Transient Conjugate Heat Transfer Research Articles

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.

Flow through a protruding bluff body–heat and irreversibility analysis

Flow over a protruding bluff body finds wide application in many engineering fields. The modeling of the conjugate heating process due to bluff body gives insight into the physical process involved and minimizes the experimental cost. In the present study, the transient conjugate heat transfer analysis of the bluff body subjected to low Reynolds number flow is considered. The governing flow and energy equations are solved numerically using a control volume approach. The heat transfer characteristics are examined through the normalized Stanton number. The entropy generation due to fluid friction and heat transfer in the fluid system is computed and ratio of rate of heat transfer to irreversibility generated is obtained. It is found that the heat transfer in the region of top and bottom edges of the bluff body is enhanced due to the convection effect. The heat transfer to irreversibility ratio decreases sharply as the heating progresses.

Analysis of Transient Conjugate Heat Transfer to a Free Impinging Jet

Transient conjugate heat transfer during the impingement of a freejet of high Prandtl number e uid on a solid disk of e nite thickness is considered. When power is turned on at t =0, a uniform heat e ux is imposed on the disk surface. The numerical model considers both solid and e uid regions. Equations for the conservation of mass, momentum,andenergy aresolvedintheliquidregion,withthetransportprocessesattheinletand exitboundaries, as well as at the solid ‐liquid and liquid ‐gas interfaces taken into account. In the solid region, only heat conduction equation is solved. The shape and location of the free surface (liquid‐gas interface ) is determined iteratively as a part of the solution process by satisfying the kinematic condition as well as the balance of normal and shear forces at this interface. Computed results include the velocity, temperature, and pressure distributions in the e uid and the local and average heat transfer coefe cients at the solid ‐e uid interface. Computations are carried out to investigate the ine uence of different operating parameters such as jet velocity, disk thickness, and disk material. Nomenclature b = thickness of the disk, m cp = specie c heat at constant pressure, kJ/kg ¢ K dn = diameter of the nozzle, m Fo = Fourier number, a ft/d 2 n g = acceleration due to gravity, m/s 2 Hn = distance of the nozzle from the disk, m h = heat transfer coefe cient, qint/(Tint i Tj), W/m 2 ¢ K hav = heat transfer coefe cient, W/m 2 ¢ K:

Coupled Dual Reciprocity Boundary Element/Finite Volume Method for Transient Conjugate Heat Transfer

A coupled finite volume/dual reciprocity boundary element method is developed to solve the transient conjugate heat transfer problem of convective heat transfer over and conduction heat transfer within a solid body. In this approach, the flowfield and forced convection heat transfer external to the body is resolved by numerically solving the time-dependent Navier-Stokes equations using a finite volume method, whereas the temperature field within the body is resolved by numerically solving the heat conduction equation using a dual reciprocity boundary element method. The boundary discretization utilized to generate the computational grid for the external flowfield provides the boundary discretization required for the boundary element method. Coupling of the two fields is accomplished by enforcing Interface continuity of heat flux and temperature. Transient heat transfer data needed to verify the code were obtained in a series of experiments that are reported. Details of the experimental setup and test conditions are provided

Transient Conjugate Heat Transfer During Flashing of Liquids in Pipes

In this article, transient conjugate heat transfer during the flashing of liquids in pipes is examined. A numerical model is formulated to simulate a blowdown of a pipeline produced by a partial rupture of a pipe. The model is based on the approach to the description of conjugate two-phase heat transfer proposed in an earlier study by the author. The effect of the area of the rupture on the wall-to-fluid heat transfer is studied. The range of applicability of the novel formulation of energy equation is determined. The use of a new fundamental dimensionless number governing the effect of conjugate heat transfer on flow behavior is shown. This parameter can be very useful for solving the problem of transient flashing liquid flow in pipes.

Transient Conjugate Heat Transfer During Flashing of Liquids in Pipes

Transient Conjugate Heat Transfer During Flashing of Liquids in Pipes

Transient conjugate heat transfer in a porous medium in concentric annuli

Transient conjugated forced convection in the thermal entry region of a thick‐walled annulus, filled with a homogeneous and isotropic porous medium, has been numerically investigated using finite‐difference techniques. Non‐Darcian effects as well as axial conduction of heat have been considered. The flow is assumed to be hydrodynamically fully developed and steady but thermally developing and transient. The thermal transient is initiated by a step change in the prescribed isothermal temperature on the outer surface of the external tube of the annulus while the inner surface of the internal tube is kept adiabatic. A parametric study is carried out to explore the effects of the Darcy number, the inertia term, the Peclet number and the porous medium heat capacity ratio on the transient thermal behavior in a given annulus.

