Measurements and analysis of load and speed effects on the instantaneous wall heat fluxes in a direct injection air‐cooled diesel engine

This work presents an experimental analysis which is carried out to study the instantaneous heat fluxes, during the engine cycle, in the cylinder head and exhaust manifold of a direct injection, air‐cooled, four‐stroke diesel engine. For temperature measurements, a new pre‐amplification unit for fast response thermocouples, appropriate heat flux sensors and an innovative, object‐oriented, control code for fast data acquisition have been designed and developed at the authors' laboratory. The experimental installation separates the engine transient temperature signals into two parts; namely the ‘long’‐ and the ‘short’‐term response ones; followed by their discrete processing in two independent data acquisition systems. One‐dimensional heat conduction with Fourier analysis of the raw temperature data are implemented in order to calculate the instantaneous engine combustion chamber and exhaust pipe heat fluxes. This study concentrates on the correct interpretation of the measured temporal variations of heat fluxes and the examination of the effect of engine load and speed on the cylinder head and exhaust manifold heat flux losses. Many interesting aspects of transient engine heat transfer are revealed. The simultaneous presentation of heat fluxes on the cylinder head and exhaust manifold, together with the engine indicator diagram, sheds light into the mechanisms governing transient heat transfer during an engine cycle. Copyright © 2000 John Wiley & Sons, Ltd.     

Transient characteristics of thermal contact conductance between isotropic rough surfaces of metals

Transient measurements of thermal contact conductance are made on the interface between isotropic rough surfaces of metals in air. We present an analytical solution for temperature distribution of the one‐dimensional symmetric system with the condition of time‐dependent temperatures at two points in each body, and thereby interface temperature drops and heat fluxes can be obtained without the condition of heat‐flux continuity at the interface. Contacting surfaces of rod samples (Naval brass, JIS?SK5 carbon tool steel, and JIS?SUS 304 stainless steel) of 25‐mm diameter are uniformly polished using an emery 320 paper. Transient characteristics of both temperatures and heat fluxes at the interface are experimentally determined using the analytical solution. It is revealed through the transient experiment that the thermal contact conductances are not constant at the early stage, but rapidly increase from zero and that the discontinuity of interface heat‐flux is observed by about 20 percent for all metal pairs. For the contact between dissimilar metals, the dependence of thermal contact conductance on the direction of heat flow is not distinguishable. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 341–356, 2001     

Transient effects in natural convection cooling of vertical parallel plates

This work presents results from a numerical study of transient natural convection between vertical parallel plates. Two boundary conditions – uniform wall temperature and uniform heat flux – are considered. Results presented include the rate of heat transfer for uniform wall temperature and the maximum wall temperature for uniform heat flux. Also presented are simple correlations to calculate the minimum heat transfer and the maximum wall temperature during the transient period. It is found that for uniform wall temperature the ratio of the minimum heat transfer to the steady state heat transfer decreases with length of the channel, and for uniform heat flux the maximum transient temperature has a maximum of about 9% over the steady state temperature.     

Determination of skin temperature distribution and heat flux during simulated fires using Green's functions over finite-length scales

One of the current practices for measuring heat flux during flash fire testing, forest fires, and other industrial cases focuses on the use of semi-infinite models to predict the heat flux during exposure through surface temperature measurements on simulated skin sensors. For short time frames, these models can be shown to have acceptable accuracy. However, when considering longer time exposures at reduced heat fluxes, such as with firefighters in a forest fire, the accuracy of these models could be brought into question. A one-dimensional, finite length scale, transient heat conduction model was developed using a Green's function approach on a rectangular sensor. The model was developed using transient temperature boundary conditions to avoid the use of complicated radiation and convection conditions at each boundary. For comparison, a semi-infinite model utilizing the same boundary condition on the exposed face was solved using both the Laplace transform method and Green's function method. Experimental data was obtained during exposure to a cone calorimeter. All measurements were taken for a minimum duration of 2 min. This temperature data was used to develop appropriate curves for the boundary conditions and validate the analytical models. It was found that the temperature obtained from the one-dimensional transient heat conduction model based on Green's functions agreed well with the experimental results over longer exposure times, and with reduced error when compared with the semi-infinite model. This suggests that modeling the problem on a finite-length scale will produce more accurate or more conservative temperature and heat flux results over extended periods of exposure in high heat load applications.     

