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     

Reverse computation of forced convection heat transfer for optimal control of thermal boundary conditions

A reverse computation based on adjoint formulation of forced convection heat transfer is proposed to obtain the optimal thermal boundary conditions for heat transfer characteristics; for example, a total heat transfer rate or a temperature at a specific location. In the reverse analysis via adjoint formulation, the heat flow is reversed in both time and space. Thus, using the numerical solution of the adjoint problem, we can inversely predict the boundary condition effects on the heat transfer characteristics. As a result, we can obtain the optimal thermal boundary conditions in both time and space to control the heat transfer at any given time. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(3): 161–174, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20002     

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     

Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder

This paper presents a numerical analysis of the flow and heat transfer characteristics of forced convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with wall conduction and buoyancy effects. The non-linear formulation governing equations and their associated boundary conditions are solved using the cubic spline collocation method and the finite difference scheme with a local non-similar transformation. This study investigates the effects of the conjugate heat transfer parameter, the Richardson number, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The effect of wall conduction on the thermal and the flow fields are found to be more pronounced in a system with a greater buoyancy effect or Prandtl number but is less sensitive with a greater micropolar material parameter. Compared to the case of pure forced convection, buoyancy effect is found to result in a lower interfacial temperature but higher the local heat transfer rate and the skin friction factor. Finally, compared to Newtonian fluid, an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

Effect of tube inclination on laminar convection in uniformly heated tubes for flat-plate solar collectors

A numerical study using a combination of boundary vorticity method and line iterative relaxation method is carried out to determine the free convection effects on fully developed upward laminar forced flow in uniformly heated inclined tubes. The combined free and forced laminar convection for water with the inclined tube configuration in the low Reynolds number flow regime has practical application in flat-plate solar collectors for water heating. The tube inclination or gravitational force orientation effects on flow and heat transfer characteristics are clarified and show that in high Rayleigh number regime the tube orientation effect has considerable influence on the results, particularly in the neighborhood of horizontal direction. The numerical results show that the perturbation analysis in terms of power series of Rayleigh number is invalid for the present problem and reveal further that a maximum value for Nusselt number does not exist for any tube inclination angle with given values of the dimensionless parameters which is clearly contrary to the result from perturbation solution.     

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     

Heat Transfer from Pulsating Laminar Impingement Slot Jet on a Flat Surface with Inlet Velocity: Sinusoidal and Square Wave

Heat transfer from a pulsating laminar impingement slot jet on a flat surface was investigated numerically and experimentally. Inlet velocity was considered sinusoidal velocity and square wave velocity. Experimental studies were done only for the sinusoidal velocity state. An inverse heat conduction method, conjugated gradient method with adjoint equation, was used for the experimental estimation of the local heat transfer coefficient along the target surface. Effect of the square wave velocity of the laminar impingement slot jet was studied numerically. The results show pulsations in flow change flow patterns and the thermal boundary layer thickness because of the newly forming thermal boundary layer is extremely small each time the flow is resumed. Heat transfer rate in this state enhances due to pulsating inlet velocity in comparison with steady state. Heat transfer increases with increasing pulsation amplitude. Enhancement in mean heat transfer on the target plate for sinusoidal velocity is rather than square wave velocity.     

非均匀热流下水平管内混合对流大涡模拟研究

针对以槽式太阳能集热器为背景的高密度、高度非均匀热流下水平管内的混合对流换热问题,采用大涡模拟方法,研究了热流密度非均匀性对水平管内混合对流瞬态涡结构、脉动强度、湍流热通量及局部平均壁温的影响;揭示了非均匀热流下自然对流对管内湍流特性的影响规律;提出了适用于不同热边界条件下管内混合对流换热的强化措施。结果表明:均匀热流时,自然对流会抑制管顶部的湍流脉动,使流动层流化,造成传热能力局部恶化;非均匀热流时,随着自然对流的增强,近壁面速度脉动强度先减小后增大,二次流逐渐增强,换热能力逐渐提高,故管内换热能力受湍流脉动与二次流协同影响;在自然对流影响下,均匀加热时管顶部可采用针对层流的强化换热措施,非均匀加热时需着重提高管底部高热流区域的湍流脉动与涡强度。     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

Determining boundary heat flux profiles in an enclosure containing solid conducting block

A numerical implementation of estimating boundary heat fluxes in enclosures is proposed in the present work. Particularly, the flow field is dynamically coupled with the heat convection in the fluid and the heat conduction in the solid domain. An iterative conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined. In this approach, no a priori information is needed about the unknown function to be determined. Numerical solutions are obtained for the case of a square enclosure centrally-inserted with a solid block and subjected to an unknown heat flux on one side and to known conditions on the remaining sides. Fluid and heat transports are visualized by the streamlines and heatlines respectively, which are evidently affected by the thermal Rayleigh number, solid body size and thermal conductivity of solid phase, and the functional form of the imposed heat flux. The accuracy of the heat flux profile estimations is shown to depend strongly on the thermal Rayleigh number, body size and relative thermal conductivity of the solid material. Effects of functional form of the unknowns, sensors number and position, and measurement errors on the accuracy of estimation are also investigated. The present work is significant for the flow control simultaneously involving the heat conduction and convection.     

