A radiation and convection fluxmeter for high temperature applications

Heat flux is an essential parameter for the diagnostic of thermal systems. In high temperature industrial environment, there are difficulties in measuring incident radiation heat flux as well as in differentiating between the convective and radiative components of heat flux on the heat transfer surface. A new method for heat flux measurement is being developed using a porous sensing element. The gas stream flowing through the porous element is used to measure the heat received by the sensor surface exposed to the hot gas environment. A numerical model of sensor with appropriate boundary condition has been developed in order to perform analysis of possible options regarding its design. The analysis includes: geometry of element, physical parameters of gas and solid and gas flow rate through the porous element. For the optimal selection of parameters, an experimental set-up was designed, including the sensor element with respective cooling and monitoring systems and a high temperature radiation source. The experimental set-up was used to obtain calibration curves for a number of sensors. The linear dependency of the heat flux and respective temperature difference of the gas were verified. The accuracy analysis of the sensor reading has proved high linearity of the calibration curve and accuracy of ±5%.     

Thermofluidynamic analysis of the flow in a sharp 180° turn channel

The aim of the present study is to obtain surface flow visualisation, as well as local and spanwise averaged heat transfer measurements near a 180° sharp turn in a rectangular channel. The channel aspect ratio (width to height ratio) varies from 1 to 5 and the ratio between the width of the channel and that of the partition wall is always equal to 5. Heat transfer measurements are performed by means of the heated-thin-foil technique, which practically corresponds to a constant heat flux boundary condition, and by using infrared (IR) thermography. Two different heating conditions, in particular heating from one side (asymmetrical), or from two sides (symmetrical), are implemented. The convective heat transfer coefficient is evaluated from the measured temperature maps and the local bulk temperature of the flow which is obtained by making a one-dimensional balance along the channel. Results are presented in terms of local, or averaged, Nusselt number which is normalised with the classical Dittus and Boelter correlation. The fluid used during the test is air and the Reynolds number, based on the flow average velocity and channel hydraulic diameter, is varied between 16,000 and 60,000.     

Solution of non-linear inverse heat conduction problems using the method of lines

 Two space marching methods for solving the one-dimensional nonlinear inverse heat conduction problems are presented. The temperature-dependent thermal properties and the boundary condition on the accessible part of the boundary of the body are known. Additional temperature measurements in time are taken with a sensor located in an arbitrary position within the solid, and the objective is to determine the surface temperature and heat flux on the remaining part of the unspecified boundary. The methods have the advantage that time derivatives are not replaced by finite differences and the good accuracy of the method results from an appropriate approximation of the first time derivative using smoothing polynomials. The extension of the first method presented in this study to higher dimensions inverse heat conduction problems is straightforward. Received on 3 May 1999     

Nonsimilar solutions for free convection from a vertical plate in porous media

A nonsimilar boundary layer analysis has been presented for the free convection along a vertical plate embedded in a fluid-saturated porous medium in the presence of surface mass transfer and internal heat generation. The transformed conservation laws are solved numerically for the cases of variable wall temperature and variable wall heat flux boundary conditions. Results are presented for the details of the velocity and temperature fields as well as Nusselt number. Received on 13 December 1996     

Free convection in non-newtonian fluids along a horizontal plate in a porous medium

A similarity solution is presented for the problem of free convection boundary layer in power-law type non-Newtonian fluids along a horizontal plate with variable wall temperature or heat flux distribution. The effects of surface mass transfer are included. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.     

A simultaneous PIV and heat transfer study of bubble interaction with free convection flow

Whole field velocity and point temperature and surface heat flux measurements were performed to characterise the interaction of a single rising ellipsoidal air bubble with the free convection flow from a heated flat surface immersed in water at different angles of inclination. Two thermocouples and a hot film sensor were used to characterise heat transfer from the surface, while a time-resolved digital particle image velocimetry technique was used to map the bubble induced flow in a plane parallel to the surface. Heat flux fluctuations, preceding and following the bubble passage, were shown to correlate with the variation in both local flow velocities and fluid temperatures. The largest increases in heat transfer were recorded when both flow and temperature effects combined to enhance the convective cooling simultaneously. Such conditions were shown to be most likely met when the block was inclined at 45°, thus forcing the bubble to slide closer to the heated surface and hence to the thermal boundary layer.     

Retrieving the heat transfer coefficient for jet impingement from transient temperature measurements

Algorithm of retrieving the heat transfer coefficient (HTC) from transient temperature measurements is presented. The unknown distributions of two types of boundary conditions: the temperature and heat flux are parameterized using a small number of user defined functions. The solutions of the direct heat conduction problems with known boundary temperature and flux are expressed as a superposition of auxiliary temperature fields multiplied by unknown parameters. Inverse problem is formulated as a least squares fit of calculated and measured temperatures and is cast in a form of a sum of two objective functions. The first results originates from an inverse problem for retrieving the boundary temperature the second comes from the inverse problem for reproducing the boundary heat flux. The final form of the objective function is obtained by enforcing constant in time value of the heat transfer coefficient. This approach leads to substantial regularization of the results, when compared with the standard technique, where HTC is calculated from separately reconstructed temperature and heat flux on the boundary. The validation of the numerical procedure is carried out by reconstructing a known distribution of the HTC using simulated measurements laden by stochastic error. The proposed approach is also used to reconstruct the distribution of the HTC in a physical experiment of heating a cylindrical sample using an impinging jet.     