Transient temperature profile inside thermoacoustic refrigerators

The linear theory used to calculate the thermal quantities inside the stack in the classical thermoacoustic refrigerators always overestimates those measured. The causes of these discrepancies have to be found in the complex processes of thermal exchanges. The analytical study of the transient response should provide an interpretation of these complex processes. This present paper provides such analytical modelling. This modelling remains within the framework of the classical linear theory. It includes the effects of the thermoacoustic heat flux carried along the stack, the conductive heat flux returning in the solid walls of the stack and through the fluid inside the stack, the transverse heat conduction in the stack and the heat leakages through the duct walls, the heat generated by viscous losses in the stack, the heat generated by vorticity at the ends of the stack, and the heat transfer through both ends of the stack. A modal analytical solution for the temperature profile is proposed, assuming the usual approximations in such thermal problems to avoid intricate calculations and expressions. The theoretical transient response of a thermoacoustic refrigerator is compared with experimental data. A good qualitative agreement is obtained between analytical and experimental results after fitting empirical coefficients.     

Heat conduction in a semi-infinite solid subject to steady and non-steady periodic-type surface heat fluxes

An analytical solution for the temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The solutions are presented for time-dependent, surface heat fluxes of the forms: (i) Q₁(t) = Q₀(1+a cos ωt); and (ii) Q₂(t) = Q_o(1+bt cos ωt), where a and b are controlling factors of the periodic oscillations about the constant surface heat flux Q₀. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of decompositions C_r and S_r of the generalized representation of the incomplete Gamma function. It is demonstrated that the present analysis covers the limiting case for large times which is discussed in several textbooks, for the case of steady periodic-type surface heat fluxes. In addition, an illustrative example problem on heating of malignant tissues, making use of transient and long-time solutions, is also presented.     

Prediction of an effective cooling output of the fin-and-tube heat exchanger under frosting conditions

In the paper, an analysis of heat and mass transfer during frost formation on a fin-and-tube heat exchanger has been presented. For calculation of an exchanged heat flux, a transient two-dimensional mathematical model of frost formation has been developed and numerically solved. The mathematical model and numerical procedure have been experimentally validated. For determination of an effectively exchanged heat flux inside the heat exchanger, the influence of the augmented heat transfer resistance and impact of the defrosting process have been taken into account. A detailed calculation of the frost growth rate has been a base for determination of heat transfer resistance of the frost layer. The influence of frost formation on the overall heat transfer coefficient has also been analysed. The effective exchanged heat flux has been calculated for different operating conditions, durations of cooling cycle as well as defrosting heat fluxes. Results have shown that the effectively exchanged heat flux significantly depends on operating conditions, such as air humidity and temperature, as well as the cooling cycle duration.     

A near-wall two-equation model for turbulent heat fluxes

A near-wall two-equation model for turbulent heat fluxes is derived from the temperature variance and its dissipation-rate equations and the assumption of gradient transport. Only incompressible flows with non-buoyant heat transfer are considered. The near-wall asymptotics of each term in the exact equations are examined and used to derive near-wall correction functions that render the modeled equations consistent with these behavior. Thus modeled, the equations are used to calculate fully-developed pipe and channel flows with heat transfer. It is found that the proposed two-equation model yields asymptotically correct near-wall behavior for the normal heat flux, the temperature variance and its near-wall budget and correct limiting wall values for these properties compared to direct simulation data and measurements obtained under different wall boundary conditions.     

