Unsteady conjugated heat transfer in laminar pipe flows with step change in ambient temperature

This study aims to numerically investigate the effects of wall heat capacity on the unsteady forced convection heat transfer in the flow in a long circular pipe resulting from a step change in the ambient temperature. Two non-dimensional parameters, Nu_o and a^*, are identified in the study, and their effects on the non-dimensional duct wall heat flux and the time evolution of temperature field are discussed in great detail. Comparisons are made with zero thermal capacity wall solution. It is found that the wall heat capacity has decisive impact on the unsteady heat transfer in the flow.     

A New Method for Analyzing Heat Exchangers- Matching of Temperature Field

In heat exchangers, the magnitude of Nu of each duct is influenced by the temperature field, since the ratio of heat capacity rate will influence the matching status of the temperature field between contacting ducts, the total heat transfer coefficient is related with the ratio of heat capacity rate. Considering this relationship, a new method for analyzing heat exchanger is proposed - matching of temperature field. First, for a single duct with the temperature field varying exponentially along the flow direction, its Nu is calculated. Then under the hypothesis that the thermal resistance of the wall is negligible, the matching condition was set like this: both the temperature and heat flux are equal for the hot and cold fluids at the wall, so the matching relationship of parameter that describes the temperature field of the hot and cold fluids, was obtained. Finally the relationship between the total Nu and the ratio of heat capacity rate along with the ratio of inherent thermal resistance is obtained. Compared with traditional analyzing methods, the temperature matching method can be used to get the total heat transfer coefficient directly, and also be used for optimization of heat exchanger design. For a parallel flow, the optimal ratio of heat capacity rate is reciprocal to the ratio of inherent thermal resistance, and for a counter flow, the optimal ratio of heat capacity rate is zero or infinity.     

Three dimensional laminar non-Newtonian fluid flow and heat transfer in the entrance region of a cross-shaped duct

The Galerkin finite element is used to solve the three dimensional momentum and energy equations for laminar non-Newtonian flow in cross-shaped straight duct. Both flow and heat transfer develop simultaneously from the entrance of the channel. Uniform wall temperature (T) and also constant wall heat flux both axially and peripherally (H2) are used as thermal boundary conditions. The power-law model is chosen to characterize the non-Newtonian behaviour of the fluid. The effect of power-law index and geometric parameter on the apparent friction factor as well as Nusselt number are presented and discussed.     

Unsteady forced convection with sinusoidal duct wall generation: the conjugate heat transfer problem

Transient heat transfer solutions are found for a fluid flowing within a parallel plate duct when there is sinusoidal generation with axial position in the duct wall. Solutions are found for wall temperature, surface heat flux and fluid bulk mean temperature as a function of position and time in this conjugated problem. To develop this solution, finite difference methods are used as well as the quasi-steady method and another method which employs a two integral representation for the surface heat flux. Accuracy limitations of the quasi-steady results are identified. Transient local Nusselt number predictions show its dependence upon time.     

Analysis of the effect of viscous dissipation for laminar flow in stadium-shaped ducts

The fully-developed laminar forced convection of a Newtonian fluid in a duct with stadium-shaped cross section has been analyzed. The effect of viscous dissipation has been taken into account. Three different thermal boundary conditions have been considered: (T) uniform wall temperature distribution; (H1) axially uniform wall heat flux distribution with peripherally uniform wall temperature distribution; (H2) axially and peripherally uniform wall heat flux distribution. The adiabatic-wall boundary condition has also been analyzed as a special case of the H2 boundary condition. The velocity and temperature distributions in the fluid, as well as the Fanning friction factor and the Nusselt number, have been evaluated numerically, by employing a Galerkin finite element method. As expected, the numerical evaluation of the dimensionless temperature distribution and of the Nusselt number reveals that increasing discrepancies between the H1 and H2 boundary conditions exist if the stadium-shaped duct is gradually flattened.     

Numerical solution of power law fluids flow and heat transfer with a magnetic field in a rectangular duct

The steady laminar flow and heat transfer of an incompressible, electrically conducting, power law non-Newtonian fluids in a rectangular duct are studied in the presence of an external uniform magnetic field. The momentum and energy equations are solved iteratively using a finite difference method. Two cases of the thermal boundary conditions are considered; (1) T thermal boundary condition “constant temperature at the wall” and (2) H2 thermal boundary condition “constant heat flux at the wall”. The viscous and Joule dissipations are taken into consideration in the energy equation. A numerical solution for the governing partial differential equations is developed and the influence of the magnetic field on the velocity distribution, the friction factor and the average Nusselt number are discussed.     

