Heat Transfer Analysis of Functionally Graded Hollow Cylinders Subjected to an Axisymmetric Moving Boundary Heat Flux

The transient heat transfer analysis of functionally graded (FG) hollow cylinders subjected to a distributed heat flux with a moving front boundary on its inner surface is presented. The heat flux is assumed to be axisymmetric, and its front boundary moves along the axis of the cylinder. A method composed of the finite element and differential quadrature methods is employed to discretize the governing equations in the spatial domain. After demonstrating the convergence and accuracy of the method, the effects of different parameters on the temperature distribution and time history of the temperature at different points of FG cylinder are investigated.     

Flow and surface heat transfer analysis of a square cylinder in turbulent cross-flow

Flow passing a heated square cylinder is investigated using a hybrid LES-RANS approach on unstructured grids at a moderate Reynolds number of 22, 050. The effects of inflow turbulence on the flow field as well as surface convective heat transfer are studied by adopting a grid-based random-number method (GRM). Validation of the GRM method is carried out by generating and simulating a decaying homogeneous isotropic turbulent flow. Analysis of the turbulent quantities and comparisons with the Synthetic Coherent Eddy Method (SCEM) suggest that the cheaper GRM is able to generate good quality inflow turbulence, despite a longer transition region is required. Studies of the heated square cylinder in crossflow show that the inflow turbulence results in an early breakup of the shear layer, which leads to further effects on the vortex shedding and surface heat transfer. The surface convective heat transfer is increased with inflow turbulence, especially on the front, top and bottom surfaces, while limited influence is found on the rear surface. It is shown by the spectra that the effects of the inflow turbulence mainly focus on the turbulent shear layers, as well as heat transfer of the corresponding surfaces.     

Immersed boundary method for the simulation of flows with heat transfer

In the present paper a direct heat source scheme is proposed to let the temperature at the immersed boundary satisfy the temperature Dirichlet boundary condition. And the explicit interactive process of the direct heat source scheme called multi-direct heat source scheme is applied to ensure the satisfaction of the temperature Dirichlet boundary condition at the immersed boundary. The second-order spacial accuracy of the solver is confirmed by simulating the Taylor–Green vortices. The simulations of natural convection between concentric cylinders, and flow past a stationary circular cylinder are conducted to validate the accuracy of present method on solving heat transfer problems. And the computation of flow past a staggered tube bank with heat transfer is conducted to verify the capability of present method on solving complex geometries problems.     

Study of mixed convection in an annular vertical cylinder filled with saturated porous medium,using thermal non-equilibrium model

The present study deals with numerical investigation of effects of different parameters on enhancement or retardation of the heat transfer rate in an annular vertical cylinder filled with saturated porous medium. The heat transfer is assumed to take place by mixed convection mode. The thermal non-equilibrium approach is considered. The inner surface of the annular cylinder is maintained at constant wall temperature whereas the outer surface remains at ambient temperature. The governing partial differential equations are solved using finite element method. The results are discussed for the effects of Peclet number, interphase heat transfer co-efficient and thermal conductivity ratio.     

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.     

Heat transfer in a conical cylinder with porous medium

In this paper, numerical study of heat transfer in a conical annular cylinder fixed with saturated porous medium is presented. The heat transfer is assumed to take place by natural convection and radiation. The inner surface of conical cylinder is maintained at uniform wall temperature. The governing partial differential equations are non-dimensionalised using suitable non-dimensional parameters and then solved by using finite element method. The porous medium is divided using triangular elements with uneven element size. A computer software is used to solve the coupled momentum and energy equations in an iterative manner. The results are discussed for various values of geometric and physical parameters of porous medium with emphasis on cone angle of the cylinder. It is seen that the cone angle plays a vital role in heat transfer from the hot surface to porous medium.     

柴油机气缸内辐射传热模型研究历程与展望

综述了国内外内燃机气缸内辐射理论研究的进展，阐述了目前研究的难点和关键总是指出作为气缸内传热的一种重要途径，气缸内辐射传热的研究工作需要进一步深入和加强。     

Numerical simulation of heat transfer and fluid flow past a rotating isothermal cylinder – A LBM approach

In this paper, a viscous fluid flowing past a rotating isothermal cylinder with heat transfer is studied and simulated numerically by the lattice Boltzmann method (LBM). A numerical strategy for dealing with curved and moving boundaries of second-order accuracy for both velocity and temperature fields is proposed and presented. The numerical strategy and method are validated by comparing the present numerical results of flow without heat transfer with those of available previous theoretical, experimental and numerical studies, showing good agreements. On this basis, the convective heat transfer performance in such rotational boundary environments is further studied and validated; the numerical results are reported in the first time. The effects of the peripheral-to-translating-speed ratio, Reynolds number and Prandtl number on flow and heat transfer are discussed in details.     

