On the role of the fluid effusivity in unsteady heat transfer between a boundary layer and a solid wall

The problem of obtaining the wall heat flux in the presence of unsteady heat transfer in two-dimensional, turbulent boundary layer flow is re-examined. A novel expression to produce estimates of the amplitude of the fluctuating wall heat flux has been proposed for the foregoing conditions. This expression is based on flow field measurements instead of measurements in the solid wall substrate, thus allowing us to take the flow dynamics directly into account in the analysis. The fluid effusivity, a measure of the ability of the fluid to exchange thermal energy with its surroundings, was shown to be the dominant parameter controlling the unsteady heat transfer process.     

Effect of thermal boundary layer on radiative heat transfer from combustion plasma

The effect of thermal boundary layer on radiative heat transfer considering nongray nonisothermal plasma has been calculated for potassium seeded watergas combustion plasma. The effect of combustion species concentration and seed concentration on radiative flux under the equilibrium flow and frozen flow condition has been studied. It has been estimated that reduction in radiative flux due to cold boundary layer may be upto 25%.     

Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition

Non-Newtonian boundary layer flow and heat transfer over an exponentially stretching sheet with partial slip boundary condition has been studied in this paper. The flow is subject to a uniform transverse magnetic field. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST), and (ii) prescribed heat flux (PHF). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. An effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameters on the velocity, skin-friction coefficient and the temperature boundary layer. It is found that the third grade fluid parameter β increases the momentum boundary layer thickness and decreases the thermal boundary layer thickness.     

Transition of natural convection boundary layers—a revisit by Bicoherence analysis

Previous studies have revealed that heat transfer through a convective thermal boundary layer can be significantly enhanced by perturbing the thermal boundary layer to advance linear to nonlinear transition. It has also been demonstrated that the enhancement of heat transfer is mostly achieved in the nonlinear regime. In this study, the transition of the thermal boundary layer adjacent to an isothermally heated vertical surface is revisited by means of Bicoherence analysis, which is a statistical approach for identifying and quantifying quadratic wave interactions. The streamwise evolution of Bicoherence spectra suggests that the thermal boundary layer can be classified into three regimes: a linear flow regime, a transitional flow regime and a nonlinear flow regime. The positions of the transition from the transitional to nonlinear regimes in the thermal boundary layer at various Rayleigh numbers, perturbation frequencies and perturbation amplitudes are determined using Bicoherence analysis. It is found that in the nonlinear flow regime, the number of resonance groups fluctuates, which indicates the occurrence of coupling and decoupling of harmonics in the boundary layer. This process may be the mechanism responsible for the resonance induced enhancement of heat transfer.     

Cattaneo–Christov heat flux model for heat transfer of Marangoni boundary layer flow in a copper–water nanofluid

The Cattaneo–Christov heat flux is first utilized to explore the heat transfer characteristics of Marangoni boundary layer flow in a copper–water nanofluid. The Marangoni boundary layer flow is driven by exponential temperature. Five different types of nanoparticle shapes including sphere, hexahedron, tetrahedron, column and lamina are considered for the copper–water nanofluid. The nonlinear system of partial differential equations is reduced by similarity transformations and then solved numerically by the shooting method. It is found that sphere nanoparticle has better heat transfer enhancement than other nanoparticle shapes and both the temperature and the thickness of the thermal boundary layer are lower for the Cattaneo–Christov heat flux model than the classical Fourier's law of heat conduction.     

Real-time solution of heat conduction in a finite slab for inverse analysis

Laplace transform is used to solve the problem of heat conduction over a finite slab. The transfer functions relating the temperature and heat flux on the front and back surfaces of the finite slab are developed. Although there are many competing methods for constructing the inverse Laplace transform, we use polynomial approximation of the transfer function. Therefore, transient solutions for given boundary conditions are easily obtained using SIMULINK. This process is much simpler than other numerical solution methods for the heat equation. Most importantly, our method of solution allows us to obtain, in real-time, the front surface temperature and heat flux based on the thermodynamic measurements on the back surface. We also demonstrate the feasibility of reconstructing the front surface temperature when sensor noise is incorporated to the back surface measurements.     