FULLY DEVELOPED LAMINAR HEAT TRANSFER IN CIRCULAR-SEGMENT DUCTS WITH UNIFORM WALL TEMPERATURE

Heat transfer to constant-property, fully developed, laminar flows in circular-segment ducts with uniform wall temperature (T) has been analyzed. Besides representing a compact surface, the segment duct geometry models the flow cross section of a circular tube with a straight-tape insert. Two variations in the T thermal boundary condition are considered: constant axial and circumferential wall temperature, and constant temperature on the curved surface but an adiabatic flat wall. These two conditions model the extremes of the fin effects of a straight-tape insert, i.e., 100% and zero fin efficiencies, respectively. Numerical solutions, obtained by using finite difference techniques, are presented for both the velocity and temperature fields. The isothermal friction factors are in excellent agreement with analytical solutions reported in the literature. The Nusselt number results for the two thermal boundary conditions are presented for different segment shapes, 0° ≤, 6 ≤, 90°, and they represent the lower limits of the heat transfer enhancement due to twisted-tape inserts.     

Fully developed mixed convection and flow reversal in a vertical rectangular duct with uniform wall heat flux

Combined forced and free flow in a vertical rectangular duct is investigated for laminar and fully developed regime. The velocity field, the temperature field, the friction factor and the Nusselt number are evaluated analytically by employing finite Fourier transforms. The thermal boundary condition considered is an axially uniform wall heat flux and a peripherally uniform wall temperature, i.e. an H1 boundary condition. The necessary and sufficient condition for the onset of flow reversal is determined either in the case of upward flow in a cooled duct or in the case of downward flow in a heated duct. The special case of free convection, i.e. the case of a purely buoyancy-driven flow, is discussed. The occurrence of effects of pre-heating or pre-cooling in the fluid is analysed. It is pointed out that although these effects occur in rectangular ducts, they are not present either in circular ducts or in parallel-plate channels.     

Improved PV/T solar collectors with heat extraction by forced or natural air circulation

The photovoltaic (PV) cells suffer efficiency drop as their operating temperature increases especially under high insolation levels and cooling is beneficial. Air-cooling, either by forced or natural flow, presents a non-expensive and simple method of PV cooling and the solar preheated air could be utilized in built, industrial and agricultural sectors. However, systems with heat extraction by air circulation are limited in their thermal performance due to the low density, the small volumetric heat capacity and the small thermal conductivity of air and measures for heat transfer augmentation is necessary. This paper presents the use of a suspended thin flat metallic sheet at the middle or fins at the back wall of an air duct as heat transfer augmentations in an air-cooled photovoltaic/thermal (PV/T) solar collector to improve its overall performance. The steady-state thermal efficiencies of the modified systems are compared with those of typical PV/T air system. Daily temperature profiles of the outlet air, the PV rear surface and channel back wall are presented confirming the contribution of the modifications in increasing system electrical and thermal outputs. These techniques are anticipated to contribute towards wider applications of PV systems due to the increased overall efficiency.     

Numerical prediction on laminar heat transfer in square duct with 30° angled baffle on one wall

A numerical investigation on periodic laminar flow and heat transfer behaviors in a three-dimensional isothermal wall square duct fitted with 30° angled baffles on lower duct wall only is presented. The computations based on a finite volume method with the SIMPLE algorithm have been conducted for the fluid flow in terms of Reynolds numbers ranging from 100 to 2000. The angled baffles with attack angle of 30° are mounted periodically on the lower duct wall to generate a longitudinal vortex flow through the tested duct. Effects of different baffle height and three pitch length ratios on heat transfer and flow characteristics in the duct are investigated. The study shows that the longitudinal vortex flow created by the baffle helps to induce impinging flows over the baffle trailing end sidewall and the inter-baffle cavity wall resulting in drastic increase in heat transfer rate over the test duct. The computational results reveal that the Nusselt number ratio and the maximum thermal enhancement factor values for using the angled baffle are, respectively, found to be about 7.9 and 3.1 at Re = 2000, BR = 0.3 and PR=1.5.     

Heat transfer for Herschel–Bulkley fluids in the entrance region of a rectangular duct

In this study, we present a numerical solution for combined laminar fluid flow and heat transfer of Herschel–Bulkley non-Newtonian fluids in the entrance region of a rectangular duct. The governing equations are solved iteratively by using finite difference method to obtain temperature, bulk temperature, and Nusselt number. Two cases of the thermal boundary conditions are considered; (i) T thermal boundary condition “constant temperature at the wall” and (ii) H2 thermal boundary condition “constant heat flux at the wall”. The results are presented in tables and figures for different parameters for the fluid and the duct geometry.     

