Axial Heat Conduction Research Articles

Effects of major parameters on micro-combustion for thermophotovoltaic energy conversion

For a micro-thermophotovoltaic (TPV) energy conversion device, high surface to volume ratio in the micro-combustor provides a great potential to achieve high surface radiation power output per unit energy input. This work investigated experimentally the effects of three major parameters on micro-combustion, namely hydrogen to oxygen mixing ratio, nozzle to combustor diameter ratio, and wall thickness to combustor diameter ratio. The results show that the high average wall temperature can be achieved at slightly oxygen rich mixing ratios. Nozzle to combustor diameter ratio affects both the magnitude and uniformity of wall temperature distribution. The newly designed thin wall combustor which yields a reduction of axial heat conduction loss is able to increase wall temperature more than 150 K. Optimized design of these parameters will have significant impact on the enhancement of radiation heat output in micro-TPV energy conversion.

Forced convection with viscous dissipation in the thermal entrance region of a circular duct with prescribed wall heat flux

The thermal entrance forced convection in a circular duct with a prescribed wall heat flux distribution is studied under the assumptions of a fully developed laminar flow and of a negligible axial heat conduction in the fluid, by taking into account the effect of viscous dissipation. The solution of the local energy balance equation is obtained analytically by employing the Laplace transform method. The effect of viscous dissipation is taken into account also in the region upstream of the entrance cross-section, by assuming an adiabatic preparation of the fluid. The latter hypothesis implies that the initial condition in the entrance cross-section is a non-uniform radial temperature distribution. Two special cases are investigated in detail: an axially uniform wall heat flux, a wall heat flux varying linearly in the axial direction.

Thermal analysis of bicomponent fibres

A one-dimensional model of amorphous bicomponent spun fibres derived from the use of perturbation methods based on the slenderness ratio is presented. The model accounts for gravitational, surface tension, axial heat conduction, viscous dissipation and the nonlinear dependence of the dynamic viscosity law on temperature, but does not consider latent heat effects and the radial gradients of temperature and assumes Newtonian rheology. Studies on the effects of the thermal parameters on the compound fibre’s geometry and solidification have been performed, and show that the activation energy of the dynamic viscosity laws have a paramount effect on the fibre’s cooling, shape, and axial stresses on the core and sheath. In particular, it is shown that, when the activation energy of the viscosity law for the core is higher than that for the sheath, the axial stresses on the core are monotonic functions of the distance along the fibre and higher than those on the sheath, whereas those in the latter may exhibit a nonmonotonic behavior as functions of the thermal conductivity, heat losses and thermal inertia. Despite its limitations, the model presented here represents an improvement over available one-dimensional models for non-isothermal compound or bicomponent fibres.

Experimental study on axial wall heat conduction for convective heat transfer in stainless steel microtube

Distilled water and nitrogen gas used as the working fluids flow through the stainless steel microtube with inner diameter 168 μm outer diameter 406 μm. Using the Joule heating, the wall temperature field photos of the microtube is acquired by employing an IR camera and the temperature and the volume flow rate of the inlet and the outlet of microtube are measured. A correlation between the axial wall heat conduction and the convective heat transfer is obtained by theoretical analysis based on the experimental results. The investigative results clearly show that the axial heat conduction can reduce the convective heat transfer in the stainless steel microtube and the decrement may reach 2% compared to the convective heat transfer when the working fluid is nitrogen gas, however, the decrement can be neglected for distilled water as the working fluid.

Transient heat conduction from a vertical rod buried in a semi-infinite medium with variable heating strength

In this paper, a variable heating strength model (VHS model) is developed to predict transient heat conduction from a vertical rod buried in a semi-infinite medium. Unlike past studies, the current VHS model permits a VHS along the rod. Both axial heat conduction through the rod and lateral heat conduction to the surrounding ground are modeled. A derived distribution of axial heating strength is then applied to a finite line heat source model to predict transient temperature changes in the surrounding medium. The predicted results show how the rod’s radius and ground’s thermal conductivity affect the vertical variation of heating strength and temperature response. Additional simulations predict the long-term temperature increase in the ground, due to a power transmission tower installed in a region of initially frozen ground.

