Conjugate heat transfer of mixed convection for viscoelastic fluid past a horizontal flat-plate fin

A conjugate mixed convection heat transfer problem of a second-grade viscoelastic fluid past a horizontal flat-plate fin has been studied. Governing equations include heat conduction equation of the fin, and continuity equation, momentum equation and energy equation of the fluid, have been analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite difference method. Solutions of a stagnation flow (β = 1.0) at the fin tip and a flat-plate flow (β = 0) on the fin surface were obtained by a generalized Falkner–Skan flow derivation. These solutions have been used to iterate with the heat conduction equation of the fin to obtain distributions of the local convective heat transfer coefficient and the fin temperature. Ranges of dimensionless parameters, the Prandtl number (Pr), the elastic number (E), the free convection parameter (G) and the conduction–convection coefficient (N_cc) are from 0.1 to 100, 0.001 to 0.01, 0 to 1.5 and 0.05 to 2.0, respectively. The elastic effect in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a horizontal flat-plate fin. In addition, same as results from Newtonian fluid flow and conduction analysis of a horizontal flat-plate fin, a better heat transfer has been obtained with a larger N_cc, G and Pr.     

Conjugate forced convection-conduction plate fin in power law fluids

The heat transfer characteristics of laminar, forced convection flow for power law fluids from a vertical plate fin are studied analytically based on the conjugate convection and conduction theory. The resulting boundary layer equations of fluids are coupled with the one-dimensional heat conduction equation of fin through interfacial conditions. Numerical results for the local heat flux, local heat transfer coefficient, and temperature distribution along the fin surface and overall heat transfer rate under the effects of the conjugate convection-conduction parameter, generalized Prandtl number and fluid flow index are illustrated. The results obtained of the non-Newtonian power law fluid are found to have trends similar to those of the Newtonian fluids.     

Conjugate mixed convection-conduction heat transfer along a vertical cylindrical fin in non-newtonian fluids

By considering the interaction between conduction within the fin and convection to the fluid surrounding the fin, an analysis is presented to study the heat transfer characteristics of laminar mixed convection of a non-Newtonian fluid flow over a vertical cylindrical fin. Due to the compatibility conditions of heat flux and temperature at the surface of fin, the boundary layer equations of the fluid are coupled with the heat conduction equation of the fin and should be solved simultaneously. Of interest are the effects of transverse curvature parameter, bouyancy parameter, power-law viscosity index, generalized Prandtl number and conjugate convection-conduction parameter on the local heat transfer coefficient, local heat flux and temperature distribution of the fin. Comparison of the calculated results with available data sets in the open literature for a Newtonian fluid shows a very good performance of the present numerical procedure.     

Laminar flow and heat transfer in plate-fin triangular ducts in thermally developing entry region

Laminar forced flow and heat transfer in plate-fin isosceles triangular ducts encountered in compact heat exchangers is investigated. The flow is hydrodynamically fully developed, but developing thermally under uniform temperature conditions. Heat conduction in the fin of finite conductance and convection in the fluid are analyzed simultaneously as a conjugate problem. The study covers a wide range of apex angles from 30° to 120°, and fin conductance parameters from 0 to infinitely large. Nusselt numbers in the developing and fully developed regions for various apex angles and fin conductance parameters are obtained, which can be used in estimation of heat transfer characteristics in plate-fin compact heat exchangers with fins of various conductivities and thickness.     

Conjugate natural convection about a vertical cylindrical fin with lateral mass flux in a saturated porous medium

The problem of conjugate natural convection about a vertical cylindrical fin with uniform lateral mass flux in a fluid-saturated porous medium has been studied numerically. Solutions based on the third level of truncation are obtained by the local nonsimilarity method. The effects of the surface mass flux, the conjugate convection-conduction parameter, and the surface curvature on fin temperature distribution, local heat transfer coefficient, local heat flux, average heat transfer coefficient, and total heat transfer rate are presented. A comparison with finite-difference solutions for the case of constant wall temperature was made, and found in a good agreement.     

Computational Conjugate Heat Transfer Analysis of a Hybrid Electric Vehicle Inverter

ABSTRACT

A physics-based computational simulation of the heat transfer characteristics of an insulated gate bipolar transistor (IGBT) developmental inverter is reported. The simulation considers the fluid/thermal multiphysics interactions via a conjugate heat transfer analysis. The fluid phase includes air and liquid coolant; the solid phase, where the heat is conducted, includes various solid materials. Numerical solutions of the heat conduction and convection phenomena in and around the IGBT modules and the inverter, built as a three-dimensional computational model, are sought for by using parallel computing. Comparisons with the available experimental data show a satisfactory agreement of the inverter temperature at three power levels under two different coolant flow rates. Detailed examination of the flow field reveals that the design features of the rectangular coolant flow chamber in the heat sink and the small clearance between the tips of the pin fin and the walls lead to an evenly distributed coolant flow around most of the pin fins. The temperature distributions of the pin fins depend highly on their locations relative to the IGBT modules. The findings from the current study can be useful in future efforts to optimize the thermal performance of IGBT inverters.     