Heat and mass diffusion fluxes on a permeable wall with foreign-gas blowing

In the present paper, we consider the variation of heat and mass diffusion fluxes on a permeable plate with blowing of a foreign gas into the boundary layer, the fluxes being considered as functions of the permeability parameter, varied through variation of blowing intensity, free-stream velocity, or longitudinal coordinate. It is shown that at a fixed distance from the leading edge of the plate one can, varying the value of blowing intensity while preserving the uniformity of the blowing over the plate length, obtain a non-monotonic variation of the wall heat and mass diffusion fluxes. In contrast to the heat and mass diffusion fluxes, the shear stress always monotonically decreases with increasing the blowing intensity. Similar to the shear stress, on increase of permeability parameter achieved through changing either the free-stream velocity or the longitudinal coordinate the heat flux and the mass diffusion flux both show a monotonic reduction. Using the integral relations of boundary-layer theory, we have derived simple analytical expressions allowing determination of the maximum values of the heat and mass diffusion fluxes in laminar and turbulent flow regimes. The obtained analytical relations were verified by performed numerical simulations.     

Image based heating rate calculation from thermographic data considering lateral heat conduction

An image based method for transient surface normal heat flux calculation from thermographic data is suggested. It is based on an analytical solution of the three-dimensional linear heat conduction equation. The method yields correct results for the surface normal heat flux even in regions with strong lateral gradients by taking into account the transient surface temperature of an area surrounding each evaluation point within the thermographic image. The solution for the heat flux can be stabilized with respect to measurement errors by an iterative regularization method. The validation of the method in synthetic test cases indicates its good accuracy over a broad range of Fourier numbers.     

To the theory of underwater ice evolution,or nonlinear dynamics of “false bottoms”

We present a mathematical model describing evolution of false bottoms often met between an under-ice melt pond and the underlying ocean during summer. The model treats a false bottom as the region of mixed phase (mushy layer) whose coordinates depend on time and determine the phase transition area. As the heat and the salt fluxes in the ocean are strongly influenced by turbulence and the ice meltwater accumulating underneath the ice cover is practically fresh, we use modified boundary conditions for heat and mass fluxes at the interfaces of phase transition. Explicit analytical solutions (thickness of false bottom and growth rates of its boundaries, temperature and salinity distributions, solid phase fraction and ocean-to-ice heat flux) of the nonlinear model under consideration are found. Model predictions are in good agreement with existing experimental data and physical concepts of phenomena under study.     

Direct numerical simulations of pool boiling curves including heater's thermal responses and the effect of vapor phase's thermal conductivity

Effects of heater's thermal properties and vapor phase's thermal conductivity on saturated pool boiling above a large horizontal heater are simulated numerically based on an improved pseudo-potential liquid-vapor phase change lattice Boltzmann model. A transient conjugate heat transfer problem is under consideration, where the conjugate thermal boundary condition is imposed and heater's thermal responses during boiling processes are investigated. Saturated pool boiling curves from onset of nucleate boiling to critical heat flux (CHF), to transition boiling regime to stable film boiling regime are obtained numerically. It is found that the simulated critical heat flux (CHF) agrees reasonably well with existing analytical models. Also, the simulated boiling heat fluxes in stable film boiling regime are shown to be in good agreement with the existing analytical solution. Thus, this improved pseudo-potential liquid-vapor phase change lattice Boltzmann model is quantitatively validated. Simulation results demonstrate that there is significant maldistribution in temperature distribution near the top of heater surface in nucleate boiling regime, CHF point and transition boiling regime. As a result, two-dimensional heat conduction can not be ignored when evaluating heat flux closely beneath the heater's top surface. It is also shown that both heater's thermal conductivity and thermal mass (the product of density and specific heat at constant pressure) have no effect on CHF value as well as the boiling curve in nucleate boiling regime and film boiling regime for a thick heater. However, the transition boiling regime of the boiling curve moves to the left with the increasing heater thermal conductivity and heater thermal mass for a thick heater. Increasing the vapor theraml conductivity has no effect on CHF but would increase boiling heat flux in film boiling regime, and hence shortening the transition boiling regime.     