The Role of the Viscous Dissipation in Heated Microchannels

Many experimental works appeared in the last decade in the open literature dealing with forced convection through microchannels. The earliest experimental results on single-phase flows in microchannels evidenced that for channels having a hydraulic diameter less than 1mm the conventional continuum models can no longer be considered as able to accurately predict pressure drop and convective heat transfer coefficients. This conclusion seemed to be valid for both gas and liquid flows. Sometimes the authors justified this conclusion by invoking new micro-effects, e.g., electrostatic interaction between the fluid and the walls or scaling effects (axial heat conduction, viscous forces, conjugate heat transfer, wall roughness, and so on). In this paper the role of the viscous dissipation in liquids flowing through heated microchannels will be analyzed by using the conventional theory. We will present a correlation between the Brinkman number and the Nusselt number for silicon ⟨100⟩ and ⟨110⟩ microchannels. It will be demonstrated that the fluid is of importance in establishing the exact limit of significance of the viscous dissipation in microchannels; a criterion to analyze the significance of the viscous effects will be presented. The role of the cross-section aspect ratio on the viscous dissipation will be highlighted. The main goal of this work is to demonstrate that the problem of heat transfer enhancement in microdevices cannot be solved by indefinitely reducing the microchannel dimensions because the viscous dissipation effects shall offset the gains of high heat transfer coefficients associated with a reduction in the channel size.

The effect of gaseous slip on microscale heat transfer: An extended Graetz problem

On the basis of Langmuir’s theory of adsorption of gases on solids, the effect of temperature jump on microscale heat transfer is investigated. A mathematical model, extended from the classical Graetz problem, is developed to analyze convective heat transfer in a microtube in various slip-flow regimes. The surface slip corrections are made by employing the Langmuir model, as well as the conventional Maxwell model. The effects of axial heat conduction are also investigated by extending the finite integral transform technique to the slip-flow case. We show that the Langmuir model always predicts a reduction in heat transfer with increasing rarefaction, as does the Maxwell model, except when the energy accommodation coefficient is relatively much smaller than that for momentum accommodation. This implies that, for most physical applications, the Reynolds analogy between heat transfer and momentum transfer is preserved in slip-flow regimes with low Mach numbers.

Laminar forced convection with viscous dissipation in a Couette–Poiseuille flow between parallel plates

In this study, analytical solutions are obtained to predict laminar heat-convection in a Couette–Poiseuille flow between two plane parallel plates with a simultaneous pressure gradient and an axial movement of the upper plate. A Newtonian fluid with constant properties is considered with an emphasis on the viscous-dissipation effect. Both hydrodynamically and thermally fully-developed flow cases are investigated. The axial heat-conduction in the fluid is neglected. Two different orientations of the thermal boundary-conditions are considered: the constant heat-flux at the upper plate with an adiabatic lower plate (Case A) and the constant heat-flux at the lower plate with an adiabatic upper plate (Case B). For different values of the relative velocity of the upper plate, the effect of the modified Brinkman number on the temperature distribution and the Nusselt number are discussed. Comparison of the present analytical results for a special case with those available in the literature indicates an excellent agreement.

Polymer Melt Flow in Plane Channels: Effects of the Viscous Dissipation and Axial Heat Conduction

ABSTRACT The plastic transforming industry has shown considerable growth in the last years. In this context, commercial simulators have been developed, some of which combine simplified mathematical models with rheological properties of commercial polymers. In spite of the successes, these approximations are not able to capture important details of the flow behavior. The present work addresses some aspects of the polymer melt flow in plane channels using a more elaborate mathematical formulation based on the full momentum and energy conservation laws. The physical equations are discretized using finite differences based on a collocated mesh and second-order spatial accuracy formulas. Solutions featuring the development of hydrodynamic and thermal boundary layers are presented for a commercial polymer.

An analytical model of a matrix heat exchanger with longitudinal heat conduction in the matrix in application for the exchanger dynamics research

The paper presents an analytical method for the solution of the problem of a fixed matrix heat exchanger with axial heat conduction within the matrix. The small parameter method and Laplace transform have been applied. A general solution has been obtained for the unsteady state in the form of function series, using single and double convolutions of functions, as well as a particular solution for both the uniform and non-uniform initial temperature of the matrix and for an arbitrary function of the fluid temperature at the inlet. Particular solutions have been used in the study of the matrix dynamics in determining dynamic characteristics for the standard input signals in the form of: Dirac δ pulse, Heaviside function and the function of sinusoidal variable temperature of the fluid at the inlet. The results obtained both illustrate and enable the assessment of the effect of axial heat conduction in the matrix on the dynamic properties of the heat exchanger.

