Transient conjugated heat transfer in thick walled pipes with convective boundary conditions

Transient conjugated heat transfer for laminar flow in the thermal entrance region of pipes is investigated by considering two dimensional wall and axial fluid conduction. The problem is handled for an initially isothermal, infinitely long, thick-walled and two-regional pipe for which the upstream region is insulated and solved numerically by a finite difference method for hydrodynamically developed flow with a step change in the ambient fluid temperature in the heated downstream region. A parametric study is done to analyse the effects of five defining parameters namely, wall thickness ratio, wall-to-fluid conductivity ratio, wall-to-fluid thermal diffusivity ratio, the Peclet number and the Biot number.     

Transient conjugated heat transfer in pipes involving two-dimensional wall and axial fluid conduction

This paper presents an analysis for an unsteady conjugated heat transfer problem in thermally developing laminar pipe flow, involving two-dimensional wall and fluid axial conduction. The problem is solved numerically by a finite-difference method for a thick-walled, infinitely long, two-regional pipe which is initially isothermal with a step change in the constant outside temperature of the heated downstream section. A parametric study is done to analyze the effects of four defining parameters, namely the Peclet number, wall-to-fluid thermal conductivity ratio, wall-to-fluid thermal diffusivity ratio and wall thickness to inner radius ratio. The predicted results indicate that, although the parameters affect the heat transfer characteristics at the early and intermediate periods, the time to reach the steady state does not change considerably. With the boundary conditions of the present problem, the thermal inertia of the system is mainly dependent on the flow conditions rather than on the wall characteristics.     

Numerical studies of simultaneously developing laminar flow and heat transfer in microtubes with thick wall and constant outside wall temperature

The effects of wall axial heat conduction in a conjugate heat transfer problem in simultaneously developing laminar flow and heat transfer in straight thick wall of circular tube with constant outside wall temperature are numerically investigated. The results show that the heat transfer process is most sensitive to wall-to-fluid conductivity ratio k_sf, and when k_sf ? 25 the increasing tube thickness and the decreasing k_sf could make the inner wall surface approaching the uniform heat flux condition. It turns out that the basic function of the wall axial heat conduction for the cases studied is to unify the inner wall surface heat flux.     

Experimental study and theoretical analysis of local heat transfer distribution between smooth flat surface and impinging air jet from a circular straight pipe nozzle

An experimental investigation is performed to study the effect of jet-to-plate spacing and Reynolds number on the local heat transfer distribution to normally impinging submerged circular air jet on a smooth and flat surface. A single jet from a straight circular nozzle of length-to-diameter ratio (l/d) of 83 is tested. Reynolds number based on nozzle exit condition is varied between 12,000 and 28,000 and jet-to-plate spacing between 0.5 and 8 nozzle diameters. The local heat transfer characteristics are estimated using thermal images obtained by infrared thermal imaging technique. Measurements for the static wall pressure distribution due to impinging jet at different jet-to-plate spacing are made. The local heat transfer distributions are analyzed based on theoretical predictions and experimental results of the fluid flow characteristics in the various regions of jet impingement. The heat transfer at the stagnation point is analyzed from the static wall pressure distribution. Semi-analytical solution for heat transfer in the stagnation region is obtained assuming an axisymmetric laminar boundary layer with favourable pressure gradient. The heat transfer in the wall jet region is studied considering fluid flow over a flat plate of constant heat flux. However, heat transfers in the transition region are explained from reported fluid dynamic behaviour in this region. Correlations for the local Nusselt numbers in different regions are obtained and compared with experimental results.     

Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios

Laminar convective heat transfer in the entrance region of microchannels of rectangular cross-section is investigated under circumferentially uniform wall temperature and axially uniform wall heat flux thermal boundary conditions. Three-dimensional numerical simulations were performed for laminar thermally developing flow in microchannels of different aspect ratios. Based on the temperature and heat flux distributions obtained, both the local and average Nusselt numbers are presented graphically as a function of the dimensionless axial distance and channel aspect ratio. Generalized correlations, useful for the design and optimization of microchannel heat sinks and other microfluidic devices, are proposed for predicting Nusselt numbers. The proposed correlations are compared with other conventional correlations and with available experimental data, and show very good agreement.     

