Analytical Solution Of Heat Transfer Research Articles

Effect of viscous dissipative fluid in a slit micro-channel with heated super-hydrophobic surface

The analytical solution of heat transfer and hydro magnetic flow for an incompressible, electrically-conducting, and viscous dissipative fluid traveling vertically through an isothermally heated parallel plate in a slit micro-channel is performed. One channel surface was super-hydrophobic slip and temperature jump, whereas the other did not. This study also examined the effects of super-hydrophobic slip and a temperature jump on characteristic flow of magneto-hydrodynamics (MHD) free convection flow with viscous dissipative fluid. The perturbation technique was used to solve the coupled nonlinear and coupled equations analytically. With the aid of illustrative graphs, the results were presented, and the effects of the relevant controlling parameters namely Brinkman number, magnetic field, velocity slip condition and temperature jump effects were analysed for temperature, velocity, skin friction and Nusselt number distributions when either wall is heated by constant wall temperature. The result demonstrated that the activities of Brinkman number, Br, substantially increase fluid velocity, whereas growing levels of magnetic field effect was seen to slow down the flow movement. In addition, the fluid velocity is higher for greater values of temperature jump and velocity slip effects respectively. Furthermore, this research can prove very useful for designers in improving the performances of mechanical systems when viscous dissipation is involved, as well as heat transfer in micro-channels, as it is in combustion.

Geographic and transport controls of temperature response in karst springs

Thermal responses of groundwater are useful signatures to reveal the recharge-discharge process and characterize aquifer structure in karst groundwater. Four karst springs with varying circulation depths ranging from ∼ 60 to 820 m in South China, were used to decipher the mechanism of heat exchange between recharge water and surrounding rock formations. An analytical solution of heat transfer in karst conduit was proposed to simulate the peak or trough temperatures of pulse flow. Hydraulic diameter, flow velocity, input temperature and circulation depth in karst aquifer, mainly depending on the recharge water volume after rainfall events, are important transport factors to control the thermal equilibrium depth and the efficiency of heat exchange that directly controls the behavior of warm peaks or cold troughs in groundwater temperature. In shallow karst aquifers wherein the circulation depth is less than its theoretical thermal equilibrium depth, the recharge water does not sufficiently exchange heat with the surrounding rocks, resulting in clear event-scale warm peaks in summer and cold troughs in winter. Otherwise, the recharge water will firstly reach a thermal equilibrium state and then mix with the warmer base flow at deeper location, which is verified in a karst spring with anomalous event-scale temperature drops after rainfall events all year around. The thermal response simulations obtained from this work provide new ways and insights to characterize geographic structure of karst aquifer and elucidate heat transfer mechanism in karst aquifer systems.

Modeling enhanced geothermal systems using a hybrid XFEM–ECM technique

Heat extraction from Enhanced Geothermal Systems (EGS) involves several multi-physics coupling processes, including the seepage through the fractured porous media, the thermal exchange between the working fluid and the matrix, and the deformation of fractured porous media, which play essential roles in exploiting the geothermal energy contained in hot dry rocks. In this study, a fully coupled numerical model for Thermo-Hydro-Mechanical simulation of EGS is presented based on the local thermal non-equilibrium using the eXtended Finite Element Method (XFEM) and Equivalent Continuum Method (ECM). The ECM can provide the equivalent tensors of not only fluid permeability but also solid compliance, which is an essential feature for coupled Thermo-Hydro-Mechanical simulation of fracture networks. In the model, the XFEM is employed for large-scale fractures to capture the mass and heat transfer between the fracture and matrix more accurately, while the ECM is applied on the network of small-scale fractures since considering their details explicitly is not usually cost-effective. Hence, the proposed model benefits from the advantages of both methods, and it allows for managing between accuracy and cost. The model is validated against the analytical solutions of heat transfer in porous media as well as single fracture problems. Moreover, its flexibility and applicability are shown by assessing the effects of the connectivity of fractures, characteristics of fracture networks, coupling conditions, and local thermal non-equilibrium assumption on the EGS simulation results. It is observed that the network connectivity and fracture alignment are both influential in the early thermal breakthrough; however, each can take dominance under different conditions. The results show the proposed computational model is a promising tool for estimation of the heat mining performance of EGS.