A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model

This work uses a thermal non-equilibrium model to study the free convection boundary layer flow driven by temperature gradients near a permeable horizontal cylinder of elliptic cross-section with constant wall temperature in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar boundary layer equations. The transformed boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt numbers are presented as functions of the porosity scaled thermal conductivity ratio, the heat transfer coefficient between solid and fluid phases, the transpiration parameter, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). An increase in the porosity scaled thermal conductivity ratio or the heat transfer coefficient between the solid and fluid phases increases the heat transfer rates. Moreover, the use of suction (positive transpiration parameter) tends to increase the heat transfer rates between the porous medium and the surface.     

A Markov Chain Monte Carlo-Metropolis Hastings Approach for the Simultaneous Estimation of Heat Generation and Heat Transfer Coefficient from a Teflon Cylinder

This paper reports the use of Markov Chain Monte Carlo (MCMC) and Metropolis Hastings (MH) approach, to solve an inverse heat transfer problem. Three-dimensional, steady state, conjugate heat transfer from a Teflon cylinder of dimensions 100 mm diameter and 100 mm length with uniform volumetric internal heat generation is considered. The goal is to estimate volumetric heat generation and heat transfer coefficient, given the temperature data at certain fixed location on the surface of the cylinder. The internal volumetric heat generation is specified as input and the temperature and heat transfer coefficient values are obtained by a numerical solution to the governing equation. The temperature values also depend on heat transfer coefficient which is obtained by solving Navier–Stokes equation to obtain flow information. In order to reduce the computational cost, a neural network is trained from the computational fluid dynamics simulations. This is posed as an inverse problem wherein volumetric heat generation and heat transfer coefficient are unknown but the temperature data is known by conducting experiments. The novelty of the paper is the simultaneous determination of volumetric heat generation and heat transfer coefficient for the experimentally measured steady-state temperatures from a Teflon cylinder using MCMC-MH as an inverse model in a Bayesian framework and finally, the estimates are reported in terms of mean, maximum a posteriori, and the standard deviation which is the uncertainty associated with the estimated parameters.     

A novel effective approach for solving nonlinear heat transfer equations

In this paper, a novel analytic technique, namely the Laplace transform new homotopy perturbation method (LTNHPM), is applied for solving the nonlinear differential equations arising in the field of heat transfer. This approach is a new modification to the homotopy perturbation method based on the Laplace transform. Unlike the previous approach implemented by the present authors for these problems, the present method does not consider the initial approximation as a power series. The nonlinear convective–radiative cooling equation and nonlinear equation of conduction heat transfer with the variable physical properties are chosen as illustrative examples. The exact solution has been found for the first case and for the others; results with remarkable accuracy have been achieved which verify the efficiency as well as accuracy of the presented approach. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20411     

Thermal boundary condition effects on forced convection heat transfer

We propose a numerical solution of an adjoint problem of forced convection heat transfer to evaluate the mean heat transfer characteristics under arbitrary thermal boundary conditions. Using the numerical solution of the adjoint problem under the Dirichlet condition, which can be computed by slightly modifying a conventional heat transfer code, we obtain an influence function of local surface temperature on total heat transfer. As a result, the total heat transfer for arbitrary surface temperature distributions can be calculated by the influence function. Similarly, using the numerical solution of the adjoint problem under the Neumann condition, we can also obtain an influence function of the local heat flux on the mean surface temperature. The influence functions for a circular cylinder and for an in-line square rod array are presented to illustrate the capability of this method. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 227–238, 1999     

On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part II: Application to test problems

ABSTRACT

In part I of this paper, a new physical-based computational approach for the solution of convection heat transfer problems on co-located non-orthogonal grids in the context of an element-based finite volume method was discussed. The test problems are presented here, in part II of the paper. These problems include five steady two-dimensional convection heat transfer problems. In all test cases, the convergence history, the required under-relaxations for the iterative solution of the linearized equations, and the order of accuracy of the method are discussed and the streamlines as well as isotherms are presented. The computational results show that the proposed method is second order accurate and might occasionally need mild under-relaxation in relatively complex problems. Excellent match between the computational results and the corresponding reliable published results is observed.     