LIMITATION OF BOUNDARY LAYER ANALYSES FOR BUOYANT CONVECTION IN STABLY STRATIFIED FLUIDS

Vertical buoyant convection in stably stratified fluids is revisited. The limitation of boundary layer analyses for such flows is quantified. This is accomplished by comparing the results of the present boundary layer numerical study with the published experimental measurements, and full numerical simulations. It is shown that boundary layer analysis underpredicts the heat transfer rates. This is explained with reference to the flow and thermal fields. The boundary layer results are shown to be inadequate for such characteristics as flow reversal and temperature defects. The underlying physical mechanisms are discussed.     

Inverse determination of building heating profiles from the knowledge of measurements within the turbulent slot-vented enclosure

Slot ventilated enclosure flows have been simulated, respectively in displacement ventilation and mixed ventilation covering from the forced convection dominated flow to the natural convection dominated flow. Direct convection simulation together with the turbulent streamlines and turbulent heatlines demonstrate that the enclosure flow pattern, indoor thermal level and heat transfer potential will depend on the interactions of external forced flow and thermal buoyancy driven flows, i.e., Reynolds number and Grashof number. In subsequent inverse convection modeling, the inverse determination of enclosure wall heat flux profiles was conducted by the use of adjoint methodology, in which the direct, sensitivity and adjoint problems are formulated and solved by finite volume method. The effects of the supplying air flow rate, thermal source strength, ventilation mode, flux functional forms, and the measurement errors on the accuracy of inverse turbulent convection estimation have been investigated. The inverse solutions of turbulent convections are of low level accuracy as the flow becomes thermal-driven turbulent flows, and they deteriorate as the noise levels increase. This work is of fundamental importance for the room air flow design and measurements involving the turbulent thermal convections.     

NATURAL CONVECTION IN VERTICAL PARALLEL PLATES WITH AN UNHEATED ENTRY OR UN HEATED EXIT

This study aims to investigate the effects of the unhealed entry or unheated exit section on the free convection heat transfer in airflow in vertical parallel plate channels resulting from the thermal boundary conditions of uniform heat flux (VHF) and uniform wall temperature (UWT). Results of average Nusselt number and dimensionless volume flow rate are presented in terms of the ratio of the length of heated section to the full channel length and a Rayleigh number, ranging from the limit for the fully developed flow to that for single-plate behavior. Analytical equations for dimensionless volume flow rate and average Nusselt number for both unheated restrictions and both thermal boundary conditions have been developed for the fully developed flow limit. The numerical solutions are shown to approach asymptotically the approximate solution for fully developed flow as the Rayleigh number approaches 1 or less. An important finding of the study is that an unheated exit characterizes greater total heat transfer and volume flow rate than an unheated entry does. The presence of the unheated entry or unheated exit severely affects the convection process, especially at low Rayleigh number. A notable effect of an unheated exit on convection characteristics was found for the case of UHF at high Rayleigh number.     

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.     

Flow of Microencapsulated Phase Change Material Slurry through Planar Spiral Coil

Forced convection cooling is an effective method in thermal management that relies mainly on dissipating heat by pumping heat transfer fluid (HTF) through the heat source. In this paper, we investigate the thermal properties enhancement of dielectric water as the HTF. To enhance the properties of the HTF, microencapsulated phase change materials (MPCM) will be added to the base fluid. The MPCMs are composed of phase change material (PCM) encapsulated with shell materials. The PCM inside the capsules may undergo a phase change. This leads to a significant heat gain and release. The numerical model is developed to solve for continuity, momentum, and heat transfer equations using the finite volume method. The behavior of the MPCM slurry in curved channels, generates unique patterns due to different viscosity values and the centrifugal forces. Our preliminary numerical data on MPCM slurry through planar spiral coil heat exchangers show the new patterns of velocity and heat transfer curves. The current paper studies the steady condition of laminar flow at different boundary conditions. The velocity and temperature profiles, heat transfer data with different mass fractions of MPCM additives to the base fluid, and their heat removal capabilities are quantified and discussed in detail.     