Analytical solution of heat-transfer in central part of tibia bone tissue using non-Fourier heat equation with a laser heat source

Hyperbolic heat transfer equation considering a laser heat source is analytically investigated using Laplace transform method to study the temperature distribution in the central part of the tibia bone tissue. The target zone is the compact layer of tibia, and the laser irradiation in four near-surface points during 2 s is taken into account. Holmium–Yttrium–Aluminum-Garnet (Ho-YAG) laser is utilized in the simulations. Results indicate that there is a trilateral relationship among the temperature changes of various points in the tissue, the power used and the wavelength. While neglecting the effects of blood circulation upon laser interaction with the bone surface, the results reveal that the temperature of the points adjacent to the bone surface dramatically increases up to 85 °C. Meanwhile, the heat source is provided based on the Beer-Lambert law, and finally it demonstrates that the penetration depth exponentially reduces the intensity and causing considerable decrease in temperature. For the first time, the non-Fourier heat transfer equation was solved using the Laplace transform method for the tibia bone, and its results were compared with the numerical solution results using the Leap- Frog method. Knowing the temperature changes caused by laser inside the tissue is very crucial in Laser tissue welding, tissue ablation, photocoagulation and photo-thermal denaturation, angioplasty, treatment of granulation tissues, change and deformation of cartilage.

In-process nip point temperature estimation in automated tape placement based on analytical solution and remote thermal measurements

The optimisation and control of automated tape placement (ATP) requires fast analysis tools able to utilise process data for predictions and monitoring. In this study, a strategy for in-process estimation of nip point temperatures is proposed. The method is based on a combination of two one-dimensional analytical solutions of heat transfer in ATP using temperature data measured on the tool surface, combined with an inverse solution for the estimation of power delivered by the heating device on the composite surface. The performance of the method is examined against a validated finite element model. Approximations of nip point temperature show good correlation for different tool materials, with an average error of 15°C and a maximum of 50°C which is satisfactory for the processing of high-temperature thermoplastic materials. The analytical scheme offers real-time estimations of the nip point temperature with the potential to be used for process control of ATP.

A review of modern numerical and analytical models of heat transfer in a dielectric layer during melting due to microwave radiation

In this work, numerical and analytical solutions of heat transfer in a dielectric layer during melting in the microwave field were considered. We considered solutions, where the source term was obtained based on the solution of Maxwell equation, as well as using the Lambert law. The conditions applicable for analytical solutions, allowing the parametric analysis, are determined. The areas of application of the technology of microwave melting of dielectrics, in particular with melting ice on water, defrosting products, etc., were also considered.

Analytical Solutions for Heat Transfer in Saturated Soil with Effective Porosity

AbstractClosed-form analytical solutions are presented for one-dimensional heat transfer through saturated soil with effective porosity and steady fluid flow. The solutions yield distributions of t...

Practicality of Analytical Solutions for Heat Transfer in Circular Systems in the Infinite Region to Describe Temperatures Due to Disposal of Heat-Decaying Nuclear Waste

Analytical solutions for temperatures in an infinite region bounded internally by a cylinder have proved to be useful for thermal analysis of heat-producing nuclear waste disposal scenarios where the thermal design criteria are peak temperatures. The practicality of an analytical solution for the temperature of the host rock used in forced-ventilation thermal analyses has been illustrated by a computational time of a few seconds. Prior to the use of an analytical temperature solution for the host rock, the computation time was on the order of hours. However, the published analytical temperature solution for the infinite region bounded internally by a cylinder with constant heat flux applied at the cylinder wall does not satisfy the boundary condition. This temperature solution is shown to be correct herein with respect to temperature predictions derived from a solution that does satisfy the boundary condition.

Analytical Solution for Heat Transfer in Electroosmotic Flow of a Carreau Fluid in a Wavy Microchannel

This article explores the heat and transport characteristics of electroosmotic flow augmented with peristaltic transport of incompressible Carreau fluid in a wavy microchannel. In order to determine the energy distribution, viscous dissipation is reckoned. Debye Hückel linearization and long wavelength assumptions are adopted. Resulting non-linear problem is analytically solved to examine the distribution and variation in velocity, temperature and volumetric flow rate within the Carreau fluid flow pattern through perturbation technique. This model is also suitable for a wide range of biological microfluidic applications and variation in velocity, temperature and volumetric flow rate within the Carreau fluid flow pattern.

Semi Analytical Solution of Heat Transfer of Magnetohydrodynamic Third-Grade Fluids Flowing Through Parallel Plates With Viscous Dissipation

Abstract This study deals with the heat transfer characteristics of magnetohydrodynamic (MHD) flow of a third-grade fluid through parallel plates, subjected to a uniform wall heat flux, but of different magnitudes. The effect of viscous dissipation has been included for both heating and cooling of the fluid. The least square method (LSM) has been adopted for solving the nonlinear equations. The expressions for the velocity and temperature fields have been derived which, in turn, is utilized to evaluate the Nusselt number. The results indicate an increase in Nusselt number for higher values of the third-grade fluid parameter during heating and indicate a reverse trend for cooling. Nusselt number increases with an increase in Hartmann number during heating, whereas it decreases with increasing values of the Hartmann number while cooling the fluid.