Numerical nonlinear inverse problem of determining wall heat flux

The inverse problem of determining time-variable surface heat flux in a plane wall, with constant or temperature dependent thermal properties, is numerically studied. Different kinds of incident heat flux, including rectangular waveform, are assumed. The solution is numerically solved as a function estimation problem, so that no a priori information for the functional waveforms of the unknown heat flux is needed. In all cases, a solution in the form of a piece-wise function is used to approach the incident flux. Transient temperature measurements at the boundary, from the solution of the direct problem, served as the simulated experimental data needed as input for the inverse analysis. Both direct and inverse heat conduction problems are solved using the network simulation method. The solution is obtained step-by-step by minimising the classical functional that compares the above input data with those obtained from the solution of the inverse problem. A straight line of variable slope and length is used for each one of the stretches of the desired solution. The influence of random error, number of functional terms and the effect of sensor location are studied. In all cases, the results closely agree with the solution.     

Einfluß der thermischen Randbedingung auf den laminaren Wärmeübergang im Kreisrohr bei hydrodynamischer Einlaufströmung

Heat transfer characteristics of hydrodynamically developing laminar flow in a circular duct with different thermal boundary conditions were calculated by solving the equations of continuity, motion and energy in finite difference form. Results are presented for linear, sinusoidal and exponential variations of the prescribed wall heat flux along the duct length. A comparison shows that the influence of the thermal boundary condition on heat transfer increases with increasing development of velocity and temperature profiles. As a side result an improved correlation for heat transfer with constant wall heat flux in hydrodynamically developing flow is presented.     

Analysis of laminar flow forced convection heat transfer in the entrance region of a circular pipe

A numerical solution, for incompressible, steady-state, laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux and constant wall temperature. The development of velocity profile is obtained from Sparrow's entrance region solution. This velocity distribution is used in solving the energy equation numerically to obtain temperature profiles. Variation of the heat transfer coefficient for these two different boundary conditions for the early stages of boundary layer formation on the pipe wall is obtained. Local Nusselt numbers are calculated and the results are compared with those given byUlrichson andSchmitz. The effect of the thermal boundary conditions is studied by comparing the uniform wall heat flux results with uniform wall temperature.     

Heat transfer experiments in rotating boundary layer flow

The influence of Coriolis force on heat transfer in a rotating transitional boundary layer has been experimentally investigated. The experiments have been conducted for local Görtler numbers up to 150. Heat transfer measurements have been performed for a flat plate with nearly uniform heat flux applied to the surface, where the temperature was measured by the thermochromic liquid crystal method. The results indicate that heat transfer is enhanced when Coriolis force acts towards the wall, i.e., on the pressure surface. The velocity measurements under equivalent conditions show that Coriolis instability induces counter-rotating longitudinal vortices which augment the lateral transport of the fluid on the pressure surface. On the other hand, the heat transfer on the suction surface remains at the same level as compared to the case without system rotation. As a consequence, the heat transfer coefficient on the pressure surface is 1.8 times higher than that measured on the suction surface when averaged over the measured surface.     

Development and Application of a Novel Technique for Direct Heat Flux Measurements in Turbomachinery Flows

The high performance and efficiency of modern gas turbines are only possible with temperatures inside the engine exceeding the allowed material temperatures in some areas by several hundred degrees. Therefore effective cooling methods are one of the key factors for the success of these engines. In order to achieve reliable predictions of the heat load of rotor or stator blades numerous research activities were performed to understand the nature of heat transfer in complex unsteady flows. Even numerical methods have made significant progress in recent years detailed experimental data are still necessary for validation and further development of the engines and the design tools. Here a new method to directly measure the heat flux at the material surface and accurately determine the heat transfer coefficienth is presented. The new sensor is based on the anisotropic characteristics of single crystals and allows the determination of the time varying heat flux on the surface of a model turbine airfoil. This feature is of special interest to study the influence of periodically disturbed flow conditions on the heat transfer characteristics of cooled turbine blades. The working principle of an anisotropic heat flux (AHF) sensor is briefly described together with the design of the actual sensor used in this study. Prior to the application of the sensor in a cascade test rig, comprehensive test of the sensor, the electronics and the data acquisition system were performed using a pulsed laser beam as heat source. To test the sensor under realistic conditions a large number of sensor was installed in a test blade and heat transfer measurements were performed in a cascade test rig equipped with a spoke-wheel wake generator. The results showed good agreement in the time mean results compared with standard techniques. Additionally time resolved data could be extracted from the sensor signals providing detailed information on the unsteady heat transfer characteristics and boundary layer development. This revised version was published online in July 2006 with corrections to the Cover Date.     