HEAT TRANSFER OF SOLID–LIQUID PHASE-CHANGE MATERIAL SUSPENSIONS IN CIRCULAR PIPES: EFFECTS OF WALL CONDUCTION

This article considers the problem of conjugate heat transfer in circular pipes with finite heated length to examine the effects of wall conduction on the heat transfer characteristics of solid–liquid phase-change material suspension flow. A mixture continuum approach is adopted in the formulation of the energy equation, with an approximate enthalpy model describing the phase-change process in the phase-change material particles. From numerical simulations via the finite-volume approach, it was found that the conduction heat transfer propagating along the pipe wall results in significant preheating of the suspension flow in the nondirectly heated region upstream of the heated section, where melting of the particles may occur and therefore the contribution of the latent heat transfer to convection heat dissipation over the heated section is markedly attenuated. Contributions of the sensible and latent heat transfer to the total heat transfer rate of the suspension flow over the heated section were delineated quantitatively for various sets of the relevant dimensionless parameters, including the particle volumetric concentration, the modified Stefan number, the Peclet number of suspending fluid, the wall thickness ratio, and the wall-to-fluid thermal conductivity ratio.     

A numerical study of single-phase convective heat transfer in microtubes for slip flow

The steady-state convective heat transfer for laminar, two-dimensional, incompressible rarefied gas flow in the thermal entrance region of a tube under constant wall temperature, constant wall heat flux, and linear variation of wall temperature boundary conditions are investigated by the finite-volume finite difference scheme with slip flow and temperature jump conditions. Viscous heating is also included, and the solutions are compared with theoretical results where viscous heating has been neglected. For these three boundary conditions for a given Brinkman number, viscous effects are presented in the thermal entrance region along the channel. The effects of Knudsen and Brinkman numbers on Nusselt number are presented in graphical and tabular forms in the thermal entrance region and under fully developed conditions.     

Numerical investigation of the coupled heat transfer of liquefied gas storage tanks

It is a common situation that the liquefied gas tanks are always heated by the outer hot environments, which affecting the safety of the tanks. In this paper, numerical studies were conducted to reveal the heat transfer characteristics of this circumstance. The coupled heat transfer process among the thermal environment, the tank wall and the fluid in the tank was thoroughly investigated by simultaneously solving the temperature fields of both the solid region and the fluid region as well as the flow fields of both the liquid phase and the vapor phase inner the tank. The results showed that affected by the near wall flow and the wall boiling, the heat transfer presented different patterns in the stable thermal stratification stage and the de-stratification stage. In the stable stratification stage, the heat flux from the liquid phase wall to the medium distributed uniformly along the axial direction of the tank, while in the de-stratification stage, it differed a lot at the different positions.     

Flow characteristics and heat transfer performances of a semi-confined impinging array of jets: effect of nozzle geometry

The flow and heat transfer characteristics of confined jet array impingement with crossflow is investigated. Discrete impingement pressure measurements are used to obtain the jet orifice discharge flow coefficient. Digital particle image velocimetry (DPIV) and flow visualization are used to determine the flow characteristics. Two thermal boundary conditions at the impinging surface are presented: an isothermal surface, and a uniform heat flux, where thermocouple and thermochromic liquid crystal methods were used, respectively, to determine the local heat transfer coefficient. Two nozzle geometries are studied, circular and cusped ellipse. Based on the interaction with the jet impingement at the surface, the crossflow is shown to influence the heat transfer results. The two thermal boundary conditions differ in overall heat transfer correlation with the jet Reynolds number. Detailed velocity data show that the flow development from the cusped ellipse nozzle affects the wall region flow more than the circular nozzle, as influenced by the crossflow interactions. The overall heat transfer for the uniform heat flux boundary condition is found to increase for the cusped ellipse orifice.     

Enhancement of convection heat-transfer in a rectangular duct

Characteristics of wall-to-air heat transfer for a fully developed forced convection have been studied in a large rectangular packed duct with 160 cm heated length, 40 cm width, and for low bed equivalent diameter to particle diameter ratio. The separation distance between the top and bottom walls is 10 cm. A uniform heat flux is supplied at the top wall, while the bottom wall is insulated. Raschig rings in two and spherical packing in three sizes have been used in the air flow passage to investigate the enhancement of heat transfer due to packing. Temperature profiles for the steady and unsteady states have been measured. In modeling, the Ergun equation and energy equations are solved to calculate the temperature profile for the steady-state only. It has been found that the introduction of the packing into the air flow passage increases the wall-to-fluid heat transfer approximately three times compared with that of empty bed. This finding can enhance the rational use of energy from solar air heaters, chemical reactors, electronic cooling and many other engineering applications.     