Spectral relaxation method analysis of Casson nanofluid flow over stretching cylinder with variable thermal conductivity and Cattaneo–Christov heat flux model

This article deals with non‐Newtonian Casson nanofluid flow and heat transfer over stretching cylinder in a porous medium. The mode of heat transfer is presented considering temperature‐dependent thermal conductivity by integrating the Cattaneo–Christov heat flux and mass flux models. Boundary layer theory is applied to develop the governing partial differential equations from the physical problem. Employing proper similarity transformation, the governing boundary layer equations are transformed into dimensionless system of nonlinear ordinary differential equations. Then, the resulting problem is numerically solved by means of spectral relaxation method. The convergence analysis of the proposed numerical scheme is presented via a table, which confirms almost the 10th order of approximation is enough for the convergence of the skin friction coefficient, local heat transfer, and mass transfer rates. The effects of various embedded parameters on velocity, temperature, and concentration profiles as well as skin friction coefficient, surface heat and mass transfer rates are examined through graphs and tables. The findings reveal that the growth of permeability and velocity slip parameters appears to decelerate the velocity distributions of fluid. Thermal boundary layer thickness tends to develop with greater values of permeability and Brownian motion parameters. Also, the local heat transfer rate is less with Fourier's law of heat conduction than Cattaneo–Christov heat flux model. Furthermore, the validity and accuracy of the present result is checked with the available literature, and very sound agreement has been obtained.     

Natural convection heat transfer of non-Newtonian fluids in porous media from a vertical cone under mixed thermal boundary conditions

This work studies the problem of the steady natural convection boundary layer flow over a downward-pointing vertical cone in porous media saturated with non-Newtonian power-law fluids under mixed thermal boundary conditions. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the power-law viscosity index and the similarity exponent on the heat transfer characteristics under mixed thermal boundary conditions have been studied. Under mixed thermal boundary conditions, both the surface heat flux and the surface temperature are found to decrease when the power-law viscosity index of the non-Newtonian power-law fluid in porous media is increased. Moreover, an increase in the similarity exponent tends to increase the boundary layer thickness and thus decreases the surface heat flux under mixed thermal conditions. The generalized governing equations derived in this work can be applied to the cases of prescribed surface temperature and prescribed heat flux.     

An experimental investigation of heat transfer in pin fin array

Detailed heat transfer measurements were performed by using 178 thermocouples in a channel with pin fin array. Local heat transfer coefficients and local heat transfer enhancement coefficients were obtained for eight Reynolds numbers ranging from 2000 to 100,000 on the endwall of the channel. The endwall boundary conditions for heat transfer investigation are heating the bottom endwall and heating symmetrically the bottom and top endwalls with constant heat flux. The mechanism of heat transfer enhancement with pin fin array has been discussed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(7): 533–541, 2001     

Adaptation of the in-cavity calibration method for high temperature heat flux sensors

The need for in situ heat flux measurements in hot structures, used in hypersonic vehicle thermal protection system development, combustion and propulsion research, and fire testing requires that heat flux sensors are characterized over their entire operating temperature range. The in-cavity heat flux sensor calibration technique has been adapted to accommodate elevated sensor temperatures, in an effort to develop a primary calibration scheme for high temperature heat flux sensors using an existing blackbody calibration system. The new scheme has been demonstrated through the calibration of a high temperature, thermopile-type heat flux sensor. The output temperature dependence of the high temperature heat flux sensor (HTHFS) has been successfully characterized over the range of 175–960 °C with acceptable uncertainty limits. The calibrated HTHFS sensitivity agrees well with a theoretical sensitivity model, suggesting that the extended in-cavity calibration technique is a viable choice for primary calibration of heat flux sensors at elevated sensor temperatures.     

Approximate Solution to the Spray Heat Transfer Problem at High Surface Temperatures and Liquid Mass Fluxes

ABSTRACT

A basic energy balance that includes phase change has been used to describe the boiling heat transfer process. By using the differential form of this energy balance, the relative change in the heat transfer coefficient can be determined when the surface and coolant temperature change. This represents a general solution to the boiling heat transfer problem under high flux conditions where fully mixed thermal boundary layer exists, although the solution procedure is approximate. The results agree quite well with experimental data. Further work remains to prescribe the heat transfer process near the critical heat flux and Leidenfrost point. This approach vastly reduces the empiricism and data required for boiling heat transfer processes, and also existing data can be used to generalize to a wide range of conditions.     