Fluid‐to‐fluid scaling of heat transfer to mixed convection flow of supercritical pressure fluids

Fluid‐to‐fluid scaling for supercritical heat transfer can effectively reduce the difficulty and cost of heat transfer experiments in supercritical boilers and supercritical water reactors and can reduce the number of experiments by converting experimental data of the model fluid to the prototype fluid in organic Rankine cycles. Currently, most existing scaling methods are only suitable for forced convection, while few are developed for mixed convection where buoyancy significantly affects the heat transfer. This paper attempts to extend the applicability of scaling method to mixed convection with the aid of computational fluid dynamic simulations. The scaling parameters were analyzed first and then the shear‐stress transport k‐ω model was used to analyze the supercritical heat transfer characteristics of water and R134a to provide further information for developing a dimensionless number. The results show that significant variations of properties and flow parameters occur in the layer of y⁺ = 5 to 100 and the axial velocity gradient in this layer changes in quite a similar manner to the wall temperature. Based on numerical results, the axial velocity gradient was used with a thermal resistance analogy to derive a new dimensionless number, Re^?0.9π_A , to scale the mass flux. Then, a set of fluid‐to‐fluid scaling laws were developed to predict the heat transfer to supercritical fluids. To validate the newly proposed scaling laws, well‐developed correlations were used for forced convection flow and a direct validation method was developed for buoyancy‐influenced flow. Results show that this new scaling method exhibits reasonable accuracy for both forced and mixed convection heat transfer with supercritical fluids.     

Numerical study of a nuclear fuel element dissipating fission heat into its surrounding fluid medium

The objective of the present work is twofold – the first to establish the criterion for the boundary layer solution to be accurate enough in the study of conjugate heat transfer problem associated with a rectangular nuclear fuel element washed by upward moving coolant and the second to predict the critical thermal performance characteristics of the fuel element with uniform volumetric energy generation. Accordingly, employing stream function–vorticity formulation, equations governing the steady, two-dimensional flow and thermal fields in the coolant are solved simultaneously with the steady, two-dimensional heat conduction equation for the fuel element using second-order accurate finite difference schemes. Keeping the Prandtl number constant at 0.005 for liquid sodium as coolant, numerical results are presented for wide range of aspect ratio, conduction–convection parameter, energy generation parameter and Reynolds number. It is found that for all value of aspect ratio greater than 15, numerical prediction using the boundary layer approximation based model is quite accurate enough. It is also concluded that other parameters being kept constant, the increase in the maximum fuel element temperature due to increase in aspect ratio beyond 15 is negligible. Further, it is found that a relatively higher value of conduction–convection parameter reduces the coolant pumping power requirement to a large extent.     

Thermal Radiation and Heat Source Effects on a MHD Nanofluid Past a Vertical Plate in a Rotating System with Porous Medium

This article studies the effect of thermal radiation on a MHD free convection flow of a nanofluid bounded by a semi‐infinite vertical plate with a constant heat source in a rotating frame of reference. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The dimensionless governing equations for this investigation are solved analytically using the regular perturbation method. The effect of various important parameters entering into the problem on velocity and temperature fields within the boundary layer are discussed for three different water‐based nanofluids such as Cu, Al₂O₃, and TiO₂ with the help of graphs. The predicted results clearly indicate that the presence of nanoparticles in the base fluid enhances the heat transfer process significantly. The present work shows the need for immediate attention in next‐generation solar film collectors, heat‐exchanger technology, material processing exploiting vertical surface, geothermal energy storage, and all those processes which are greatly exaggerated by heat‐enhancement concepts. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21101     

Conjugate Forced Convection Heat Transfer From a Heated Flat Plate of Finite Thickness and Temperature- Dependent Thermal Conductivity

In this paper, a conjugate forced convection heat transfer from a good conducting plate with temperature-dependent thermal conductivity is studied. The semi-analytical solution for the nonlinear integro-differential equation occurring in the problem is handled easily and accurately by implementing the differential transform method (DTM). The horizontal plate is heated with uniform heat flux at the lower surface while being cooled at the upper surface under laminar forced convection flow. A numerical approach is also performed via a finite-volume method to examine the validity of the results obtained by DTM. The results of DTM show closer agreement with the results of the numerical method than the results obtained by the perturbation method existing in the literature. It is concluded that for a good conducting plate with a finite thickness the distribution of the conjugate heat flux at the upper surface is significantly affected by the plate thickness. Moreover, we conclude that in the conjugate heat transfer case the temperature distribution of the plate is flatter than the one in the nonconjugate case.     

Melting of nano-enhanced phase change material in a cavity heated sinusoidal from below: Numerical study using lattice Boltzmann method

Natural convection and melting of ice as a phase change material dispersed with copper nanoparticles are numerically investigated. Square cavity filled with nano-mixture (Cu−ice) subjected to sinusoidal temperature distributions from the hot bottom boundary. The phase change process and heat transfer are formulated and solved using the enthalpy-based lattice Boltzmann method. Home-built numerical code is developed and validated. The effect of Rayleigh number (Ra = 10⁴, 10⁵, and 10⁶) and copper nanoparticle concentration (ϕ = 0%, 1%, 3%, and 5%) on the flow characteristics and thermal performance of NePCM during the melting process is examined. According to the numerical results, the melting and charging times decrease by increasing the Rayleigh number. It is also observed that increasing the volume fraction of nanoparticle decrease melting time by up to 10%.