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Concept# Heat transfer

Summary

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species (mass transfer in the form of advection), either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.
Heat conduction, also called diffusion, is the direct microscopic exchanges of kinetic energy of particles (such as molecules) or quasiparticles (such as lattice waves) through the boundary between two systems. When an object is at a different temperature from another body or its surroundings, heat flows so that the body and the surroundings reach the same temperature, at which point they are in ther

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Thermal conduction

Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its thermal conductivity, and is denote

Convection

Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (

Thermal conductivity

The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa.
Heat transfer occurs at a

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The course will deepen the fundamentals of heat transfer. Particular focus will be put on radiative and convective heat transfer, and computational approaches to solve complex, coupled heat transfer problems.

This course covers fundamentals of heat transfer and applications to practical problems. Emphasis will be on developing a physical and analytical understanding of conductive, convective, and radiative heat transfer.

This course covers the theoretical and practical analysis of two-phase flow and applications. Fundamental two-phase heat transfer in the form of condensation and boiling are studied in detail. Advanced topics such as microchannel two-phase flow, microfinned tubes and oil effects are also handled.

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Dynamics of nucleate boiling are strongly affected by the formation and behaviour of the microlayer, a layer of liquid underneath growing bubbles. As a result of its minute thickness, very high heat fluxes occur within the microlayer and its evaporation contributes significantly to the overall heat transfer. Microlayer formation is, however, not guaranteed and the transition from the contact-line to the microlayer regime of nucleate boiling is not fully understood. The difficulty of experimental investigation of the microlayer and the uncertainties surrounding its formation and subsequent evolution motivate the use of Direct Numerical Simulation (DNS) to model its behaviour. In this work, a computational strategy for utilising DNS to model nucleate boiling by resolving explicitly the microlayer is developed. The numerical method is based on the resolution of continuum conservation equations for incompressible two-phase flows in Cartesian and axisymmetric cylindrical coordinates. The phasic interface is tracked by means of the geometric Volume-of-Fluid (VOF) method and the algorithm is applicable both to adiabatic and volatile flows. Online, implicit coupling of the fluid and solid domains for the solution of the conjugate heat-transfer problem is included and closure models for the treatment of the interfacial heat-transfer resistance and the dynamic contact angle are introduced. A rigorous verification and validation exercise is performed to evaluate the efficacy of the numerical algorithm. Subsequently, a theoretical criterion for modelling the transition between contact-line and microlayer regimes is derived, and tested. Very good agreement is found with the reference experimental and simulation data and the predictive power of the criterion is demonstrated with the aid of DNS results. The computational procedure is then validated for simulations of nucleate boiling with resolved microlayer using relevant experimental data recently measured at the Massachusetts Institute of Technology; it is shown that the main observed growth features and surface heat-transfer characteristics are well-reproduced using the overall method. A sensitivity study of the dependence of the initial microlayer thickness on the growth conditions is performed and a universal equation describing the thickness distribution is proposed with liquid properties and bubble expansion rate being the governing parameters. Finally, the computational method is extended to coarse-mesh problems by introducing several reduced-order models and the full bubble-growth cycle from nucleation to detachment is simulated. Good agreement with reference measurements is again achieved and the experimental findings regarding the force balance during nucleate boiling are confirmed.

Multi-microchannel evaporators used for the cooling of high heat flux electronics have been of interest to both industry and academia for more than a decade. Such interest has sparked a large number of research studies on the flow boiling pressure drop and heat transfer in multi-microchannel evaporators. However, there are still several aspects that need to be addressed in order to better understand the complicated flow boiling process taking place in such micro-evaporators. Firstly, the mechanism governing flow boiling heat transfer in microchannels is arguable; secondly, the availability of fine-resolution local heat transfer data is very limited; thirdly, over-simplified heat conduction models are used in the literature to reduce such local heat transfer data; finally, rare attention has been taken on the thermal behavior of such micro-evaporators under transient status.\ Inspired by the forgoing aspects, an extensive experimental program has been conducted to study the flow boiling pressure drop and heat transfer of refrigerants in multi-microchannel evaporators under steady and transient status. For the steady-state tests, three fluids ( R245fa, R236fa and R1233zd(E)) were tested in two multi-microchannel evaporators. The silicon microchannel evaporators were 10 mm long and 10 mm wide, having 67 parallel channels, each 100 $\times$ 100 $\mu$m$^2$, separated by a fin with a thickness of 50 $\mu m$. Two types of micro-orifices (25 and 50 $\mu$m$^2$ in width) were placed at the entrance of each channel to stabilize the two-phase flow and to obtain good flow distribution. The test section backside temperatures were measured by a self-calibrated infrared (IR) camera. The operating conditions for stable flow boiling tests were: mass fluxes from 1250 to 2750 kg~m$^{-2}$s$^{-1}$, heat fluxes from 20 to 64 W cm$^{-2}$, inlet subcoolings of 5.5, 10 and 15 K, and nominal outlet saturation temperatures of 31.5, 35 and 40 $^{\circ}\mathrm{C}$. The resulting maximum exit vapor quality at the outlet manifold was 0.51. \ The steady-state experimental data were reduced by solving a 3D inverse heat conduction problem to obtain the local heat transfer coefficients on a pixel-by-pixel basis. The required fluid temperature in the subcooled region was calculated from the local energy balance, while that in the saturated flow boiling region came from the general pressure drop model proposed in this manuscript based on the present data base. According to the present data base of fine-resolution local heat transfer coefficients, a new flow pattern based prediction model was developed here starting from the subcooled region all the way through the annular flow regime. This new flow pattern based model predicted the total local heat transfer database (1,941,538 local points) well with a MAE of 14.2% and with 90.1% of the data predicted within $\pm$30%. It successfully tracks the experimental trends without any jumps in predictions when changing flow patterns.\ For the transient tests, an extensive experimental study was conducted to investigate the base temperature response of multi-microchannel evaporators under transient heat loads, including cold startups and periodic step variations in heat flux using two different test sections and two coolants (R236fa and R245fa) for a wide variety of test conditions. In addition, a transient flow boiling test under a heat flux disturbance was performed, and a new method of solving the transient 3D inverse heat conduction problem was proposed to obtain the local transient flow boiling heat transfer coefficients.

Tom Saenen, John Richard Thome

A fully dynamic model of a microchannel evaporator is presented. The aim of the model is to study the highly dynamic parallel channel instabilities that occur in these evaporators in more detail. The numerical solver for the model is custom-built and the majority of the paper is focused on detailing the various aspects of this solver. The one-dimensional homogeneous two-phase flow conservation equations are solved to simulate the flow. The full three-dimensional (3D) conduction domain of the evaporator is also dynamically resolved. This allows for the correct simulation of the complex hydraulic and thermal interactions between the microchannels that give rise to the parallel channel instabilities. The model uses state-of-the-art correlations to calculate the frictional pressure losses and heat transfer in the microchannels. In addition, a model for inlet restrictions is also included to simulate the stabilizing effect of these components. In the final part of the paper, validation results of the model are presented, in which the stability results of the model are compared with the existing experimental data from the literature. Next, a parametric study is performed focusing on the stabilizing effects of the solid substrate properties. It is found that increasing the thermal conductivity and thickness of the solid substrate has a strong stabilizing effect, while increasing the number of microchannels has a small destabilizing effect. Finally, representative dynamic results are also given to demonstrate some of the unique capabilities of the model.