Transient heat flux measurement of natural convection in an inclined enclosure with time-periodically-varying wall temperature

The transient natural convection in an inclined enclosure filled with water is studied experimentally for the time-periodically-varying wall temperature on one side wall and constant average temperature on the opposing side wall. This system has no temperature difference between the opposing two side walls in time-averaged sense. The temperatures of two opposing walls and the heat flux across the enclosure are measured by a heat flux meter. Based on the experimental results, the effects of time-periodically-varying wall temperature and inclined angles of the enclosure on heat transfer characteristics are studied. The experimental results show that, with the upper wall temperature oscillating, the heat flux across the enclosure is also periodically varied with time, and the net heat flux is from the lower wall to the upper wall. Numerical computations are also conducted and numerical results are qualitatively assured by the experimental measurements.     

Performance evaluation of compact channels with surface modifications for heat transfer enhancement: An interferometric study in developing flow regime

Performance evaluation of surface roughened compact channels for heat transfer applications has been investigated using non-intrusive, real time laser-based interferometric technique with water as the coolant medium. The lower wall of the channel has been roughened by creating hemispherical inward dimples. Projection data of the temperature field has been recorded using a Mach Zehnder interferometer. In order to facilitate direct comparison, experiments have also been conducted in smooth channel of similar dimensions. Results have been presented in the form of thermal boundary layer profiles, whole field temperature distributions and local variations of heat transfer coefficients. Direct interferometric measurements clearly reveal the disruption of thermal boundary layer due to the presence of inward dimples. Near wall temperature gradients were seen to be stronger in the case of dimpled channel in comparison with that of the smooth one resulting into a clear enhancement in heat transfer rates. At low Reynolds numbers, variation of heat transfer coefficients along the length of the dimpled channel showed the presence of local maxima. On the other hand, the corresponding profiles for the smooth channels showed a monotonic decrease with respect to the axial direction. The dynamic measurements, that are purely non-intrusive, revealed an improved thermal performance of surface roughened compact channels.     

Series solutions of boundary-layer flows in porous media with lateral mass flux

Approximate analytical solutions for free convection boundary layers on a heated vertical plate with lateral mass flux embedded in a saturated porous medium are presented using the modified Adomian decomposition method and Padé technique. Several values of the wall temperature exponent for illustrating the effects of suction/injection parameter on the flow and heat transfer are considered. This study also includes the influence of the exponent on an impermeable surface. The results obtained are comparable to the exact analytical solutions and elucidate reliability and efficiency of the technique.     

Momentum and heat transfer of a special case of the unsteady stagnation-point flow

This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.     

Heat transfer in film-cooled turbulent boundary layers at different blowing ratios as affected by longitudinal vortices

Effects of embedded longitudinal vortices on heat transfer in film-cooled turbulent boundary layers at different blowing ratios are discussed. These results were obtained in boundary layers at free-stream velocities of 10 and 15 m/s. Film coolant was injected from a single row of holes at blowing ratios of 0.47–1.26. A single longitudinal vortex was induced upstream of the film-cooling holes using a half-delta wing attached to the wind tunnel floor. Heat transfer measurements were made downstream of injection using a constant heat flux surface with 126 thermocouples for surface temperature measurements. For all blowing ratios examined, the embedded vortices cause significant alterations to wall heat transfer and to film cooling distributions. Measurrments of mean temperatures and mean velocities in spanwise planes show that high wall heat transfer regions are associated with regions of high near-wall longitudinal velocity where very little film coolant is present. In addition to high heat transfer regions associated with the vortex downwash, there are also secondary heat transfer peaks. These secondary peaks develop due to shear layer mixing and interaction between the vortex and cooling jets and become higher in magnitude and more persistent with downstream distance as the blowing ratio increases from 0.47 to 1.26.     

Thin Layer Thermography - a new heat transfer measurement technique

 In order to overcome the shortcomings of conventional temperature instrumentation to compute heat transfer rates, a novel technique for heat transfer measurement is presented. Stemming from infrared thermography, the potential for further development of the ‘Thin Layer Thermography’ is demonstrated. This new measurement technique is based on the wavelength dependent transmissivity of thin layers. It captures temperature distributions on the wall surface and simultaneously in a prescribed and well defined depth of the wall of a given object of interest. This enables the calculation of a temperature gradient normal to the surface and therefore the determination of the wall heat flux. Received: 8 April 1998/Accepted: 12 August 1998     

Convective heat transfer for viscoelastic fluid in a curved pipe

In this paper, fully developed convective heat transfer of viscoelastic flow in a curved pipe under the constant heat flux at the wall is investigated analytically using a perturbation method. Here, the curvature ratio is used as the perturbation parameter and the Oldroyd-B model is applied as the constitutive equation. In the previous studies, the Dirichlet boundary condition for the temperature at the wall has been used to simplify the solution, but here exactly the non-homogenous Neumann boundary condition is considered to solve the problem. Based on this solution, the non-axisymmetric temperature distribution of Dean flow is obtained analytically and the effect of flow parameters on the flow field is investigated in detail. The current analytical results indicate that increasing the Weissenberg number, viscosity ratio, curvature ratio, and Prandtl number lead to the increase of the heat transfer in the Oldroyd-B fluid flow.