High heat flux point source sensitivity and localization analysis for an ultrasonic sensor array

State estimation procedures using the extended Kalman filter are investigated for a transient heat transfer problem in which a high heat flux point source is applied on one side of a thin plate and ultrasonic pulse time of flight is measured between spatially separated transducers on the opposite side of the plate. This work is an integral part of an effort to develop a system capable of locating the boundary layer transition region on a hypersonic vehicle aeroshell. Results from thermal conduction experiments involving one-way ultrasonic pulse time of flight measurements are presented. Uncertainties in the experiments and sensitivity to heating source location are discussed. One key finding is that sensitivity to heating source location is greater in the direction normal to the ultrasonic pulse propagation path. Scaled sensitivities to boundary conditions and thermal conductivity are presented and analyzed for all possible source locations using a square sensor grid. While sensitivity to the primary heat flux was determined to be the highest, sensitivity to the other parameters is either on the same order of magnitude or one order of magnitude less. Two different measurement models are compared for heating source localization: (1) directly using the one-way ultrasonic pulse time of flight as the measurement vector and (2) indirectly obtaining distance from the one-way ultrasonic pulse time of flight and then using these obtained distances as the measurement vector in the extended Kalman filter. Heating source localization results and convergence behavior are compared for the two measurement models. Two areas of sensitivity analyses are presented: (1) heat source location relative to sensor array position, and (2) sensor noise. The direct measurement model produced the best results when considering accuracy of converged solution, ability to converge to the correct solution given different initial guesses, and smoothness of convergence behavior.     

Periodic heat transfer by forced laminar boundary layer flow over a semi-infinite flat plate

The paper reports a study of periodic convection in a steady forced laminar boundary layer flow over a semi-infinite impermeable flat plate due to periodical variation of the wall heat flux. The Fourier transform based approach allows to obtain a transfer function for the boundary layer that can be used to solve also transient (non-periodic) heating problems, and examples are reported comparing with available studies in the open literature. The effect of periodic heating on the value of the the average heat transfer coefficient is analysed and it is found to be important for relatively high frequency fluctuations of the imposed heat flux, whereas fluctuation amplitude of the instantaneous heat transfer coefficient is non-negligible also for lower exciting frequency.     

Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger

In the paper, numerical and experimental analyses of heat and mass transfer during frost formation on a fin-and-tube heat exchanger have been presented. Modelling of the frost formation on cold surfaces placed in a humid air stream, requires a complex mathematical approach. A transient two-dimensional mathematical model of frost formation has been developed. The applied mathematical model has been defined using governing equations for the boundary layer that include air and frost sub-domains as well as a boundary condition on the air–frost interface. The mathematical model with initial and boundary conditions has been discretised according to the finite volume method and solved numerically using the SIMPLER algorithm for the velocity–pressure coupling. Results have shown that the frost layer formation significantly influences the heat transfer between air and fins. As a result of numerical calculations, time-wise frost thickness variations for different air humidities, temperatures and velocities have been presented. Using the developed mathematical model, the algorithm and the computer code, which have been experimentally validated, it is possible to predict a decrease of exchanged heat flux in the heat exchanger under frost growth conditions.     

Prediction of turbine blade heat transfer and aerodynamics using a new unsteady boundary layer transition model

The effects of periodic unsteady flow on heat transfer and aerodynamic characteristics, particularly on the boundary layer transition along the suction and the pressure surfaces of a typical gas turbine blade, are experimentally and theoretically investigated. Comprehensive aerodynamic and heat transfer experimental data are collected for different unsteady passing frequencies that are typical of gas turbines. To predict the effect of the impinging periodic unsteady flow on the heat transfer and the aerodynamics of turbine blades, a new unsteady boundary layer transition model is developed. The model is based on a universal unsteady intermittency function and utilizes an inductive approach that implements the results of comprehensive experimental and theoretical studies of unsteady wake development and the boundary layer flow. Three distinct quantities are identified as primarily responsible for the transition of an unsteady boundary layer: (1) the universal relative intermittency function, (2) maximum intermittency, and (3) minimum intermittency. The analysis of the experimental results and the comparison with the model prediction confirm the validity of the model and its capability to accurately predict the unsteady boundary layer transition.     

