Transient Conjugate Heat Transfer Research Articles

A high order time-accurate loosely-coupled solution algorithm for unsteady conjugate heat transfer problems

Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Noting that time-accurate computations of transient CHT problems can be computationally expensive, we consider the use of high order implicit time integration schemes which have the potential to be computationally more efficient relative to the commonly used second order implicit schemes. For thermally weak couplings, we present a loosely-coupled solution algorithm where high order implicit–explicit (IMEX) Runge–Kutta schemes are employed for time integration. The IMEX schemes consist of the explicit first-stage singly diagonally implicit Runge–Kutta (ESDIRK) schemes, for advancing the solution in time within each separate fluid and solid subdomain, and the explicit Runge–Kutta (ERK) schemes, for explicit integration of part of the coupling terms. By considering a numerical example (an unsteady conjugate natural convection in an enclosure), temporal order preservation of the coupling algorithm (without subiterating) is demonstrated. In addition, the stability of the loosely-coupled algorithm is investigated numerically for the CHT test-case; when the ratio of the thermal effusivities of the fluid and solid subdomains is much smaller than unity, using large Fourier numbers of the subdomains is possible, indicating that time-step size is restricted by accuracy rather than stability. Furthermore, the (computational) work-(temporal) precision character of several time integration schemes in solving the CHT test-case is compared over a range of accuracy requirements; for time-accurate solutions, the fourth and fifth order IMEX schemes are 1.5 times more efficient than Crank–Nicolson and 2.7 times more efficient than BDF2. The computational gain is higher for smaller tolerances.

Transient Free Convective Conjugate Heat Transfer from a Vertical Slender Hollow Cylinder

A numerical study has been carried out for the conjugate heat transfer on unsteady natural convection boundary layer flow of a viscous incompressible fluid over a vertical slender hollow cylinder. A Crank-Nicolson type of implicit method is used to solve the governing unsteady, non-linear and coupled equations. The resulting system of equations are solved by using the Thomas algorithm. The computations are carried out for different values of Prandtl number Pr and conjugate-conduction parameter P.

마이크로채널 기판에서 비정상 복합 열전달의 수치적 연구

A numerical study of transient conjugate heat transfer on micro heater in a micro-channel substrate under pulsed heating was conducted. It was found that the time constant is not affected by the pulse heating magnitude at same operating condition. Furthermore, the time constant increases with low substrate thermal diffusivity, low Reynolds number, and large channel diameter. Since the time constant is a dominant parameter to characterize transient heat transfer, it should be considered for transient convective heat transfer coefficient.

Fluid flow and heat transfer in a latent thermal energy unit with different phase change material (PCM) cavity volume fractions

Abstract In present work, the effects of different cavity volume fractions of phase change material (PCM) on fluid flow and heat transfer behavior in a latent thermal unit are studied numerically. The commercial Computational Fluid Dynamics (CFD) package, Fluent, is used for the numerical solution based on transient conjugate heat transfer. The numerical results have been verified and validated against numerical and experimental data available in published literature. The volume expansion ratio, the time of complete thermal storage, heat flux, liquid fraction, velocity and temperature fields are investigated for the range of PCM cavity volume fractions ( ϕ max ) from 35% to 95%. It is noted that a vortex (as a heat transfer enhancer) is present near the heating plate wall for the PCM cavity volume equal to 85%. It is found that the volume expansion ratio decreases as ϕ max increasing, whereas the time for complete energy storage increases. Further, the correlations of the volume expansion ratio and the time of complete thermal storage are developed as a function of ϕ max. The detailed knowledge regarding interface heat transfer rate provides a deeper understanding the heat transfer mechanisms.

A Simplified Model with a Hybrid Analytical-Numerical Solution for Predicting the Unsteady Conjugate Heat Transfer Process in Pipelines

This work presents a new, simplified and yet efficient model for studying the transient conjugate heat transfer process in pipelines. The simplified model consists of assuming the thermal transport by fluid flow in bulk form and the pipe–wall heat conduction as two-dimensional. The scale analysis of the dimensionless equations resulting from the simplified model allows for the identification of two predicting parameters useful in determining when axial diffusion in the pipe wall is important, ψ = Pe Γ/ξ < 1 and λ = 4 Nu E 2/ξ < 1, and when radial diffusion is important, ψ > 1 and λ > 1. When these criteria are satisfied, in which case the existing analytical solution becomes invalid, the simplified model proposed here becomes an efficient alternative to the full-scale numerical simulations required for solving the problem. The scale analysis predictions and the hybrid analytical-numerical solutions of the simplified model, involving the Laplace transform and the finite-volume method, are validated first by comparison against the existing analytical solution, and then by comparison against experimental results of turbulent flow, showing excellent agreement in both cases.

