The Effect of Plate Size on the Natural Convective Heat Transfer Intensity of Horizontal Surfaces

Abstract

Natural convective heat transfer from flat horizontal isothermal plates has been investigated for more than a century. In the present study, the influence of the size of the plate on the heat flux is investigated. Two ranges of the heat transfer intensity are proposed for this problem: for the plates with characteristic length smaller than 0.1–0.2 m, the heat transfer coefficient is inversely proportional to the plate width; for plates wider than 0.2 m, the heat flux is not influenced by the plate width. The explanation for the discrepancy between the two ranges of natural convective heat transfer based on analysis and comparison of experimental data available in the literature has been proposed.     

Numerical Simulation of Re-Entry Flow: Heat Flux Evaluation

Abstract

The problem of heat transfer in a four channel plate heat exchanger involving the effect of unsymmetrical heat transfer in the outer two channels is studied analytically and experimentally. An energy balance over a control volume yields the governing system of differential equations that has been solved exactly for the cases of parallel flow and counterflow to give the temperature distribution in the channels. The results show that zero or even reversed heat flow may be obtained at the middle plate of the heat exchanger. Expressions for the heat exchanger efficiency and the log-mean temperature difference correction factor in terms of the heat capacity rate ratio and the number of transfer units are presented. Experiments carried out with a counterflow plate heat exchanger show reasonable agreement between the experimentally observed and the theoretically calculated efficiencies and mean driving temperature differences.     

An Investigation of Capillary Flow Effect on Condensation Heat Transfer on a Grooved Plate

A simple model predicting the effect of capillary flows on the condensation heat transfer occurring on a vertical grooved plate is presented. The model includes the effect of capillary flows along the axial direction of the grooves and the direction from the apex to the cornered region of the groove. Numerical results indicated that the capillary flow induced by the capillary force significantly affects the condensation heat transfer, as does the plate height, groove width, and groove angle. In order to verify the theoretical prediction, an experimental investigation was conducted, and the theoretical prediction agrees well with the experimental data. Results of the investigation will assist in optimizing the condensation heat transfer performance in heat pipes.     

Continuous Monitoring of Whey Protein Fouling Using a Nonintrusive Sensor

Abstract

In this work, a nonintrusive device to monitor fouling of a plate heat exchanger is presented. This device is composed of a flat electrical resistance covering a thermocouple located on the external face of a tubular holding section. The tubular holding section is placed immediately after the investigated plate heat exchanger, constituting the heating zone for which fouling monitoring is required. The principle of detection consisted in following the evolution of the measured temperature with time when a fixed thermal heat flux imposed by the resistance is dissipated through the temperature sensor. The measured temperature is supposed to vary with time since the inner temperature on the inner surface of the holding tubular zone is linked to the fouling growth. It is shown that the device response is highly correlated to the fouling occurring in the plate heat exchanger and could be a promising way for monitoring fouling rate (cheap and easy to implement avoiding cleanability drawbacks).     

Validated Numerical Analysis of CaSO4 Fouling

In scaling experiments, the formation of fouling layers on heat transfer surfaces usually proceeds in a non-uniform manner. The result is a non-uniform layer, and hence a varying thermal resistance over the area covered with scale. Consequently, a non-uniform heat flux distribution results over the heat transfer surface. To evaluate the changes in the heat flow distribution resulting from a non-uniform scale layer, numerical calculations have been performed using a case where CaSO₄ scales form on a heated copper plate subjected to a shear flow. The calculated heat flux is used to calculate fouling resistances from measured temperatures. The results of the numerical calculations confirm that a non-uniform heat flux distribution occurs over the surface when the plate is partially covered with scale. Further, it is seen that the heat flux, the surface temperature, and the driving force all decrease with increase in scale accumulation.     

Dynamic Thermoelastic Response of a Heated Thin Composite Plate Using the Dual-Phase-Lag Heat Conduction Model

This paper investigates the dynamic thermoelastic response of a heated thin composite plate. The plate is composed of a dominant matrix domain and an insert domain. A step-function heat source is generated within the matrix domain, causing the heating of the whole plate. The dual-phase-lag heat conduction model is used to determine the thermal behavior of the plate in the form of the spatial and time variations of the temperatures in both domains. The temperature of the matrix is used to evaluate the thermoelastic behavior of the plate in the form of the induced displacements and thermal stresses. The Laplace transformation technique combined with the Rieman-sum method is used to calculate the temperatures. The finite difference method is used to solve the governing equation of plate deflection and then calculate the thermal stresses. The resulting thermal stresses are found to be compressive and follow the same behavior as that of the temperature.     