Theoretical study of periodic turbulent forced convection inside a parallel-plate channel

This study analyses the transient conjugated heat transfer in turbulent duct flow, subjected to sinusoidally varying inlet temperature. A boundary condition accounts for the effects of external convection. Wall thermal capacitance and transverse heat conduction in the wall are considered. The results obtained with a usual turbulent model which introduces the thermal eddy diffusivity together with the velocity profiles are compared with the elementary quasi-steady approach which employs a classical heat transfer coefficient at interface liquid–solid. It is concluded that for the smaller values of inlet frequency, the quasi-steady approach is able to predict the temperature behaviour inside the channel, but for higher frequencies this model becomes inadequate.

Unsteady conjugate heat transfer for a single particle and in multi-particle systems at low Reynolds numbers

Two cases of the transient conjugate heat transfer in fluid-particle systems are analysed. The first refers to the single rigid spherical particle at particle Reynolds numbers greater than one. The subject of the second is the assemblages of rigid spherical particles at low particle Reynolds numbers, i.e. Re ⩽ 20. In this case the classical cell models are used to describe the hydrodynamics. In both cases the momentum and the heat balance equations are solved numerically. The velocity field is assumed to be steady, axisymmetric and laminar. The finite difference methods are used for discretization. The single particle problem is solved for Re = 10 (50), Pe = 100.0, and a wide domain of variation of the conductivity and volume heat capacity ratios. Simulation results reveal that the conductivity and heat capacity ratios affect the heat transfer remarkably. For the particle assemblages, the analysis is focused on the specific problems of the interphase heat transfer in packed beds at low Peclet numbers. The results show that the theoretical predictions of the unsteady conjugate heat transfer in cell models are not a good description of the packed bed experimental data.

Transient Response of Microchannel Heat Sinks in a Silicon Wafer

The transient conjugated heat transfer in forced convection for simultaneously developing laminar flow inside a microchannel heat sink is studied by solving the steady momentum equation and the transient energy equation. A parametric study is performed to understand the effects of channel depth and width, Reynolds number, spacing between channels, and solid to fluid thermal conductivity ratio. Silicon as well as indium phosphide are used as wafer’s material. Step and pulsed variations of the heat load are analyzed. Results show that the time required for the heat transfer to reach steady state condition is longer for the system with larger channel depth or spacing and smaller channel width or Reynolds number. Characteristic results for the fluid mean temperature at the exit, solid maximum temperature, local Nusselt number, and local heat flux are presented graphically as functions of position and time.

Transient conjugate heat transfer on a naturally cooled body of arbitrary shape

Transient conjugate heat transfer relating the heat conduction inside a solid body of arbitrary shape and the natural convection around the solid is studied in the present investigation. A single set of governing equations covering both solid and fluid is solved by using the weighting function scheme along with the NAPPLE algorithm and the SIS solver. All of the computations are performed on a Cartesian grid system. Numerical results of velocities and isotherms are presented for Pr = 7 and Gr = 10 7 and 10 8 . An interesting observation on formation, growth, merging and decay of several plumes is discussed. The solution shows that there is a dead fluid inside the cavity under the solid body due to an upward temperature gradient. The maximum temperature thus occurs there in a late stage of the heat transfer process. An increase in the Grashof number is found to enhance the heat transfer. Through this study, the present numerical method is shown to have a good performance for conjugate heat transfer on solid body of arbitrary shape without the need of a body-fitted grid system.

Asymptotic Analysis of the Transient Conjugate Heat Transfer Process Between Two Forced Counterflowing Streams

In this paper we analyze the transient conjugate heat transfer process between two counterflowing forced streams separated by a wall with finite thermal conductivity. The influence of the longitudinal heat conduction through the wall on the overall heat transfer rates is very important and has been analytically deduced. We present a classification of the solutions of the problem in terms of two main parameters: $\varepsilon $, the ratio of thickness to the height of the wall, which is small in our analysis, and $\alpha $, measuring the ratio of the thermal resistance of one of the boundary layers to the thermal resistance of the wall. Conditions under which longitudinal conduction and transversal temperature variations are important in the solid are clarified. In the asymptotic limit $\alpha \rightarrow \infty $ and using the Lighthill approximation, it can be shown that the balance equations reduce to a single integrodifferential equation with only the parameters $\alpha $, $\beta $, where $\beta $ relat...