Analytical solutions of the 1-D heat conduction problem for a single fin with temperature dependent heat transfer coefficient - II. Recurrent direct solution

The recurrent direct solution of the 1-D heat conduction problem for a single straight fin and spine with power-law-type temperature dependent heat transfer coefficient has been derived using inversion of the closed-form solution obtained in the first part of the study. The expression with improving convergence to calculate accurately the dimensionless temperature excess T_e at the fin tip for a given values of the fin parameter N and exponent n in heat transfer equation has been obtained by a linearization method. Equation for the temperature excess distribution throughout the fin has also been derived. The obtained formula for T_e allows to calculate the fin base thermal conductance and augmentation factor. Obtained expressions are seen to be simple and convenient for the engineering design of the fins and finned surfaces.     

Numerical analysis of heat transfer and flow field around cross-flow heat exchanger tube with fouling

Fouling is one of the main problems of heat transfer which can be described as the accumulation on the heat exchanger tubes, i.e.; ash deposits on the heat exchanger unit of the boiler. A decrease in heat transfer rate by this deposition causes loss in system efficiency and leads to increasing in operating and maintenance costs. This problem concerns with the coupling among conduction heat transfer mode between solid of different types, conjugate heat transfer at the interface of solid and fluid, and the conduction/convection heat transfer mode in the fluid which can not be solved analytically. In this paper, fouling effect on heat transfer around a cylinder in cross flow has been studied numerically by using conjugate heat transfer approach. Unlike other numerical techniques in existing literatures, an unstructured control volume finite element method (CVFEM) has been developed in this present work. The study deals with laminar flow where the Reynolds number is limited in the range that the flow field over the cylinder is laminar and steady. We concern the fouling shape as an eccentric annulus with constant thermal properties. The local heat transfer coefficient, temperature distribution and mean heat transfer coefficient along the fouling surface are given for concentric and eccentric cases. From the results, we have found that the heat transfer rate of cross-flow heat exchanger depends on the eccentricity and thermal conductivity ratio between the fouling material and fluid. The effect of eccentric is dominant in the region near the front stagnation point due to high temperature and velocity gradients. The mean Nusselt number varies in asymptotic fashion with the thermal conductivity ratio. Fluid Prandtl number has a prominent effect on the distribution of local Nusselt number and the temperature along the fouling surface.     

有内热源的肋片散热数值分析

利用流体区域与固体区域温度场耦合的方法求解含内热源肋片的稳态自然对流换热问题,讨论了肋片材料、肋片间距和内热源强度对整个散热的影响。得出各种情况下流场和温度场的变化和不同情况下散热效果的标志性参数——最高温度的变化规律如下：内热源越强,最高温度越高;肋片间距增加,最高温度降低;提出了具体的计算式;导热系数大于10W／（m·K）的金属材料,肋片最高温度不受材料热物理性质的影响。     

TRANSIENT ANALYSIS OF COMBINED FORCED AND FREE CONVECTION-CONDUCTION ALONG A VERTICAL CIRCULAR FIN IN MICROPOLAR FLUIDS

The conjugate, transient, laminar, combined convection and conduction problem of mi-cropolar fluids along a vertical circular fin has been investigated. The coupled governing equations in dimensionless form are solved numerically using cubic spline collocation formulation. The analyses of heat transfer are divided into constant root temperature and constant heat flux from the root. Numerical results show that the heat transfer rate increases with increasing buoyancy force. A comparison of the heat transfer characteristics between a Newtonian fluid and a micropolar fluid is also discussed.     

Experimental study of heat transfer and flow friction insolar air heaters with and without selective absorbers

High thermal performances have been needed for the use of solar air collectors andcompact heat exchangers. The thermal performance improvements have prompted us to lead thiscomparative study on the solar air heaters with and without selective absorbers. Rectangular finsare soldered staggered on the collectors back. The interstices are let between two consecutive finslocated in the same rows. The fluid flow undergoes constrictions followed one after the other byexpansions. A turbulent fluid flow is developed, that permits the improvement of the thermalheat transfer of these collectors in comparison to the flat-plate. For the same fin configurations,the thermal heat transfer coefficient has been evaluated with selective or non-selectiveabsorber-plate. The results obtained with the fin configurations with black-painted absorber(non-selective absorber), are compared with those of the fin configuration with coppersunabsorber-plate (selective absorber). The aim of this study is to show that the nature of theabsorber-plate (selective or nonselective) has no important effect on the thermal performances ofthe fanned system collector. Only a trivial increase is noted on behalf of the selective absorbercollector.     

