Effects of an unsteady thermal boundary condition on forced convection heat transfer

A numerical analysis based on adjoint formulation of unsteady forced convection heat transfer is proposed to generally evaluate effects of the thermal boundary condition on the heat transfer characteristics. A numerical solution of the adjoint problem enables us to predict the heat transfer characteristics, such as the total heat transfer rate or the temperature at a specific location, when the thermal boundary conditions change arbitrarily with time. Moreover, using the numerical solution of the adjoint problem, we can obtain the optimal thermal boundary conditions in both time and space to maximize the heat transfer at any arbitrary time. Numerical solutions of the adjoint problem in a lid‐driven cavity are presented to illustrate the capability of the present method. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(3): 237–247, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10032     

Influence of thermal and flow boundary perturbations on convection heat transfer characteristics: Numerical analysis based on adjoint formulation

A numerical approach based on adjoint formulation of convection heat transfer is proposed to predict the change of heat transfer characteristics for arbitrary thermal and flow boundary perturbations. In order to obtain the adjoint system of the convection heat transfer problem, we formally linearize the governing equations by the perturbation method and then derive the adjoint system for the perturbation system. As a result, it is shown that the numerical solutions of the base and the adjoint problems enable us to predict the changes of heat transfer characteristics, such as the change of total heat transfer rate or the change of temperature at a specific location, when the thermal and flow boundary conditions are perturbed. An application example is presented to demonstrate the proposed method. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 1–12, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10065     

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     

Analysis of the Impact of Nonlinear Heat Transfer Laws on Temperature Distribution in Irradiated Biological Tissues: Mathematical Models and Optimal Controls

In this paper, we consider nonlinear control problems governed by some generalized transient bioheat transfer-type models with the nonlinear Robin boundary conditions. The control estimates the blood perfusion rate, the heat transfer parameter, the distributed energy source terms, and the heat flux due to the evaporation, which affect the effects of thermal physical properties on the transient temperature of biological tissues. The result can be very beneficial for thermal diagnostics in medical practices, for example, for laser surgery, photo and thermotherapy for regional hyperthermia often used in treatment of cancer. First, the mathematical models are introduced and the existence, uniqueness, and regularity of a solution of the state equation are proved as well as the stability and maximum principle under extra assumptions. Afterwards, the optimal control problem is formulated in order to control the online temperature given by radiometric measurement. We prove that an optimal solution exists and obtain necessary optimality conditions. Some strategy for numerical realization based on the adjoint variables are provided.      

Transient analysis of energy storage in a thermally stratified water tank

A one-dimensional transient heat conduction model to describe the decay of the thermocline in a stratified water tank is presented. The problem is formulated as an initial boundary value problem and the resulting governing equations in the fluid and in the storage wall are solved numerically to obtain the temperature profiles in the wall and the fluid. The formulation considers the axial conduction of heat, both in the fluid and in the solid wall. The mixing parameters introduced in the boundary conditions at the top and bottom of the tank in the fluid region account for mixing due to inlet and outlet streams with the stored fluid. The model is applicable to the storage of both hot and chilled water. The model is validated with experimental data from the literature. The parameters that influence the operation of a stratified thermal energy storage for both heat and cool storage are examined. © 1998 John Wiley & Sons, Ltd.     

Second‐law analysis and optimization of microchannel flows subjected to different thermal boundary conditions

Entropy generation and transfer in microchannel flows were calculated and analyzed for different thermal boundary conditions. Due to the small flow cross‐sectional area, fluid temperature variation in the lateral direction was neglected and a laterally lumped model was developed and used in the first‐ and second‐law analyses. Since the Peclet numbers of microchannel flows are typically low, heat conduction in the flow direction was taken into consideration. Computed fluid temperature and entropy generation rate were cast into dimensionless forms, thus can be applied to different fluids and channels of different sizes and configurations. Local entropy generation rate was found to be only dependent upon the temperature gradient in the flow direction. The optimization results of microchannel flows exchanging heat with their surroundings indicate the optimal fluid temperature distribution is a linear one. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimal homotopy asymptotic method for heat transfer in hollow sphere with robin boundary conditions