Theoretical analysis of heat transfer in laminar pulsating flow

Pulsation effect on heat transfer in laminar incompressible flow, which led to contradictory results in previous studies, is theoretically investigated in this work starting from basic principles in an attempt to eliminate existing confusion at various levels. First, the analytical solution of the fully developed thermal and hydraulic profiles under constant wall heat flux is obtained. It eliminates the confusion resulting from a previously published erroneous solution. The physical implications of the solution are discussed. Also, a new time average heat transfer coefficient for pulsating flow is carefully defined such as to produce results that are both useful from the engineering point of view, and compliant with the energy balance. This rationally derived average is compared with intuitive averages used in the literature. New results are numerically obtained for the thermally developing region with a fully developed velocity profile. Different types of thermal boundary conditions are considered, including the effect of wall thermal inertia. The effects of Reynold and Prandtl numbers, as well as pulsation amplitude and frequency on heat transfer are investigated. The mechanism by which pulsation affects the developing region, by creating damped oscillations along the tube length of the time average Nusselt number, is explained.     

Analysis of the heat transfer in the entrance region of optimised corrugated wall channel

In this work the analysis of the heat transfer in the entrance region of a channel composed by a corrugated profile and a flat wall is presented. The laminar and incompressible flow of a Newtonian fluid is assumed inside the channel, and an uniform heat flux is imposed on the external surface of the corrugated wall. The governing equations are solved with the help of a finite-element method, and the results are compared with the heat transfer coefficient in the entrance region of a flat channel. In order to investigate the sensitivity of the convective heat transfer coefficient to the Reynolds number under laminar conditions, the analysis have been performed for different values of the flow rate. The effect on the flowfield of the of the corrugated profile amplitude is also discussed.     

理想流体对流传热问题的理论解

研究理想流体受迫对流传热和自然对流传热问题的理论解。采用流体无垂直于壁面法线方向运动(即无穿透)的条件取代黏性流体在壁面无滑移条件，解决了流体在边界上有滑移时计算对流传热系数的困难，给出了理想流体与平壁受迫对流传热、理想流体与竖直壁面自然对流传热和理想流体在管内受迫对流传热的理论解。结果表明：理想流体的对流传热与黏性流体同样存在着热边界层。在外部流动的情况下，无论受迫对流传热还是自然对流传热，对流传热系数都与流体的导热系数、密度和比热三乘积的二分之一次方成正比。在管内受迫对流的情况下，当无因次长度大于0．05时，局部Nu和界面无因次温度分布都不再变化，对于恒热流边界条件，Nu等于8，截面无因次平均温度等于2；对于恒壁温边界条件，Nu等于5．782，截面无因次平均温度等于2．316。     

A New Method for Analyzing Heat Exchangers- Matching of Temperature Field

In heat exchangers, the magnitude of Nu of each duct is influenced by the temperature field, since the ratio of heat capacity rate will influence the matching status of the temperature field between contacting ducts, the total heat transfer coefficient is related with the ratio of heat capacity rate. Considering this relationship, a new method for analyzing heat exchanger is proposed - matching of temperature field. First, for a single duct with the temperature field varying exponentially along the flow direction, its Nu is calculated. Then under the hypothesis that the thermal resistance of the wall is negligible, the matching condition was set like this: both the temperature and heat flux are equal for the hot and cold fluids at the wall, so the matching relationship of parameter that describes the temperature field of the hot and cold fluids, was obtained. Finally the relationship between the total Nu and the ratio of heat capacity rate along with the ratio of inherent thermal resistance is obtained. Compared with traditional analyzing methods, the temperature matching method can be used to get the total heat transfer coefficient directly, and also be used for optimization of heat exchanger design. For a parallel flow, the optimal ratio of heat capacity rate is reciprocal to the ratio of inherent thermal resistance, and for a counter flow, the optimal ratio of heat capacity rate is zero or infinity.     