An exact analytical solution for fractional-order thermoelasticity in a multi-stacked elliptic plate

Abstract

Thermoelastic analysis of an isotropic homogeneous multi-stacked elliptical plate has been considered in this research. For which multi-layered plate is taken into consideration on a plane-parallel elliptic geometry perpendicular to the z-direction. The governing equations are considered in the context of time-fractional derivative of the order α with temperature distribution in each s layer of the stacked plate with time-dependent sectional heat supply on the lower and upper face. The multi-stacked profile consists of s discrete plates each of a different material with perfect thermal contact at each of its s-1 interface. The general solution, which perfectly satisfies the fundamental equation of heat conduction, is obtained using an integral transformation technique. It is solved using a type of quasi-orthogonality relationship by modifying Vodicka’s method and the Laplace transformation. The analysis is based on the small-deflection theory corresponding to the fundamental solutions for the fractional-order heat conduction equation. In addition to this, the intensities of bending moments, forces, maximum normal stresses and its associated stresses are formulated involving the Mathieu functions. As a special case, a multi-stacked circular plate is also discussed in detail as a limiting case. Numerical calculations are also performed, and the results are graphically illustrated.     

Plate Heat Exchangers: Calculation Methods for Singleand Two-Phase Flow

Plate heat exchangers were first developed about 100 years ago but have won increasing interest during the last two decades, primarily due to the development of methods of manufacturing brazed plate heat exchangers. This type of heat exchanger offers very good heat transfer performance in single-phase flow as well as in evaporation and condensation. Part of the reason is the small hydraulic diameters, typically being less than 5 mm. Other advantages of plate heat exchangers are the extremely compact design and the efficient use of the construction material. In spite of their long use, the calculation methods for predicting heat transfer and pressure drop are not widely known. It is the purpose of this article to present such calculation methods for single-phase flow and for flow boiling and to discuss some of the specifics of this type of heat exchangers.     

Heat Transfer and Flow Characteristics of Al2O3/Water Nanofluid in Various Heat Exchangers: Experiments on Counter Flow

Abstract

On account of nanofluids influence on heat exchangers (HEs), a vigorous discussion can be made to concurrently contrast HEs to one another under the same conditions to detect maximum efficacy. Based on an extensive experimental study, this research is established to examine the effect of nanofluids on the performance of heterogeneous HEs with the same heat transfer surface area considering counter flow arrangement. A double pipe HE, a shell and tube HE and a plate HE are intended to accomplish the experiments. The experiments are executed under turbulent flow conditions using distilled water and Al₂O₃/water nanofluid with 0.2, 0.5, and 1% particle volume concentrations. From the results shown in the article, the double pipe HE revealed the best outcome for the heat transfer coefficient with a maximum enhancement of 60% while a maximum enhancement in the heat transfer coefficient of 11% was reported for the plate HE. Utilizing a nanofluid represented the lowest penalty in the pressure drop with a maximum enhancement of 27% for the plate HE while the highest penalty in the pressure drop with a maximum enhancement of 85% was observed in the double pipe and shell and tube HEs.     

Study on heat conduction of functionally graded plate with the variable gradient parameters under the H(t) heat source

Abstract

A hybrid numerical method for heat conduction of functionally graded plate with the variable gradient parameters under the H(t) heat source was studied. A weighted residual equation of heat conduction was considered under thermal boundary conditions. In order to calculate temperature distribution of functionally graded plate with variable gradient parameters, the Fourier transform and inverse Fourier transform were applied and the temperature field was obtained under the H(t) heat source. Results show that the influences of the gradient parameters on temperature distribution are dramatic. But with the increase of gradient parameters, the influences of parameters on the temperature distribution are gradually reduced. When the gradient parameters reach a certain critical value, the temperature does not change anymore. By comparing the temperature distribution of the upper and lower surfaces, it is seen that the temperature presents a gentle downward trend with the increase of the heat source distance, while the temperature does not change with the time in farther distance from heat source. Also, the results show that the influence of the heat source has only partial and limited influence on the temperature, which is in accordance with St. Venant’s Principle. The law of the temperature distribution of the lower surface varies with the gradient parameters, which is also discussed, an optimal gradient parameter with the thermal insulation effect of the functionally graded plate is obtained.     