Unsteady conjugated heat transfer in turbulent channel flows with convection from the ambient

A numerical study is carried out to investigate the transient conjugated heat transfer in turbulent channel flows with convection from the ambient. The solutions take wall conduction and heat capacity effects into consideration. Major nondimensional groups identified in this work are the wall-to-fluid conductivity ratio K, the wall-to-fluid thermal diffusivity ratio A, the dimensionless wall thickness β, the Reynolds number Re, the Prandtl number Pr, the outside Nusselt number Nu o and the dimensionless cooling length L. The influences of wall material, β, Pr, Re and Nu o on the interfacial heat flux, outer wall temperature and interfacial temperature are examined in detail. Results show that wall conduction plays a significant role in the transient conjugated heat transfer problem. In addition, the time required for heat transfer to reach the steady state condition is longer for systems with a larger β or smaller A, Re and Nu o.

Transient conjugated heat transfer in concentric annuli

The paper presents a finite‐difference scheme to solve the transient conjugated heat transfer problem in a concentric annulus with simultaneously developing hydrodynamic and thermal boundary layers. The annular forced flow is laminar with constant physical properties. Thermal transient is initiated by a step change in the prescribed isothermal temperature of the inner surface of the inside tube wall while the outer surface of the external tube is kept adiabatic. The effects of solid‐fluid conductivity ratio and diffusivity ratio on the thermal behaviour of the flow have been investigated. Numerical results are presented for a fluid of Pr = 0.7 flowing in an annulus of radius ratio 0.5 with various values of inner and outer solid wall thicknesses.

Conjugate heat transfer during falling film evaporation

An analytical solution is derived for a transient conjugate heat transfer problem in three domains: a solid wall, an evaporating falling liquid film, and a flowing gas. The physical model comprises a vertical wall, heated on one side by radiation and convection and cooled on its other side by two fluids: a falling water film at the top and by rising air from below. At a certain location along the wall the initially subcooled water film becomes saturated due to heat absorption from the wall. The water film then evaporates and eventually dries out completely further downstream, thus forming two moving fronts at the saturation and dryout lines. Making some simplifying assumptions, the problem is formulated as a set of 1-D time dependent equations. Combining the wall and coolant equations leads to a unified hyperbolic type equation, which is solved by employing Riemann's method. The present analysis is applied to assess the performance of a containment cooling system of an advanced nuclear reactor.

Transient Conjugated Heat Transfer Analysis from a Sphere with Nonlinear Boundary Conditions

The problem of conjugate unsteady convective and radiative heat transfer from a solid spherical particle is numerically investigated for Reynolds numbers up to 100 using a Chebyshev-Legendre spectral method. The treatment of nonlinear boundary condition of the radiation heat transfer from the sphere surface is assessed and successfully implemented. This work is an extension of the previous effort of simulating flow around a sphere using spectral method to include heat transfer. The assumption of quasi-steady flow field for the unsteady heat transfer calculation is compared with the fully transient treatment of both the flow and the temperature fields. It is found that the quasi-steady assumption underestimates the overall heat transfer rate at very early time stages (up to 9% underestimation for the mean Nusselt number). However, the discrepancy becomes smaller as time elapses. The underprediction of the quasi-steady assumption becomes larger as the Reynolds number increases for a fixed Prandtl number. The results for different alternate radiation-conduction number cases are presented.

Transient conjugate heat transfer between a laminar stagnation zone and a solid disk

An explicit finite difference technique is used to solve the case of transient, forced convective conjugate heat transfer between an axisymmetric incompressible laminar impinging jet and a solid disk. The solution to the governing equations is based on the assumptions of constant physical properties and no viscous dissipation. The hydrodynamics of the flow are considered to be steady state, whereas thermal transients take place with a step temperature change at the jet upstream boundary condition. The unexposed bottom surface of the disk is treated as an isothermal boundary, and the radial boundary of the disk is modeled as adiabatic. In this work, the effect of the ratios of thermal conductivity and thermal diffusivity between fluid and solid on transient heat transfer characteristics of the system have been investigated.

Transient conjugated heat transfer analysis from a sphere

The phenomena of conjugate unsteady heat transfer from a solid spherical particle in a convective environment is numerically investigated for Reynolds numbers in the range from 0.1 to 100. The flow and energy equations for both dispersed and continuous phases are solved using a Chebyshev-Legendre spectral method. This work is an extension of the previous effort of simulating flow around a sphere using spectral method [2] to include heat transfer. General findings indicate that quasi-steady analysis underestimates the overall heat transfer rate significantly at very early time stages, however the extent of underprediction becomes less as time progresses. The underprediction of the quasi-steady assumption becomes larger as Reynolds number increases for a fixed Prandtl number.

Transient Conjugated Heat Transfer in Developing Laminar Pipe Flow

Transient Conjugated Heat Transfer in Developing Laminar Pipe Flow