Transient conjugate heat transfer from a hemispherical plate during free liquid jet impingement on the convex surface

This paper considers the analysis of transient heating of a hemispherical solid plate of finite thickness during impingement of a free liquid jet. A constant heat flux was imposed at the inner surface of the hemispherical plate at t = 0 and heat transfer was monitored for the entire duration of the transient until a steady state condition was reached. Calculations were done for Reynolds number (Re) ranging from 500 to 1,500 and dimensionless plate thicknesses to nozzle diameter ratio (b/d n) from 0.083 to 1.5. Results are presented for local and average Nusselt number using water as the coolant and various solid materials such as silicon, constantan, and copper. It was detected that increasing the Reynolds number decreases the time for the plate to achieve the steady-state condition. Also, a higher Reynolds number increases the Nusselt number. Hemispherical plate materials with higher thermal conductivity maintain lower temperature non-uniformity at the solid–fluid interface. Increasing the plate thickness decreases the maximum temperature in the solid and increases the time to reach the steady-state condition.

Unsteady conjugated heat transfer in thick walled pipes involving two-dimensional wall and axial fluid conduction with uniform heat flux boundary condition

Transient conjugated heat transfer in thick walled pipes for thermally developing laminar flow is investigated involving two-dimensional wall and axial fluid conduction. The problem is solved numerically by a finite-difference method for hydrodynamically developed flow in a two-regional pipe, initially isothermal in which the upstream region is insulated and the downstream region is subjected to a suddenly applied uniform heat flux. A parametric study is done to analyze the effects of four defining parameters namely, wall thickness ratio, wall-to-fluid thermal conductivity ratio, wall-to-fluid thermal diffusivity ratio and the Peclet number. The results are given by non-dimensional interfacial heat flux values, and it is observed that, heat transfer characteristics are strongly dependent on the parameter values.

Numerical Simulation of Transient Thermal Transport on a Rotating Disk Under Partially Confined Laminar Liquid Jet Impingement

Abstract This paper considers the transient conjugate heat transfer characterization of a partially confined liquid jet impinging on a rotating and uniformly heated solid disk of finite thickness and radius. A constant heat flux was imposed at the bottom surface of the solid disk at t=0, and heat transfer was monitored for the entire duration of the transient until the steady state condition was reached. Calculations were done for a number of disk materials using water as the coolant, covering a range of Reynolds numbers (225–900), Ekman numbers (7.08×10−5−∞), nozzle-to-target spacing (β=0.25–1.0), confinement ratios (rp/rd=0.2–0.75), disk thicknesses to nozzle diameter ratios (b/dn=0.25–1.67), and solid to fluid thermal conductivity ratios (36.91–697.56). It was found that a higher Reynolds number decreases the time to achieve the steady state condition and increases the local and average Nusselt number. The duration of the transient increases with the increment of the Ekman number and disk thickness, and the reduction in the thermal diffusivity of the disk material.

Transient behavior of vascularized walls exposed to sudden heating

Vascular flow architectures are proposed for controlling the temperature of walls that are subjected suddenly to intense heating from one side. After a short delay, single-phase coolant starts flowing from the other side, and fights off the heating effect. The time-dependent behavior of such vascularized composites is studied and optimized based on full numerical simulations of transient conjugate heat transfer. The focus is on the hot-spot temperatures that build up inside the composite – their evolution, spatial migration, and highest levels. Of interest are vasculature designs that keep the hot-spot temperatures below the safe level associated with long-term operation with steady heating from one side and steady coolant flow from the other side. It is shown that when the driving pressure difference is fixed, the approach to the steady-state temperature is the shortest when the dendrites have an optimal (finite) number of bifurcation levels. The allowable delay time is approximately the same as the duration that the hot-spot temperature reaches the steady-state hot-spot temperature in the absence of coolant.