Effects of viscous dissipation and fluid axial heat conduction on heat transfer for non-Newtonian fluids in ducts with uniform wall temperature: Part II. Annular ducts

The present paper, which is an extension of a previous study [O. Jambal, T. Shigechi, D. Ganbat, S. Momoki, Int. Commun. Heat Mass Transf. 32(9) (2005) 1165] on laminar heat transfer to non-Newtonian fluids in parallel plates and circular ducts, deals with concentric annular ducts subjected to a step change in wall temperature. A finite-difference scheme is applied to determine the velocity and temperature fields. Developing Nusselt numbers are graphically shown for various Brinkman numbers and Peclet numbers and the effects of viscous dissipation, fluid axial heat conduction, non-Newtonian behavior together with the radius ratio effect on heat transfer are discussed.

Effects of viscous dissipation and fluid axial heat conduction on heat transfer for non-Newtonian fluids in ducts with uniform wall temperature: Part I: Parallel plates and circular ducts

Laminar heat transfer in parallel plates and circular ducts subject to uniform wall temperature is studied by taking into account both viscous dissipation and fluid axial heat conduction in an infinite region. Developing temperature fields are evaluated numerically by a finite-difference method for various Brinkman numbers ( Br) and Peclet numbers ( Pe). Nusselt numbers are presented graphically for Pe = 10 and Pe → ∞, and Br = 0, ± 0.5 and ± 1 for non-Newtonian fluids described by the power-law model with the flow index of n = 0.5, 1.0 and 1.5. It is shown that Nusselt number has a single fixed value independent of Br in the thermally developing region and its numerical value is equal to that at the fully developed region for non-zero Br, when the preheating of incoming fluid due to both viscous dissipation and fluid axial heat conduction is considered.

Viscous-dissipation effects on the heat transfer in a Poiseuille flow

In this study, laminar heat-convection in a Poiseuille flow of a Newtonian fluid with constant properties is analyzed by taking the viscous dissipation into account. At first, both hydrodynamically and thermally fully-developed flow case is investigated. Then, consideration is given to thermally-developed laminar forced-convection. The axial heat-conduction in the fluid is neglected. Two different thermal boundary-conditions are considered: the constant heat-flux and the constant wall-temperature. Both the hot-wall and the cold-wall cases are considered. In the literature, the viscous-dissipation effect is commonly represented by the Brinkman number. Several different definitions of the Brinkman number arise depending on the thermal boundary conditions. Either for the thermally fully-developed case or the thermally-developing case (the Graetz problem), temperature distributions and the Nusselt numbers are analytically determined as functions of the Brinkman number.

Effects of viscous dissipation on the heat transfer in a forced pipe flow. Part 2: Thermally developing flow

In this part of the study, consideration is given to thermally developing laminar forced convection in a pipe including viscous dissipation. The axial heat conduction in the fluid is neglected. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). Both the wall heating (the fluid is heated) case and the wall cooling (the fluid is cooled) case are considered. The distributions for the developing temperature and local Nusselt number in the entrance region are obtained. Results show that the temperature profiles and local Nusselt number are influenced by the Brinkman number ( Br ) and the thermal boundary condition used for the wall. Significant viscous dissipation effects have been observed for large Br .

Axial heat conduction model to predict maximum heat remove of miniature heat pipe based on grey model theory

Computer chip is always accompanied by the increase of heat dissipation and miniaturization. The miniature heat pipes are widely used in notebook computer to resolve the heat dissipation problems. Maximum heat removed model of miniature heat pipes building by grey model is presented. In order to know the foundation for modeling, the smooth grade of error examination is inquired and the accuracy of grey relational grade is verified. The model can be used to select a suitable heat pipes to solve electric heat problems in the future. Final results show that the grey model only needs four experiment data and its error value is less than 10%, further, it is better than computational fluid dynamics (CFD) model.