Forced convection heat transfer from a heated circular cylinder with arbitrary surface temperature distributions

A Fredholm-type boundary integral expression for evaluation of the forced convection heat transfer from an object with arbitrary surface temperature distributions is proposed. The Fredholm kernel function for a heated circular cylinder was calculated by numerical simulation of the forced convection fields, and then generalized heat transfer coefficients for arbitrary surface temperature distributions were defined. By use of the generalized heat transfer coefficients, it is shown that the difference in local heat transfer characteristics between the case of an isothermal cylinder and that of a uniform heat flux one can be interpreted only as the difference of the surface temperature distributions. Moreover, the mechanism of the effect of the surface temperature distribution on the characteristics of forced convection heat transfer from a cylinder is clarified in detail through the generalized heat transfer coefficients. © 1999 Scripta Technica, Heat Trans Asian Res, 28(6): 484–499, 1999     

MODIFIED CONDUCTION SHAPE FACTORS FOR ISOTHERMAL BODIES EMBEDDED IN A SEMI-INFINITE MEDIUM

Numerical finite-element method calculations were performed for isothermal surfaces embedded in a semi-infinite medium with convection boundary conditions. A modified shape factor was defined that combines the conduction heat transfer in the medium and the convection to the environment, with the geometrical characteristics of the problem. Infinite finite elements are used; these form the last layer of elements in the infinite directions. The modified shape factors for a sphere and for a long horizontal cylinder are presented in graphs and correlations, both using nondimensional parameters. The heat flux distribution on the surface of the body and the temperature and heat transfer on the surface of the medium are also presented.     

An embedding finite element analysis of heat transfer on the surface of circular cylinders in flow

The present study establishes an embedding finite element method appropriate for solving primitive variable forms of the Navier–Stokes equations and energy equation in a complex physical domain. The stationary solid obstacle in the flow domain is embedded in a non-uniform Cartesian grid and the governing equations are calculated through a finite element formulation. A compact interpolating scheme near the immersed boundaries is used to ensure the accuracy of the solution in the cut cells. We have developed a numerical algorithm based on the operator splitting technique, balance tensor diffusivity (BTD), Runge–Kutta time-stepping method, and a bi-conjugate gradient iterative solver. Three numerical examples are chosen to test the accuracy and flexibility of the proposed scheme. Simulation of flow past a stationary circular cylinder is conducted to validate the accuracy of the present method for solving heat transfer problems. Flow over circular cylinders in a tandem arrangement and a staggered tube bank with convective heat transfer is computed to demonstrate the model’s ability to handle complex geometries.     

PREDICTION OF SURFACE RADIATIVE HEAT TRANSFER USING THE MODIFIED DISCRETE TRANSFER METHOD

An ideal surface radiation model applied in many manufacturing and materials processing systems must be able to take into account specular, spectral, and shadowing effects with complex geometries, and must be computationally efficient to permit its inclusion in the fluid flow and heat transfer models. In this study, a novel surface radiative heat transfer method is developed to meet all these practical needs. The present model is based on the discrete transfer method (DTM). A direct application of the DTM to modeling surface radiative heat transfer may result in a large error due to strong ray effects. In order to eliminate these ray effects, the DTM is modified by considering radiation contribution from all surface cells intercepted by a control angle. Calculation of these surface cell areas represents one of the most important tasks in the modified DTM (MDTM), and it is described in detail in this study. To investigate the accuracy and efficiency of the MDTM, three benchmark problems covering different geometric and boundary conditions are considered, and the present solution is compared with the solutions from the exact approach, the DTM, and discrete ordinates method (DOM). For each problem, the accuracy of the MDTM, DTM, and DOM appears to be affected by the angular discretization. For a reasonable fine angular discretization, the solutions from the MDTM and DOM match the exact solution very well, while the solution from the DTM usually shows strong ray effects. The CPU times spent on the MDTM and DTM are very similar, but they are usually orders of magnitude less than that for the DOM. The present study indicates that the MDTM is not only accurate but also very efficient for modeling complicated surface radiation problems. Such a model will greatly benefit the simulation of many manufacturing and materials processing systems.     

Spectral relaxation method analysis of Casson nanofluid flow over stretching cylinder with variable thermal conductivity and Cattaneo–Christov heat flux model

This article deals with non‐Newtonian Casson nanofluid flow and heat transfer over stretching cylinder in a porous medium. The mode of heat transfer is presented considering temperature‐dependent thermal conductivity by integrating the Cattaneo–Christov heat flux and mass flux models. Boundary layer theory is applied to develop the governing partial differential equations from the physical problem. Employing proper similarity transformation, the governing boundary layer equations are transformed into dimensionless system of nonlinear ordinary differential equations. Then, the resulting problem is numerically solved by means of spectral relaxation method. The convergence analysis of the proposed numerical scheme is presented via a table, which confirms almost the 10th order of approximation is enough for the convergence of the skin friction coefficient, local heat transfer, and mass transfer rates. The effects of various embedded parameters on velocity, temperature, and concentration profiles as well as skin friction coefficient, surface heat and mass transfer rates are examined through graphs and tables. The findings reveal that the growth of permeability and velocity slip parameters appears to decelerate the velocity distributions of fluid. Thermal boundary layer thickness tends to develop with greater values of permeability and Brownian motion parameters. Also, the local heat transfer rate is less with Fourier's law of heat conduction than Cattaneo–Christov heat flux model. Furthermore, the validity and accuracy of the present result is checked with the available literature, and very sound agreement has been obtained.