Transient heat flux measurement analysis from coaxial thermocouples at convective based step heat load

The measurement of surface heating rate is an imperative parameter in the force convection ground-based facility for short duration investigation due to the heat transfer rate is changing rapidly. The coaxial thermocouples are suitable to measure the transient heat flux in fast varying heat transfer application because of having fast response time in the range microseconds or less. In this addition, the K-type, E-type, and J-type of coaxial thermocouples are contrived as well as the thermal coefficient resistance (TCR) and sensitivity (S) has been calculated from oil-bath based technique. These handmade coaxial thermocouples are exposed in a forced convection flow facility having three different input step heat loads as well as their transient heat fluxes are estimated using one-dimensional heat conduction modeling for the semi-infinite body. The numerical simulation has also been carried out with the analogous experimental parameters using ANSYS-FLUENT v.15.0 and compared with the outcome of the experimental approach and it is found that the average value of the transient temperatures having 0.3% error and surface heat flux recovered from this temperature is 10%. This study reveals the measuring ability of these handmade coaxial thermocouples at low temperature and low velocity on short duration transient measurements.     

Models for transient conduction in a flat plate subjected to a variable heat flux

This work presents analytical models allowing to identify the transient temperature distribution in a flat plate. The plate is exposed to a convective heat transfer on a face and to a heat flux on the other one. The heating flux is Heaviside (crenel type) and is maintained during a t₁ time. The heating phase is followed by a relaxation one. The theoretical method is original because it uses Green’s functions method to determine the analytical solutions of the heat propagation equation in the plate during the heating and relaxation phases. These analytical solutions allow to identify the temperature distribution as well as wall heat flux versus time. The results of our work can be useful at different levels: during the identification of parameters (such as the thermal conductivity or the thermal diffusivity of a plate), during the identification of the boundary conditions (like the heating flux or the convection coefficient) in industrial processes using this kind of systems, or even with educational intents for teaching transient conduction.     

Numerical prediction of critical heat flux in pool boiling with the two-fluid model

Three-dimensional numerical simulations of the atmospheric saturated pool boiling are performed with the aim of predicting the critical heat flux. The two-phase mixture in pool boiling is described with the transient two-fluid model. The transient heat conduction in the horizontal heated wall is also solved. Dynamics of vapor generation on the heated wall is modeled through the density of nucleation sites and the bubble residence time on the wall. The heater’s surface is divided into zones, which number per unit area equals the density of nucleation sites, while the location of nucleation site within each zone is determined by a random function. The results show a replenishment of the heater’s surface with water and surface wetting for lower heat fluxes, while heater’s surface dry-out is predicted at critical heat flux values. Also, it is shown that the decrease of nucleation site density leads to the reduction of critical heat flux values. Obtained results of critical heat flux are in good agreement with available measured data. The presented approach is original regarding both the application of the two-fluid two-phase model for the prediction of boiling crisis in pool boiling and the defined boundary conditions at the heated wall surface.     

Prediction of transient temperature of hydrogen flowing from pre-cooler of refueling station to inlet of vehicle tank

A thermodynamic analytical approach is proposed to obtain the transient temperature rise of hydrogen when pre-cooled hydrogen is heated through filling equipment at a refueling station. In this approach, the filling equipment is assumed to be a simple and straight pipeline, and the heat balance based on the thermodynamics for hydrogen flowing in the pipeline is analyzed. The internal surface temperature of the pipeline wall is required to calculate the heat flux into hydrogen. Therefore, we propose a solution to obtain the temperature distribution in the pipeline wall when hydrogen with lower temperature than the pipeline flows unsteadily. Based on the proposed solution, we calculate the heat flux and acquire the hydrogen temperature. The hydrogen temperatures predicted by this approach are compared with experimental data for the temperature rise of hydrogen heated through actual filling equipment, and a good agreement is shown. Thus, we show that this approach is useful for simulating the temperature rise of hydrogen flowing in the filling equipment.     