Nonlinear dynamics of automobile exhaust gas converters: the role of nonstationary kinetics

Continuation software has been used for bifurcation analysis of the lumped approximation (a short monolith, CSTR) of the three-way catalytic converter (TWC). A nonstationary TWC reaction scheme evaluated from dynamic experiments on Pt/Ce/ γ - Al 2 O 3 has been employed in the model. Multiple steady states (hysteresis) and oscillations are predicted both for the CO oxidation submodel and the full TWC scheme (the CO and hydrocarbon oxidation and the NO x reduction) in a certain range of operation parameters. The autocatalytic loops are identified by reaction network analysis. The operation of the monolith is then simulated by spatially 2D mathematical model of TWC converter where the description of internal diffusion in the washcoat and axial heat conduction are included. Kinetic oscillations reflect in complex spatiotemporal patterns in the washcoat along the monolith.

The extended Graetz problem with piecewise constant wall temperature for pipe and channel flows

Axial heat conduction effects within the fluid can be important for duct flows if the Prandtl number is relatively low (liquid metals). In addition, axial heat conduction effects within the flow might also be important, if the heating zone is relatively short in length. The present paper shows an entirely analytical solution to the extended Graetz problem with piecewise constant wall temperature boundary conditions. The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. The obtained analytical solution is as simple to compute as the one without axial heat conduction. The analytical results are compared to available numerical calculations and good agreement is found.

Segmented and shielded structures for reduction of thermal expansion-induced tilt errors

The design and prototype tests of a segmented and shielded instrumentation structure, based on tube modules connected by canoe ball type kinematic couplings, are presented with application to a high-precision microscope for biological science experiments. The segmented tube design is shown to be significantly less sensitive to deformation from uneven thermal disturbances than a single tube structure. The gaps between the tube segments relieve thermal strains and restrict axial heat conduction, and the large-radius kinematic couplings provide high thermal resistance interconnects without significantly degrading structural stiffness. Simulation results, based on two- and three-dimensional models of heat conduction, are verified with experimental measurements of prototype structures and are used to predict the dependence of the tilt error on the geometry, boundary conditions, and material properties of the tubular segments. Adding layers of low-cost foam insulation and thin metal shielding to the walls of the structure further improves performance. Kinematic couplings could allow the structure to be disassembled and reassembled without re-calibration, and thus, pre-calibrated tube modules with different components could be easily and quickly interchanged between experiments.

Generalized thermoelastic analysis of layer interface excited by pulsed laser heating

In order to investigate the temperature and stress distribution at the interface of an elastic layer and a rigid foundation under laser thermal shock, a boundary element method is presented. The effective stress and temperature fields are calculated at the interface. The bounded layer absorbs the thermal energy from a repetitively pulsed laser in its surface plane. The pulse duration is of the order of the characteristic time for heat to diffuse across the layer thickness, and thus axial heat conduction cannot be neglected. The generalized thermoelasticity assumption based on the Lord and Shulman model on the temperature and stress distribution at the interface of an elastic layer is considered. Comparison with the classical coupled and uncoupled models are investigated. The effects of the pulse duration and layer thickness on the effective stress and temperature distribution of the layer is studied using the classical theory of thermoelasticity. It is found that for the same maximum surface temperature rise, a shorter pulsed laser induces much stronger effective stress wave front. The layer thickness, on the other hand, has minor effect on the effective stress distribution.

Thermal entry flow for a viscoelastic fluid: the Graetz problem for the PTT model

A theoretical study of the entrance thermal flow problem is presented for the case of a fluid obeying the Phan-Thien and Tanner (PTT) constitutive equation. This appears to be the first study of the Graetz problem with a viscoelastic fluid. The solution was obtained with the method of separation of variables and the ensuing Sturm–Liouville system was solved for the eigenvalues by means of a freely available solver, while the ordinary differential equations for the eigenfunctions and their derivatives were calculated numerically with a Runge–Kutta method. The scope of the present study was quite wide: it encompassed both the plane and axisymmetric geometries for channel and tube flows; two types of thermal boundary conditions with either an imposed wall temperature or an applied heat flux; inclusion of viscous dissipation; and elastic (through the Weissenberg number) and elongational (through the PTT parameter ϵ) effects. The main underlying assumptions were those of constant physical properties, negligible axial heat conduction, and fully developed hydrodynamic conditions. The results are discussed in terms of the main effects brought about by viscoelasticity and viscous dissipation on the Nusselt number variation and the bulk temperature.