FULLY DEVELOPED MIXED CONVECTION IN A HORIZONTAL CHANNEL HEATED UNIFORMLY FROM ABOVE AND BELOW

Abstract

Calculations were performed for fully developed, laminar, mixed convection flow in a horizontal, parallel plate channel heated uniformly at the top and bottom plates. Spanwise conduction within the plates was considered, and calculations were performed for Pr = 0.7, 0 < Ra? < 2.5 × 10⁴, and values of a nondimensional conductance ratio in the range 10^?5 < γ < 10³. It is shown that mixed convection heat transfer enhancement is restricted to the lower surface and that the attendant secondary flow induces large spanwise surface temperature variations for which the maximum temperature exceeds values associated with the upper surface. Increased conduction within the bottom plate weakens the secondary flow and decreases spanwise temperature variations. Results of the calculations have important implications in situations for which there is interest in maintaining reduced temperatures, as well as large heat transfer enhancement, at the bottom plate.     

An alternative space–time meshless method for solving transient heat transfer problems with high discontinuous moving sources

ABSTRACT

The aim of this work is the development of a space–time diffuse approximation meshless method (DAM) to solve heat equations containing discontinuous sources. This work is devoted to transient heat transfer problems with static and moving heat sources applied on a metallic plate and whose power presents temporal discontinuities. The space–time DAM using classical weight function is convenient for continuous transient heat transfer. Nevertheless, for problems including discontinuities, some spurious oscillations for the temperature field occur. A new weight function, respecting the principle of causality, is used to eradicate the physically unexpected oscillations.     

Two-Phase Flow Visualization in Chevron and Bumpy Style Flat Plate Heat Exchangers

Adiabatic flow visualization in a chevron plate, a 1:1 aspect ratio bumpy plate, and a 2:1 aspect ratio bumpy plate heat exchangers were investigated for vertical upward flow with R134a. Qualities ranging from 5% to 90% and mass fluxes of 60, 90, and 125 kg/m²-s were investigated. The flow visualization experiments were conducted at a 10°C inlet temperature. Four flow regimes were observed for the flat plate geometries investigated: bubbly flow, rough annular flow, smooth annular flow, and mist flow. The four flow regimes are mapped out on a mass flux versus quality basis for each geometry. The chevron geometry was seen to undergo flow transitions at lower qualities and mass fluxes than the bumpy plate geometries, and the 2:1 aspect ratio bumpy plate geometry was seen to undergo flow transitions at lower qualities and mass fluxes than the 1:1 aspect ratio bumpy plate geometry.     

Comparison of CFD Simulation to Experiment for Convection Heat Transfer in an Enhanced Channel

The numerical and experimental study of heat transfer characteristics in an enhanced channel with turbulent flow is presented. Numerical computations have been done for a periodic element of the channel with periodically fully developed flow using a commercial finite element code. The main objective of this study was to use computational fluid dynamics to obtain convection heat transfer coefficients with air as the fluid. Numerical predictions were compared with experimental results, and a reasonably good agreement was found between the two. It is shown that the channel investigated in this study improves the convection heat transfer coefficient. For high Reynolds number flow conditions, Nusselt numbers in this channel exceeded those in the parallel plate channel by approximately 220%.     

An Extension of the Flow Boiling Correlation to Transition,Laminar, and Deep Laminar Flows in Minichannels and Microchannels

The thermal performance of rectangular plate fins circumscribing elliptic tubes is presented in this paper. Based on the assumption of uniform convective heat transfer the two-dimensional conduction equation has been formulated, and the solution has been obtained through the finite element method. Performance of rectangular plate fins for both inline and staggered arrangement of tubes has been investigated for a variation of geometric and thermo-geometric parameters. The necessity of optimizing the fin geometry for a given fin surface area has also been highlighted.     

Multicellular convection flow in a cylindrical enclosure partitioned by a plate

Abstract

This work performed a numerical investigation on the laminar natural convection in a cylindrical enclosure with a thin flat plate that is concentrically placed within the enclosure and is inclined with respect to the gravitational direction. The enclosure and plate are kept at low and high temperatures, respectively. The objective of this work is to explore the effects of the two geometrical parameters, i.e., the inclination angle and plate length, on the thermal and flow characteristics, with emphasis on the partitioning effect brought by the plate in generating the multicellular structures and weakening the intensities of fluid circulation and convection. The simulations were carried out using our in-house fourth-order finite difference code which is well validated in earlier studies. The effects of the two parameters are demonstrated by the variations of several characteristic quantities, including the overall heat transfer rate, temperature and stream-function distributions, spatial evolution of multiple vortices and local heat transfer pattern. Numerical results reveal that the inclined plate weakens the fluid circulation and lowers the heat transfer rate of the enclosure-plate system; the partitioning effect is strong for the long plate at nearly horizontal orientations. Depending on the magnitude of the two parameters, there can be at most three vortices within both the left and right halves of the enclosure, in which the primary vortices can be squeezed below the plate and the secondary or tertiary vortex occasionally emerges above the plate, and the thermal field is consequently determined especially in the top half of the enclosure. The spatial variation of the multiple vortices is greatly dependent on the two parameters, especially the two primary vortices. Finally, we observed that for a longer plate, the conduction in the gap between the end of plate and the enclosure becomes pronounced, as reflected by the magnitude and location of maximum local heat transfer rate on the enclosure surface.     