In this article, we have investigated heat transfer from a hollow sphere using a powerful and relatively new semi‐analytic technique known as the optimal homotopy asymptotic method (OHAM). Robin boundary conditions are applied on both the inner and outer surfaces. The effects of Biot numbers, uniform heat generation, temperature‐ dependent thermal conductivity, and temperature parameters on the dimensionless temperature and heat transfer are investigated. The results of OHAM are compared with a numerical method and are found to be in good agreement. It is shown that the dimensionless temperature increases with an increase in Biot number at the inner surface and temperature and heat generation parameters, whereas it decreases with an increase in the Biot number at the outer surface and the dimensionless thermal conductivity and radial distance parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 124‐133, 2014; Published online 20 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21067     

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.     

SENSITIVITY ANALYSIS AND OPTIMAL DESIGN FOR STEADY CONDUCTION PROBLEM WITH RADIATIVE HEAT TRANSFER

ABSTRACT

A steady heat conduction problem is considered, that is described by the heat conduction equation and the thermal boundary conditions (i.e., Dirichlet, Neumann, Henkel, and radiation conditions on the external boundary, and radiation condition on the hole boundary). An arbitrary behavioral functional is defined and its first-order sensitivity is derived using both the direct and the adjoint approaches. The shape optimization problem is next formulated and two optimization functionals are discussed. The simple numerical example is presented.     

A study of thermal performance with frosting under forced convection on a flat plate: Prediction of frost growth using nonhomogeneous property

The purpose of this study is the evaluation of thermal performance of a heat exchanger with frosting and decision of optimal defrosting cycle. Because the increase of flow resistance is the principal factor of a drop of heat transfer performance with frosting, thermal performance characteristics were examined. Based on those experimental results, we proposed a one‐dimensional nonhomogeneous frost growth model, and compared it with the experimental data in time and space. In a nonhomogeneous model with the frost property distribution taken into account, density distribution similar to the experimental result can be predicted. It is possible to make prediction closer to the experimental result compared with the conventional homogeneous model with respect to the temporal variation of frost height. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(8): 674–689, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10122     

MHD Flow and Heat Transfer of a Dusty Fluid Over a Stretching Hollow Cylinder with a Convective Boundary Condition

In this study, we deal with the problem of a steady two‐dimensional magnetohydrodynamic (MHD) flow of a dusty fluid over a stretching hollow cylinder. Unlike the commonly employed thermal conditions of constant temperature or constant heat flux, the present study uses a convective heating boundary condition. The multi‐step differential transform method (multi‐step DTM), one of the most effective methods, is employed to find an approximate solution of the system of highly nonlinear differential equations governing the problem. Comparisons are made between the results of the proposed method and the numerical method in solving this problem and excellent agreement has been observed. The influence of important parameters on the flow field and heat transfer characteristics are presented and discussed in detail. The results show that both the thermal boundary layer thickness and the heat transfer rate at the wall increases with increasing Biot number Bi, while it has no effect on the skin friction coefficient. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 221–232, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21073     

Flow characteristics and heat transfer performances of a semi-confined impinging array of jets: effect of nozzle geometry

The flow and heat transfer characteristics of confined jet array impingement with crossflow is investigated. Discrete impingement pressure measurements are used to obtain the jet orifice discharge flow coefficient. Digital particle image velocimetry (DPIV) and flow visualization are used to determine the flow characteristics. Two thermal boundary conditions at the impinging surface are presented: an isothermal surface, and a uniform heat flux, where thermocouple and thermochromic liquid crystal methods were used, respectively, to determine the local heat transfer coefficient. Two nozzle geometries are studied, circular and cusped ellipse. Based on the interaction with the jet impingement at the surface, the crossflow is shown to influence the heat transfer results. The two thermal boundary conditions differ in overall heat transfer correlation with the jet Reynolds number. Detailed velocity data show that the flow development from the cusped ellipse nozzle affects the wall region flow more than the circular nozzle, as influenced by the crossflow interactions. The overall heat transfer for the uniform heat flux boundary condition is found to increase for the cusped ellipse orifice.     