有限热源影响下VM循环热泵的热力学分析

对于低温余热,VM循环热泵是一种高效节能的利用途径.文中采用有限时间热力学方法,推导了基于牛顿线性导热定律的内可逆VM循环热泵泵热率的表达式.分析表明:采用VM循环热泵用于地板辐射采暖时,随着有限高温热源的入口温度和有限低温热源进口温度的增加,泵热率将增大;而随着有限高温热源的出口温度和有限低温热源出口温度的增加,泵热率将减小.并且低温有限热源温度的变化对泵热率的影响远大于高温有限热源温度的变化.     

A way to explain the thermal boundary effects on laminar convection through a square duct

A way using the reformulation of the energy conservation equation in terms of heat flux to explain the thermal boundary effects on laminar convective heat transfer through a square duct is presented. For a laminar convection through a square duct, it explains that on the wall surface, the velocity is zero, but convection occurs for uniform wall heat flux (UWHF) boundary in the developing region due to the velocity gradient term; for uniform wall temperature (UWT) boundary, only diffusion process occurs on the wall surface because both velocity and velocity gradient do not contribute to convection; for UWHF, the largest term of the gradient of velocity components (the main flow velocity) on the wall surface takes a role in the convection of the heat flux normal to the wall surface, and this role exists in the fully developed region. Therefore, a stronger convection process occurs for UWHF than for UWT on the wall surface. The thermal boundary effects on the laminar convection inside the flow are also detailed.     

A numerical study of single-phase convective heat transfer in microtubes for slip flow

The steady-state convective heat transfer for laminar, two-dimensional, incompressible rarefied gas flow in the thermal entrance region of a tube under constant wall temperature, constant wall heat flux, and linear variation of wall temperature boundary conditions are investigated by the finite-volume finite difference scheme with slip flow and temperature jump conditions. Viscous heating is also included, and the solutions are compared with theoretical results where viscous heating has been neglected. For these three boundary conditions for a given Brinkman number, viscous effects are presented in the thermal entrance region along the channel. The effects of Knudsen and Brinkman numbers on Nusselt number are presented in graphical and tabular forms in the thermal entrance region and under fully developed conditions.     

Numerical and experimental analysis of unsteady heat transfer with periodic variation of inlet temperature in circular ducts

This work focusses on a numerical and experimental analysis of unsteady forced convection in hydrodynamically developed and thermally developing laminar air flow in a circular duct, subjected to a periodic variation of the inlet temperature. The experiments were conducted over a wide range of Reynolds number (281.2 ≤ Re ≤ 1024.3) and inlet frequency (0.01 ≤ β ≤ 0.20 Hz) of the periodic heat input. In the numerical study, the non-uniform inlet temperature amplitude profile derived from the experiments, was included in the numerical model. A fully explicit, second-order accurate finite difference scheme was developed and used for the solution of the unsteady energy equation. Numerical results are obtained with the fully developed parabolic velocity profile under the boundary condition of the first kind, which was verified by the experiments. Temperature variations along the centerline of the circular duct are observed to be thermal oscillations with the same frequency as the inlet periodic heat input and amplitudes that decayed exponentially with distance along the duct. Thermal response along the wall exhibits negligible amplitude variation with changes in Reynolds number and inlet frequency. The variation in the periods and amplitudes of the thermal oscillations are observed to be a function of spacial system variables only. Satisfactory agreement between the numerical and experimental results are obtained.     

Convective Heat Transfer in a Vertical Rectangular Duct Filled with a Nanofluid

An analysis is performed to study natural convective heat transfer in a vertical rectangular duct filled with a nanofluid. One of the vertical walls of the duct is cooled by a constant temperature, while the other wall is heated by a constant temperature. The other two sides of the duct are thermally insulated. The transport equations for a Newtonian fluid are solved numerically with a finite volume method of second‐order accuracy. The influence of pertinent parameters such as Grashof number, Brinkman number, aspect ratio and solid volume fraction on the heat transfer characteristics of natural convection is studied. Results for the volumetric flow rate and skin friction for Copper and Diamond nanoparticles are also drawn. The Nusselt number for various types of nanoparticle such as silver, copper, diamond and titanium oxide are also tabulated. The results indicate that inclusion of nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximizes the heat transfer rate.     