Mechanisms of thermal nanofluids on enhanced critical heat flux (CHF)

Research on thermal nanofluids has progressed rapidly since their enhanced thermal conductivities were identified about a decade ago. Thermal nanofluids have been observed to increase the critical heat flux (CHF) remarkably under pool-boiling conditions, which could not be explained by conventional theories developed for pure fluids. This paper proposes an alternative mechanism, the long-range structural disjoining pressure arising from the confinement of nanoparticles in a meniscus, and investigates its role under high heat flux conditions. The structural disjoining pressure is incorporated into a four-zoned dry patch model and an analytical model is established to calculate the equilibrium meniscus shape in the presence of nanoparticles. The results show that the structural disjoining pressure can significantly increase the wettability of the fluids and inhibit the dry patch development. Other possible mechanisms on the enhanced CHF are discussed and future studies to resolve remaining issues are recommended.     

A transient model for heterogeneous nucleation under pulse heating in pool boiling

A transient analysis on heterogeneous nucleation under pulse heating in pool boiling is developed based on changes in Gibbs free energy and availability, with temperature distributions determined from one-dimensional transient heat conduction theory. Numerical solutions are obtained for critical radius and nucleation heat fluxes under various pulse widths in different working fluids. It is found that both the critical radius and nucleation work increase with pulse width while the nucleation heat flux decreases with pulse width. To verify the proposed theory, experiments are carried out for onset of nucleation in water, alcohol and R113 under pulse heating at different pulse widths. It is found that the experimental data for nucleation heat flux at short pulse widths agree well with the proposed transient model, and those at long pulse widths approach the previous steady model. Predicted results of critical radius, nucleation heat flux and the change in availability at various pulse widths for water, alcohol and R113 are presented and compared.     

Temperature Distribution in Flux Channels with Discrete Contact Boundary Conditions

An analytical approach for the thermal behavior of two-dimensional rectangular flux channels with arbitrary boundary conditions on the source plane is presented. The boundary condition along the source plane can be a combination of the first kind boundary condition (Dirichlet or prescribed temperature) and the second kind boundary condition (Neumann or prescribed heat flux). To model the boundary conditions along the source plane, the method of least squares is used. The proposed solution is in the form of Fourier series expansion and can be applied to both symmetrical and non-symmetrical channels. This method is more general than other approaches and there is no need to use equivalent heat flux distributions to model isothermal heat sources. The general approach for obtaining the multidimensional temperature profile in flux channels and the advantages of the least-square method is discussed. The proposed solution can be used to calculate the temperature at any specified point in the flux channel. Two case studies are presented. The first case study is a flux channel with five discretely specified contact temperatures along the source plane. The second case study has both of the first kind and second kind boundary conditions on the source plane. The analytical results for both systems are compared with finite element method using a commercial software package. It is shown that the proposed approach can precisely model the temperature profile over the flux channel.     

Fully-developed heat transfer in annuli with viscous dissipation

For Newtonian concentric annular flows analytical solutions are obtained under imposed asymmetric constant wall heat fluxes as well as under imposed asymmetric constant wall temperatures, taking into account viscous dissipation and for fluid dynamic and thermally fully-developed conditions. Results for the special case of the heat flux ratio for identical wall temperatures and the critical Brinkman numbers marking changes of sign in wall heat fluxes are also derived.Equations are presented for the Nusselt numbers at the inner and outer walls, bulk temperature and normalised temperature distribution as a function of all relevant non-dimensional numbers. Given the complexity of the derived equations, simpler exact expressions are presented for the Nusselt numbers for ease of use, with their coefficients given in tables as a function of the radius ratio.