Natural convection heat transfer from a thermal heat source located in a vertical plate fin

A steady state conjugate conduction–convection investigation is performed on vertical plate fin in which a small heat source is located. Heat from the fin surface is transferred to the surroundings by laminar natural convection. The governing equations for the problem are the heat conduction equation for the fin and the boundary layer equations, which are continuity, momentum and energy equations, for the fluid. A computer program is written by using the finite difference method in order to solve the governing equations which are nonlinear and coupled. The best location of the heat source in the fin for maximum heat transfer rate depends on two parameters which are the conduction–convection parameter and the Prandtl number. The obtained results have shown that for the fin with large conduction–convection parameter, a heat source location for maximum heat transfer rate exists.     

Heat transfer from a horizontal fin array by natural convection and radiation—A conjugate analysis

The problem of natural convection heat transfer from a horizontal fin array is theoretically formulated by treating the adjacent internal fins as two-fin enclosures. A conjugate analysis is carried out in which the mass, momentum and energy balance equations for the fluid in the two-fin enclosure are solved together with the heat conduction equations in both the fins. The numerical solutions by using alternating direction implicit (ADI) method yield steady state temperature and velocity fields in the fluid, and temperatures along the fins. Each end fin of the array is exposed to limited enclosure on one side and to infinite fluid medium on the other side. Hence a separate analysis is carried out for the problem of end fin exposed to infinite fluid medium with appropriate boundary conditions. From the numerical results, the heat fluxes from the fins and the base of the two-fin enclosure, and the heat flux from the end fin are calculated. Making use of the heat fluxes the total heat transfer rate and average heat transfer coefficient for a fin array are estimated. Heat transfer by radiation is also considered in the analysis. The results obtained for a four-fin array are compared with the experimental data available in literature, which show good agreement. Numerical results are obtained to study the effectiveness for different values of fin heights, emissivities, number of fins in a fixed base, fin base temperature and fin spacing. The numerical results are subjected to non-linear regression and equations are obtained for heat fluxes from the two-fin enclosure and single fin as functions of Rayleigh number, aspect ratio and fin emissivity. Also regression equations are obtained to readily calculate the average Nusselt number, heat transfer rate and effectiveness for a fin array.     

Recursive formulation on thermal analysis of an annular fin with variable thermal properties

This study introduces a discrete model which is pertinent for calculating thermal performance of singular annular fin with variable thermal properties. The singular annular fin can be divided into several circular sections, and each section can take its variable thermal properties, such as heat transfer coefficient and thermal conductivity, into account. The result from each section can be combined and calculated together by a recursive formula. Then, the solutions of temperature distribution and heat transfer rate on singular annular fin can be quickly obtained. For this model, the recursive formulae for both conditions with and without heat transfer on fin tip are demonstrated. Finally, some examples including composite materials for an annular fin have been successfully simulated through the present approach.     

Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant

The heat transfer and thermal distribution through porous fins have gotten a lot of attention in recent years due to their extensive applications in the manufacturing and engineering field. In porous fins, the impact of magnetic field aids in improved heat transfer enhancement. Also, the combination of an electric effect and a magnetic field considerably enhances heat transfer. In this direction, the thermal distribution through a convective–radiative longitudinal trapezoidal porous fin with the impact of an internal heat source and an electromagnetic field is discussed in the present analysis. The governing heat equation is nondimensionalized with nondimensional terms, and the transformed nonlinear ordinary differential equation is solved analytically using the DTM–Pade approximant algorithm. Furthermore, the graphical discussion is presented to explore the impact of various nondimensional parameters, such as convection-conduction parameter, fin taper ratio, thermomagnetic field, radiation–conduction parameter, internal heat generation parameter, and thermoelectrical field on the temperature gradient of the fin. The investigation's key findings disclose that as the magnitude of the convection–conduction parameter, fin taper ratio, and radiation–conduction parameter increase, the thermal distribution through the fin reduces. The thermal distribution inside the fin increases for the heat-generating parameter, thermoelectric, and thermomagnetic fields.     