Numerical study on the melting thermal characteristics of a microencapsulated phase change plate

ABSTRACT

The melting thermal characteristics of a microencapsulated phase change material (MEPCM) plate under constant heat flux are numerically investigated. The effective property relations of the MEPCM plate related to the parameters of base materials are first established and verified by the measured thermal properties of 10 samples. A one-dimensional phase change thermal model based on the enthalpy method is built, and the predicted results are also verified with test data. The temperature profile and phase interface movement in the MEPCM plate are discussed, and the effects of Stefan number, phase change temperature range, particle and core fraction, and additive fraction are also analyzed. Three states of solid, mushy, and fluid phases of phase change material (PCM) core divide the melting process of the MEPCM plate into five stages as follows: Fo ≤ 0.1, 0.1 < Fo ≤ 0.2, 0.2 < Fo ≤ 0.9, 0.9 < Fo ≤ 1.2, and Fo ≥ 1.2. The time point of regular regime for heat transfer in the MEPCM plate is Fo = 0.2. The addition of conductivity additive homogenizes the temperature profile in the MEPCM plate. Under the combined effects of thermal diffusivity and Ste number, an optimum additive fraction exists for the MEPCM plate to achieve the minimum melting completion time or the maximum latent storage efficiency.     

Effect of Rectangular Winglet Pair in Common Flow Down Configuration on Heat Transfer from an Isothermally Heated Plate

ABSTRACT

Present three-dimensional numerical study aims to investigate the effect of mounting rectangular winglet pair (RWP) on heat transfer enhancement in flow over a flat plate. Computations for incompressible flow of air have been carried out using commercial software ANSYS Fluent. Flow of air has been considered over the surface of an isothermally heated horizontal plate in presence of RWP in the range of Reynolds number from 400 to 2000. Common flow down configuration of RWP has been considered to study the effect of various geometric parameters, such as length of RWP, spacing between leading edges of the winglets and angle of attack of RWP, on flow characteristics and enhancement in heat transfer. Flow and temperature field characteristics have been presented using streamlines and temperature contours near the plate surface and streamlines in cross-stream planes. Enhancement in heat transfer in presence of RWP has been quantified using cross-stream variation of local Nusselt number, streamwise variation of span-averaged Nusselt number and surface-averaged overall Nusselt number.     

THERMAL STRESS ANALYSIS OF A RECTANGULAR PLATE AND ITS THERMAL STRESS INTENSITY FACTOR FOR COMPRESSIVE STRESS FIELD

Abstract

In this study, a transient thermal stress problem of a rectangular plate due to a nonuniform heat supply is treated theoretically and, thereafter, fracture behaviors of the plate with a crack are examined for compressive stress states. Assuming that a crack located on an arbitrary position, with an arbitrary direction, is sufficiently small and is closed because of the compressive stress field, a temperature field, in a transient state, is analyzed by taking into account the effect of relative heat transfer on both surfaces of the plate. Thereafter, the corresponding thermal stress analysis is developed on the basis of the two-dimensional plane stress problem using Airy's stress function method, and the stress intensity factor is analyzed for the biaxial stress state. As an analytical model, we consider mechanical boundary conditions of prescribed displacement and estimate the stress intensity factor of a crack tip using parameters of the crack configuration such as the location, direction, length, and coefficient of friction. These numerical results are shown in graphical form.     

Thermal Stresses Around a Crack in a Non-Homogeneous Diffusion Layer Between a Coating Plate and an Elastic Half-Plane

ABSTRACT

This article proposes a method for determining the thermal stress field around a crack in a thin non homogeneous layer located between a ceramic plate and a metallic half-plane. For these calculations, the crack surfaces are assumed to be insulated and a uniform heat flux flows perpendicular to the crack. The material properties of the layer are assumed to vary continuously from those of the ceramic plate to those of the half-plane. The Fourier transform technique is employed to transform the problem into a set of integral equations. These equations are solved by expanding the differences in the crack surface temperature and the crack surface displacements in a series of functions that are automatically zero outside the crack. The Schmidt method is then used to determine the unknown coefficients in the series. Using this procedure, the stress intensity factors are calculated numerically for several ceramic plate thickness values.