Analysis of transient heat transfer in multilayer thin films with nonlinear thermal boundary resistance

Transient energy transport in thin-layer films with a nonlinear thermal boundary resistance is analyzed theoretically within the framework of the dual-phase-lag heat conduction model. An iterative finite difference numerical method is used and is verified using a derived semi-analytical solution of the problem. Effects of the thermo-physical properties on energy transport when a two-layer film is exposed to a thermal pulse of certain duration and strength are presented. The thermal boundary resistance, the heat flux and temperature gradient phase lags and the thermal conductivities and heat capacities all are important factors that characterize energy transport through the interface and the temperature distribution in the two layers. The maximum interfacial temperature difference that takes place in the transient process of thermal pulse propagation is found to be the proper choice to measure the perfect-ness of the interface with a finite thermal boundary resistance. The results show that even with high values of the thermal boundary resistance the maximum interfacial temperature difference can be very small when the thermal pulse propagates from a high-thermal conductivity and heat capacity layer to a low-thermal conductivity and heat capacity layer. For a certain range of the thermal conductivities and heat capacities, the maximum interfacial temperature difference approaches zero even with high values of the thermal boundary resistance. Thermal conductivities and heat capacities are much more important in characterizing transient heat transfer through the imperfect interface than the phase lags of the heat flux and temperature gradient.     

TRANSIENT NATURAL CONVECTION IN A CAVITY WITH WALLS OF FINITE THICKNESS

Numerical studies are made of transient natural convection in a square cavity. The top and bottom end walls are thermally insulated. The vertical solid side walls are of finite thickness and of finite thermal conductivity. Flow is driven, from the motionless isothermal initial state, by impulsively increasing (decreasing) the temperature at the outer surface of one (the other) vertical side wall. Numerical solutions art sought to the time-dependent Navier-Stokes equations for the fluid and the solid regions. The ratios of thermophysical properties between solid and fluid are the significant parameters. As the thermal capacity ratio increases, the development of flow in the fluid region is retarded. The conductive and convective timescales are estimated. The effects of the thermal conductivity ratio and of the thickness of the side wall are delineated. The effect of the system Rayleigh number on transient heat transport is analyzed. The applicability of the approximate one-dimensional thermal conductance model to the transient features is scrutinized.     

NUMERICAL ANALYSIS OF CONVECTIVE HEAT TRANSFER IN THE ENTRANCE REGION OF CUSPED DUCTS

Abstract

This study presents the numerical solution of connective heat transfer in the thermal entrance region of cusped ducts. These ducts are formed contiguously by assembling three, four, or five cylindrical rods having the same diameter next to each other. The ducts are also subjected to a constant wall temperature. The solution to the discretization of these duct geometries is obtained by using the numerically generated boundary fitted coordinate system. According to this method, the complex domain in the physical plane is transformed into a regular square domain in the computational plane. The finite difference method based on the control volume is then used to discretize the transformed governing equation. To prove the validity of the results, the present method is also used to obtain the convective heat transfer solution in the entrance region of square and equilateral triangular ducts. Comparison of the results for square and equilateral triangular ducts with available data published in the open literature gives excellent agreement. The representative curves illustrating variations of the bulk temperature and Nusselt numbers with pertinent parameters are plotted for the three different duct geometries.     

Conduction-combined forced and natural convection in lid-driven enclosures divided by a vertical solid partition

Numerical simulations of the conduction-combined forced and natural convection (mixed convection) heat transfer and fluid flow have been performed for 2-D lid-driven square enclosure divided by a partition with a finite thickness and finite conductivity. Left vertical wall of enclosure has two different orientations in positive or negative vertical coordinate. Buoyancy forces are taken into account in the system. Horizontal walls are adiabatic while two vertical walls are maintained isothermal temperature but the temperature of the left moving wall is higher than that of the right stationary wall. Thus, heat transfer regime between moving lid and partition is mixed convection. Conduction occurs along the partition. And, pure natural convection is formed between the partition and the right vertical wall. This investigation covers a wide range of Richardson number which is changed from 0.1 to 10, thermal conductivity ratio varies from 0.001 to 10. It is observed that higher heat transfer was formed for higher Richardson number for upward moving wall for all values of thermal conductivity ratio. When forced convection becomes effective, the orientation of moving lid becomes insignificant. Heat transfer is a decreasing function of increasing thermal conductivity ratio for all cases and Richardson numbers.