3-D Transient conjugated heat transfer and fluid flow analysis for the cooling process of sintered bed

Three-dimensional turbulent, transient fluid flow and heat transfer analysis over a sintered bed during a cooling process are studied numerically and experimentally. The sintered bed is modeled as a packed 4-row bed of spheres and the conjugated convective heat transfer in the flow field and heat conduction in the spheres are considered also. The effects of two different porosity ( Φ = 0.4, 0.5) and three different particle sphere diameters ( D = 50 mm, 70 mm and 100 mm) are investigated in detail for the Reynolds number ranging from 1300 to 11,000. It is shown that, the smaller the particle diameter or porosity, the greater the Nusselt number and friction factor are. The numerical results are in good agreement within 15–20% with the experimental data. The correlation equations for the steady-state average mean Nusselt number and friction factor f are obtained as: Nu = 1 ϕ 8.75 + 0.013 Re 0.896 f = 2.3 Φ Re - 0.306 These correlations are accurate within 7% for 0.4 ⩽ Φ ⩽ 0.5 and 1300 ⩽ Re ⩽ 11000.

Transient Conjugate Heat Transfer During Free Liquid Jet Impingement on a Rotating Solid Disk

This article presents the transient conjugate heat transfer characterization of a free liquid jet impinging on a rotating solid disk of finite thickness and radius. Calculations were done for a range of Reynolds number (500–1400), Ekman number (6.62 × 10−5–∞), disk thicknesses to nozzle diameter ratio (0.17–1.67), and solid to fluid thermal conductivity ratio (36.91–697.56) using water as the coolant. It was detected that the duration of the transient increased with disk thickness and decreased with Reynolds number and thermal conductivity ratio. A correlation for average Nusselt number for the transient heat transfer is presented.

A posteriori error analysis for a transient conjugate heat transfer problem

We consider the accuracy of an operator decomposition finite element method for a transient conjugate heat transfer problem consisting of two materials coupled through a common boundary. We derive accurate a posteriori error estimates that account for the transfer of error between components of the operator decomposition method as well as the errors in solving the iterative system. We address a loss of order of convergence that results from the decomposition, and show that the order of convergence is limited by the accuracy of the transferred gradient information. We extend a boundary flux recovery method to transient problems and use it to regain the expected order of accuracy in an efficient manner. In addition, we use the a posteriori error estimates to adaptively compute the recovered boundary flux only within the domain of dependence for a quantity of interest.

Steady and transient thermo-hydraulic performance of disc with tree-shaped micro-channel networks with and without radial inclination

Steady and transient conjugate heat transfer and fluid flow through tree-shaped radially branching micro-channel networks, embedded in a disk-shaped heat sink, are investigated using numerical simulations. The typical dimensions of the disk are taken as 20 mm radius and 2 mm thickness while the hydraulic diameters of the micro-channel network are in the range of 0.67–0.44 mm, with a constant 0.5 mm height. In steady state, increased levels of complexity of the tree network result in more uniform temperature distribution in the disc ( T ¯ max → T ¯ avg ). However the degree of reduction in temperature reduces for higher complexity. Using the steady state result for minimal flow resistance that yields minimal thermal resistance for heat transfer, the transient response of the disk with differing levels of tree complexities is shown to behave more uniformly under similar imposed heat transfer load. The effect of radial inclination of the flow tree channels on the overall pressure drop of the coolant flow and the disk temperature distribution is also investigated. By allowing 0.1 mm radial inclination to the channel network shows 45 percent reduction in pressure drop for the first level of branching complexity ( k = 1 , n = 3 ) and 25 percent for the highest level ( k = 4 , n = 3 ) as compared to the corresponding planar channel.

Thermal-performance evaluation of coolant passages with staggered arrays of pin fins

Three-dimensional laminar forced convection including steady-periodic transition is investigated up to periodic-chaotic transition in the fully developed region of coolant passages with staggered arrays of pin fins. Comparative examples concern overall pressure losses and heat transfer characteristics of circular, square and elliptical pins made of nickel and copper. In the numerical model, transient conjugate heat transfer is assumed and space periodicities in pressure, velocity components and temperatures are taken into account. In the range of operative conditions investigated, overall friction factors increase almost linearly with the Reynolds number, while the increase of overall Nusselt numbers with the Reynolds number is characterized by two slope changes connected with the onset of streamwise vortices, and the shedding of transverse vortices, respectively. The use of copper, instead of nickel, increases the overall Nusselt number with all shapes, but is particularly beneficial to the elliptical section. Square pins are characterized by the highest values of friction factors, but are also the best performers as far as convection enhancing is concerned. The reverse is true for the elliptical pins which are characterized by the lowest values of friction factors, but are the worst performers as far as convection enhancing is concerned. On the basis of overall performances, the elliptical pins made of copper are the best choice, at least in the upper range of Reynolds numbers investigated.