Evaporation heat transfer characteristics of a grooved heat pipe with micro-trapezoidal grooves

A detailed mathematical model predicting the effect of contact angle on the meniscus radius, thin film profile and heat flux distribution occurring in the micro-trapezoidal grooves of a heat pipe has been presented. The model can be used to determine the maximum evaporating heat transfer rate in the evaporator including the effects of disjoining pressure and surface tension. The equation of meniscus radii calculation in the evaporator at given heat load based on the liquid wicks configuration has been put forward. The numerical results show that while the capillary limitation governs the maximum heat transport capability in a grooved heat pipe, the thin film evaporation determines the effective thermal conductivity in a grooved heat pipe. The ratio of the heat transfer through the thin film region to the total heat transfer through the wall to the vapor phase decreases when the contact angle increases. The superheat effects on the heat flux distribution in the thin film region also have been conducted and the results show that the disjoining pressure plays an important role in this region. The current investigation will result in a better understanding of thin film evaporation and its effect on the effective thermal conductivity in a grooved heat pipe.     

Parametric study of turbulent slot-jet impingement heat transfer from concave cylindrical surfaces

Numerical investigation of convective heat transfer process from concave cylindrical surfaces due to turbulent slot-jet impingement is performed. Constant heat flux condition is specified at the concave surfaces. The flow and thermal fields in the vicinity of the surfaces are computed using the RNG k–? turbulence model with a two-layer near wall treatment. Parametric studies are carried out for various jet-exit Reynolds numbers, surface curvature, and nozzle-to-surface spacing. Results presented include streamlines, isotherms, velocity and temperature profiles in the wall-jet region, and the local Nusselt number distribution on the impingement concave wall for various parameter values in the study. The results indicate that while the jet-exit Reynolds number and the surface curvature have a significant effect on the heat transfer process, it is relatively insensitive to the jet-to-target spacing. A correlation for the average Nusselt number at the concave surface as a function of the parameters considered in the study is also derived.     

Effect of viscous heating on heat transfer performance in microchannel slip flow region

Based on the superposition principle, an analytical solution for steady convective heat transfer in a two-dimensional microchannel in the slip flow region is obtained, including the effects of velocity slip and temperature jump at the wall, which are the main characteristics of flow in the slip flow region, and viscous heating effects in the calculations. The cases of constant heat flux boundary conditions and one wall as adiabatic and the other wall at constant heat flux input are studied. The solution method is verified for the cases where micro-scale effects are neglected. The effects of viscous heating on the temperature profiles and on the heat transfer performance are analyzed in detail. It is concluded that the effect of viscous heating, like an internal energy source, heats the fluid along the flow direction and severely distorts the temperature profiles. The effects of key parameters, such as the Brinkman and Knudsen numbers, on the Nusselt number, which expresses the heat transfer performance are investigated.     

The effect of heated wall thickness and materials on nucleate boiling at high heat flux

The present work is to numerically investigate the effect of heater side factors on the nucleate boiling at high heat flux, which is characterized by the existence of macrolayer. Two-region equations are proposed to study both thermo-capillary driven flow in the liquid layer and heat conduction in the solid wall. The numerical results indicate that the thermo-capillary driven flow in the macrolayer and evaporation at the vapor-liquid interface constitute a very efficient heat transfer mechanism to explain the high heat transfer coefficient of nucleate boiling heat transfer near CHF. For a very thin wall and/or wall with a poor thermal conductivity (heat side factors) are found to have significant effect on flow pattern in the liquid layer and the temperature distribution in the heated wall.     

Analysis of three-dimensional heat transfer in micro-channel heat sinks

In this study, the three-dimensional fluid flow and heat transfer in a rectangular micro-channel heat sink are analyzed numerically using water as the cooling fluid. The heat sink consists of a 1-cm² silicon wafer. The micro-channels have a width of 57 μm and a depth of 180 μm, and are separated by a 43 μm wall. A numerical code based on the finite difference method and the SIMPLE algorithm is developed to solve the governing equations. The code is carefully validated by comparing the predictions with analytical solutions and available experimental data. For the micro-channel heat sink investigated, it is found that the temperature rise along the flow direction in the solid and fluid regions can be approximated as linear. The highest temperature is encountered at the heated base surface of the heat sink immediately above the channel outlet. The heat flux and Nusselt number have much higher values near the channel inlet and vary around the channel periphery, approaching zero in the corners. Flow Reynolds number affects the length of the flow developing region. For a relatively high Reynolds number of 1400, fully developed flow may not be achieved inside the heat sink. Increasing the thermal conductivity of the solid substrate reduces the temperature at the heated base surface of the heat sink, especially near the channel outlet. Although the classical fin analysis method provides a simplified means to modeling heat transfer in micro-channel heat sinks, some key assumptions introduced in the fin method deviate significantly from the real situation, which may compromise the accuracy of this method.     

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.