DNS of turbulent heat transfer in a channel flow with a varying streamwise thermal boundary condition

Direct numerical simulation (DNS) was performed for the turbulent heat transfer in a channel flow. In the present study, the effect of the thermal boundary condition was examined. DNS was carried out for varying streamwise thermal boundary conditions (Re_τ = 180) with Pr = 0.71 to obtain statistical mean temperatures, temperature variances, budget terms, and time scale ratios. The results obtained indicate that the time scale ratio varies along the stream direction. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(4): 265–278, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20114     

An experimental study of heat transfer enhancement with a pulsating flow

A pulsating flow in a pipe was experimentally investigated to determine the effect of pulsation on the rate of heat transfer. The influence of hydrodynamic parameters and characteristics of the pulsation on heat transfer was carefully studied. In order to adjust the pulsating parameters, a self‐oscillator was designed so the length of the resonator and the length of the outlet nozzle could be adjusted. The results show that the heat transfer rate is strongly affected by both the hydrodynamic parameters and the configuration of the resonator. With the increase of the flow rate of the liquid and the length of the chamber, heat transfer is enhanced. There is an optimal length at which the heat transfer enhancement attends to the best. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(5): 279–286, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20020     

高孔隙率泡沫金属相变材料储能、传热特性

以高孔隙率泡沫金属材料作为骨架制备而成的新型复合相变储能材料的导热系数将大大高于相变材料本身的导热系数,在储能过程中具有更好的传热效果。给出了较通用的高孔隙率泡沫金属材料等效导热系数的估算公式,并利用准稳态方法建立了复合相变材料在凝固过程的数值模型,对其凝固过程的传热特性进行了理论分析。以铝—石蜡和铜—石蜡复合材料作为研究对象。分析表明,采用复合储能材料可以使得其传热性能得到很大提高,但是也会使复合材料的储能能力有所降低。提出了一种平衡储能能力和传热性能的方法,当泡沫金属处于平衡孔隙率时,在传热性能得到极大提高的同时也使得其储能能力降低不多。同时,分析得到了外部换热环境对储能能力、传热性能以及平衡孔隙率的影响,即较大的对流换热时,若要取得适当的储能能力和传热性能,则需要较小的孔隙率。     

Meshless element free Galerkin method for unsteady nonlinear heat transfer problems

In this paper, meshless element free Galerkin (EFG) method has been extended to obtain the numerical solution of nonlinear, unsteady heat transfer problems with temperature dependent material properties. The thermal conductivity, specific heat and density of the material are assumed to vary linearly with the temperature. Quasi-linearization scheme has been used to obtain the nonlinear solution whereas backward difference method is used for the time integration. The essential boundary conditions have been enforced by Lagrange multiplier technique. The meshless formulation has been presented for a nonlinear 3-D heat transfer problem. In 1-D, the results obtained by EFG method are compared with those obtained by finite element and analytical methods whereas in 2-D and 3-D, the results are compared with those obtained by finite element method.     

Heat Transfer in a Casson Rheological Fluid from a Semi‐infinite Vertical Plate with Partial Slip

The laminar boundary layer flow and heat transfer of Casson non‐Newtonian fluid from a semi‐infinite vertical plate in the presence of thermal and hydrodynamic slip conditions is analyzed. The plate surface is maintained at a constant temperature. Increasing velocity slip induces acceleration in the flow near the plate surface and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in the Casson rheological parameter acts to elevate considerably the skin friction (non‐dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures, however, are very slightly decreased with increasing values of Casson rheological parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21115     

Freezing of Water in a Slab with Boundary Conditions of the Third Kind

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Heat transfer enhancement by crossflow‐induced vibration

A new method of heat transfer enhancement by water crossflow‐induced vibration is presented. A heat transfer element which involves elastic tube bundles has been designed. This system has excellent response characteristics of vibration to the crossflow. A triangular pole device for producing pulsating flow was adopted. This device can induce vibration in a fixed range of frequencies and has a profound influence on heat transfer augmentation. For the constant heat flux boundary condition, experiments are carried out on the heat transfer characteristics of elastic tube bundles augmented by flow‐induced vibration in a water crossflow. Compared with static tube bundles, the out‐tube average convective heat transfer coefficients of the elastic tube bundles are increased by 100–150% under the condition of crossflow‐induced vibration. Dimensionless equations describing the outside heat transfer coefficient for the elastic tube bundles were acquired. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(4): 211–218, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20012     

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.