Comparison of Whole-Domain and Sequential Algorithms for Function Specification Method in the Inverse Heat Transfer Problem of Laminar Convective Pipe Flow

This article compares the application of the whole-domain function specification method (WDFSM) and the sequential function specification method (SFSM) to the inverse problem of transient conjugate heat transfer of laminar forced convection in a circular pipe. The two inverse methods are used to estimate the time-varying inlet temperature and the outer-wall heat flux simultaneously on the basis of temperature measurements taken at two different locations within the pipe flow. The numerical results reveal that the estimations obtained from the WDFSM method are marginally better than those obtained from the SFSM approach.

Numerical study of transient conjugate heat transfer of a turbulent impinging jet

This study presents the numerical study of transient conjugate heat transfer in a high turbulence air jet impinging over a flat circular disk. The numerical simulation of transient, two-dimensional cylindrical coordinate, turbulent flow and heat transfer is adopted to test the accuracy of the theoretical model. The turbulent governing equations are resolved by the control-volume based finite-difference method with a power-low scheme, and the well-known low- Re κ– ω turbulence model to describe the turbulent structure. The SIMPLE algorithm is adopted to solve the pressure–velocity coupling. The parameters studied include turbulent flow Reynolds number ( Re = 16,100–29,600), heated temperature of a circular disk ( T h = 373 K) or heat flux ( q″ = 63–189 kW/m 2), and orifice to heat-source spacing ( H/ D = 4–10). The numerical results of the transient impinging process indicate that the jet Reynolds number has a significant effect on the hydrodynamics and heat transfer, particularly in the stagnation region of an impinging jet. High turbulence values lead to greater heat transfer coefficients in the stagnation region and cause a bypass of the laminar-to-turbulent transition region in the wall jet region. Induced turbulence from the environment around the jet also influences the variation of the stagnation heat transfer. The modeling approach used here effectively captures both the stagnation region behavior and the transition to turbulence, thus forming the basis of a reliable turbulence model.

Prediction of electronic component-board transient conjugate heat transfer

Numerical analysis of electronic component transient heat transfer has generally been confined to nonconjugate methods. This study discusses the need for conjugate (conduction/convection) analysis, both for component temperature and thermo-mechanical behavior prediction in operational, assembly and reliability qualification environments. The capability of computational fluid dynamics (CFD) analysis to predict component transient conjugate heat transfer is investigated using an industry-standard CFD code for the thermal analysis of electronics. The test cases are based on a single board-mounted, 160-lead plastic quad flat pack (PQFP) component, subjected to dynamic power- and air temperature conditions, in still-air and forced airflows. Benchmark criteria are based on component junction temperature and component-printed circuit board (PCB) surface temperature, measured using thermal test dies and infrared thermography respectively. Using both nominal component/PCB geometry dimensions and material properties, component junction temperature is found to be accurately predicted. The results suggest that CFD analysis could play an important role in providing critical boundary conditions for component electrical performance and thermo-mechanical behavior analyses, optimizing accelerated life test (ALT) parameters and convective assembly processes.

05/01319 Numerical solutions of transient conjugate heat transfer and thermally induced stress distribution in a heated and rotating hollow disk

05/01319 Numerical solutions of transient conjugate heat transfer and thermally induced stress distribution in a heated and rotating hollow disk

Numerical analysis of the transient conjugated heat transfer in a circular duct with a power-law fluid

We treat numerically in this paper, the tran- sient analysis of a conjugated heat transfer process in the thermal entrance region of a circular tube with a fully developed laminar power-law fluid flow. We apply the quasi-steady approximation for the power-law fluid, identifying the suitable time scales of the process. Thus, the energy equation in the fluids is solved analytically using the well-known integral boundary layer technique. This solution is coupled to the transient energy equation for the solid where the transverse and longitudinal heat conduction effects are taken into account. The numerical results for the temporal evolution of the average tem- perature of the tube wall, hav, is plotted for different nondimensional parameters such as conduction param- eter, a, the aspect ratios of the tube, e and e0 and the index of power-law fluid, n.

Numerical solutions of transient conjugate heat transfer and thermally induced stress distribution in a heated and rotating hollow disk

Numerical solutions of transient conjugate heat transfer and thermally induced stress distribution in a heated and rotating hollow disk