as flooding-type CHF and dryout in annular flow. The CHF in downward flow may vary from extremely unstable flow CHF as low as near the flooding CHF value to stable flow CHF as high as that of upflow, depending on the upstream conditions of the test section. The CHF correlation by Mishima and that by Weber were proposed for the presentation of the lower and upper limits of the CHF for downward flow in a vertical tube at low-flow rate and low-pressure conditions.     

Saturated critical heat flux in a multi-microchannel heat sink fed by a split flow system

An extensive experimental campaign has been carried out for the measurement of saturated critical heat flux in a multi-microchannel copper heat sink. The heat sink was formed by 29 parallel channels that were 199 μm wide and 756 μm deep. In order to increase the critical heat flux and reduce the two-phase pressure drop, a split flow system was implemented with one central inlet at the middle of the channels and two outlets at either end. The base critical heat flux was measured using three HFC Refrigerants (R134a, R236fa and R245fa) for mass fluxes ranging from 250 to 1500 kg/m² s, inlet subcoolings from ?25 to ?5 K and saturation temperatures from 20 to 50 °C. The parametric effects of mass velocity, saturation temperature and inlet subcooling were investigated. The analysis showed that significantly higher CHF was obtainable with the split flow system (one inlet–two outlets) compared to the single inlet–single outlet system, providing also a much lower pressure drop. Notably several existing predictive methods matched the experimental data quite well and quantitatively predicted the benefit of higher CHF of the split flow.     

Laminar mixing and heat transfer for constant heat flux boundary condition

In a recent paper we have investigated mixing and heat transfer enhancement in a mixer composed of two circular rods maintained vertically in a cylindrical tank. The rods and tank can rotate around their revolution axes while their surfaces were maintained at a constant temperature. In the present study we investigate the differences in the thermal mixing process arising from the utilization of a constant heat flux as a boundary condition. The study concerns a highly viscous fluid with a high Prandtl number for which this chaotic mixer is suitable. By solving numerically the flow and energy equations, and using different statistical tools we characterize the evolution of the fluid temperature and its homogenization. Fundamental differences are reported between these two modes of heating or cooling: while the mixing with an imposed temperature results in a homogeneous temperature field, with a fixed heat flux we observe a constant difference between the maximal and minimal temperatures that establish in the fluid; the extent of this difference is governed by the efficiency of the mixing protocol.     

Effects of channel dimension,heat flux,and mass flux on flow boiling regimes in microchannels

Experiments are conducted with a perfluorinated dielectric fluid, Fluorinert FC-77, to investigate the effects of channel size and mass flux (225–1420 kg/m²s) on microchannel flow boiling regimes by means of high-speed photography. Seven different silicon test pieces with parallel microchannels of widths ranging from 100 to 5850 μm, all with a depth of 400 μm, are considered. Flow visualizations are performed with a high-speed digital video camera while local measurements of the heat transfer coefficient are simultaneously obtained. The visualizations and the heat transfer data show that flow regimes in the microchannels of width 400 μm and larger are similar, with nucleate boiling being dominant in these channels over a wide range of heat flux. In contrast, flow regimes in the smaller microchannels are different and bubble nucleation at the walls is suppressed at a relatively low heat flux for these sizes. Two types of flow regime maps are developed and the effects of channel width on the flow regime transitions are discussed.