Thermal performance of straight porous fin with variable thermal conductivity under magnetic field and radiation effects

The present numerical study reports the thermal performance of the straight porous fin with temperature-dependent thermal conductivity, radiation, and magnetic field effects. The heat transfer model comprising the Darcy's law for simulating flow with solid-fluid interactions in porous medium, Rosseland approximation for heat transfer through radiation, Maxwell equations for magnetic field effect and linearly varying temperature dependent thermal conductivity, results into highly nonlinear ordinary differential equation. The governing equation is solved using a finite difference scheme with suitable boundary conditions. The obtained solutions are physically interpreted by considering the impact of different nondimensional parameters on thermal performance, efficiency, and effectiveness of the system through plotted graphs. A detailed result with regard to the Nusselt number at the fin base is calculated. The results obtained are observed to be in excellent agreement with previous studies. From the study, it is observed that there is a significant effect on the thermal performance of the fin in the presence of porous constraints; also, results reveal that the nonlinear thermal conductivity parameter strengthens the thermal performance, efficiency, and effectiveness of the fin. Furthermore, the results of the study reveal that the rate of heat transfer of the fin increases with the increase in the magnetic parameter and radiation parameter.     

Numerical study of the fin efficiency and a modified fin efficiency formula for flat tube bank fin heat exchanger

In this paper, a three-dimensional numerical heat transfer analysis has been performed in order to obtain the temperature distribution and the fin efficiency using the experimentally determined local heat transfer coefficients from the naphthalene sublimation technique and heat and mass transfer analogy. The influences of the fin material, fin thickness, and transversal tube pitch on the fin efficiency are studied for flat tube bank fin heat exchangers. The fin efficiency, obtained by a numerical method using the averaged heat transfer coefficient, is compared with that using the local heat transfer coefficient. The reliability of the generally used formula for fin efficiency is tested also, and then a modified fin efficiency formula with a new equivalent fin height is provided. The results show that the difference between the fin efficiency obtained by the numerical method using the local heat transfer coefficient and the fin efficiency using the averaged heat transfer coefficient is small, but the fin efficiency obtained by the generally used formula is lower than that obtained by the numerical method using the local heat transfer coefficient; the fin efficiency obtained by the modified formula matches very well with the fin efficiency obtained by the numerical method using the local heat transfer coefficient. The modified formula for the fin efficiency calculation is more reliable, and it can be applied directly to the design of a flat tube bank fin heat exchanger and also will be useful in engineering applications.     

An inverse problem in estimating the base heat flux of an annular fin based on the hyperbolic model of heat conduction

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent base heat flux of an annular fin from the knowledge of temperature measurements taken within the fin. The inverse solutions will be justified based on the numerical experiments in which two specific cases to determine the unknown base heat flux are examined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent base heat flux can be obtained for the test cases considered in this study.     

Performance of a flat-plate solar thermal collector using supercritical carbon dioxide as heat transfer fluid

Energetic and exergetic performance analyses of flat-plate solar collector using supercritical CO₂ have been done in this study. To take care of the sharp change in thermophysical properties in near critical region, the discretisation technique has been used. Effects of zonal ambient temperature and solar radiation, fluid mass flow rate and collector geometry on heat transfer rate, collector efficiency, heat removal factor, irreversibility and second law efficiency are presented. The optimum operating pressure correlation has been established to yield maximum heat transfer coefficient of CO₂ for a certain operating temperature. Effect of metrological condition on heat transfer rate and collector efficiency is significant and that on heat removal factor is negligible. Improvement of heat transfer rate is more predominant than increase in irreversibility by using CO₂. For the studied ranges, the maximum performance improvement of flat-plate solar collector by using CO₂ as the heat transfer fluid was evaluated as 18%.     

Viscous Joule heating MHD–conjugate heat transfer for a vertical flat plate in the presence of heat generation

The problem of steady conjugate heat transfer through an electrically-conducting fluid for a vertical flat plate in the presence of transverse uniform magnetic field taking into account the effects of viscous dissipation, Joule heating, and heat generation is formulated. The general governing equations which include such effects are made dimensionless by means of an apposite transformation. The ultimate resulting equations obtained by introducing the stream function with the similarity variable are solved numerically using the implicit finite difference method for the boundary conditions based on conjugate heat transfer process. A representative set of numerical results for the velocity and temperature profiles, the skin friction coefficients as well as the rate of heat transfer coefficient and the surface temperature distribution are presented graphically and discussed. A comprehensive parametric study is carried out to show the effects of the magnetic parameter, viscous dissipation parameter, Joule heating parameter, conjugate conduction parameter, heat generation parameter and the Prandtl number on the obtained solutions.