Heat transfer in a viscoelastic boundary layer flow over a stretching sheet

Studies are made on the viscoelastic fluid flow and heat transfer characteristics over a stretching sheet with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for the cases of prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The momentum equation is decoupled from the energy equation for the present incompressible boundary layer flow problem with constant physical parameters. Exact solution for the velocity field and the skin-friction are obtained. Also, the solutions for the temperature and heat transfer characteristics are obtained in terms of Kummer’s function. The work due to deformation in energy equation, which is essential while formulating the viscoelastic boundary layer flow problems, is considered. This paper examines the effect of viscoelastic parameter, Eckert number, Prandtl number and non-uniform heat source/sink parameter on temperature distribution, wall temperature gradient for PST-case and wall temperature for PHF-case.     

Effects of slip on sheet-driven flow and heat transfer of a third grade fluid past a stretching sheet

The entrained flow and heat transfer of an electrically conducting non-Newtonian fluid due to a stretching surface subject to partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). The constitutive equation of the non-Newtonian fluid is modeled by that for a third grade fluid. The heat transfer analysis has been carried out for two heating processes, namely, (i) with prescribed surface temperature (PST case) and (ii) prescribed surface heat flux (PHF case). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip, magnetic field and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that slip decreases the momentum boundary layer thickness and increases the thermal boundary layer thickness, whereas the third grade fluid parameter has an opposite effect on the thermal and velocity boundary layers.     

Heat flux dispersion in natural convection in porous media

Analytical solutions derived in this paper confirm the experimental and numerical results revealing a widespread dispersion of heat flux data in natural convection in porous media. The weak non-linear method of solution is used to evaluate the heat flux in a porous layer heated from below and subject to weak boundary and domain imperfections. Little attention has been paid so far to the effect that the lower branch of the imperfect bifurcation has on the average heat flux. The results presented in this paper demonstrate the latter effect and explain the reason behind the dispersion of data. The comparison of the results with existing experimental and numerical data confirms the findings. In addition the latter effect is shown to be essential in ones ability to control heat transfer enhancement via natural convection in porous metal foams, for example.     

Critical heat flux in subcooled flow boiling with water in a tube with axially nonuniform heating

Critical heat flux (CHF) in subcooled flow boiling under axially nonuniform heating conditions was experimentally investigated using a tube heated with a dc power source. The thickness of the tube wall in the axial direction was varied to attain axially nonuniform heating. The different thicknesses, therefore, separated the tube into regions of high heat flux and regions of low heat flux. The lengths of these regions of the tube were also varied to study the effect on the CHF. The objective of this system is to initiate boiling in the high-heat-flux region, thus increasing heat transfer, and to interrupt the bubble boundary layer in the low-heat-flux region. Because it is the initiation of boiling that increases heat transfer, the performance of such a system is linked to its effectiveness in repeatedly interrupting and re-establishing the bubble boundary layer. Our experiments, involving tubes that had sections of different thicknesses and different lengths, showed that when the heat flux in the low-heat-flux region was below the net vapor generation (NVG) heat flux, this system enhanced the CHF, but not when it was above the NVG. Also, for relatively short low-heat-flux regions, the CHF was not enhanced, presumably because there was insufficient time to interrupt the bubble boundary layer. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(2): 169–178, 1998     

Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet

Viscoelastic boundary layer flow and heat transfer over an exponential stretching continuous sheet have been examined in this paper. Approximate analytical similarity solution of the highly non-linear momentum equation and confluent hypergeometric similarity solution of the heat transfer equation are obtained. Accuracy of the analytical solution for stream function is verified by numerical solutions obtained by employing Runge-Kutta fourth order method with shooting. These solutions involve an exponential dependent of stretching velocity, prescribed boundary temperature and prescribed boundary heat flux on the flow directional coordinate. The effects of various physical parameters like viscoelastic parameter, Prandtl number, Reynolds number, Nusselt number and Eckert number on various momentum and heat transfer characteristics are discussed in detail in this work.