Evaluation of burn-through in MIG/MAG welding of high-strength, low thickness pipelines

The aim of this study was the development of repair procedures of pipelines with low residual thickness (3.0 and 3.2 mm), manufactured from high-strength steels (API 5L X70) and ASTM 106 GrB pipe, to minimize the risk of burn-through. For this purpose, a weld test bench with adjustable flow and pressure of the fluid was constructed, in order to know internal fluid pressures (2 and 5 bar) and flow (20, 40 and 80 l/min). Using the semiautomatic MIG/MAG (GMAW) process, longitudinal welds were performed on pipes containing water, with later evaluation of the appearance of the least penetration of the weld bead. Thus, two welding techniques were used: pushing and pulling the weld pool, as well as the metallic transfer modes in short circuit or pulsed current. In the study of limiting conditions for the occurrence of perforation, welding parameters based on specific flow and pressure conditions were researched. The internal temperature of the pipe wall was determined by an analytical solution for heat transfer in the welding. The results showed that for the pulsed current MIG/MAG process and the technique of pushing the weld pool, maintaining all other welding variables constant, the weld bead penetration is small. Moreover, the welding power levels for the occurrence of burn-through proved to be greater than those reported in the literature for SMAW, indicating MIG/MAG as a robust and suitable process for in-service welding.

Analytical Solutions of Heat Transfer and Film Thickness with Slip Condition Effect in Thin-Film Evaporation for Two-Phase Flow in Microchannel

Physical and mathematical model has been developed to predict the two-phase flow and heat transfer in a microchannel with evaporative heat transfer. Sample solutions to the model were obtained for both analytical analysis and numerical analysis. It is assumed that the capillary pressure is neglected (Morris, 2003). Results are provided for liquid film thickness, total heat flux, and evaporating heat flux distribution. In addition to the sample calculations that were used to illustrate the transport characteristics, computations based on the current model were performed to generate results for comparisons with the analytical results of Wang et al. (2008) and Wayner Jr. et al. (1976). The calculated results from the current model match closely with those of analytical results of Wang et al. (2008) and Wayner Jr. et al. (1976). This work will lead to a better understanding of heat transfer and fluid flow occurring in the evaporating film region and develop an analytical equation for evaporating liquid film thickness.

Arc Welding Procedures on Steels for Molds and Dies

This work aims to present a method to establish arc welding procedures on steels for molds and dies. The welding of AISI P20 steel was studied. Simple and multi-pass welding were undertaken using the Tungsten inert gas process, evaluating the bead geometry, hardness distribution, microstructure and quality features after grinding, polishing and texturing. By the bead implant test and analytical heat transfer solutions, multi-pass welding techniques were optimized to cause the tempering effect to the weld metal and heat affected zone by a second thermal cycle of welding. In the welding of P20 steel it is necessary to apply the double layer and temper bead techniques. The temper bead demands refined techniques to control the welding variables.

Analytical solutions of heat transfer for laminar flow in rectangular channels

Abstract The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type). The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.

Analytical solution of heat transfer in a shell-and-tube latent thermal energy storage system

An analytical solution of a latent heat storage unit (LHSU) consisting of a shell-and tube was obtained by using the Exponential Integral Function and the variables separation technique. The working fluid (water) circulating by forced convection inside the inner tube charges and discharges the storage unit. The comparison between analytical predictions and experimental data shows good agreement. Extensive parametric studies were conducted in order to examine the effect of the pertinent parameters (such as natural convection, mass flow rate of HTF, outer tube radius, pipe length etc.) on the melting and solidification processes of paraffin as a PCM. In order to provide guidelines for system performance and design optimisation, unsteady temperature distributions within PCM during melting/solidification, energy stored, position of moving interface and thermal efficiency have been obtained by a series of numerical calculations and represented graphically.

Experimental determination of thermal conductivity and thermal diffusivity of whole green (unripe) and yellow (ripe) Cavendish bananas under cooling conditions

Bananas are cooled to 13°C after their harvest to extend their shelf life and prevent post-harvest losses. Since they are subjected to chilling injuries at temperatures below 11°C, thermal properties should be known to design a cooling process. For this purpose, thermal diffusivity and thermal conductivity of green and yellow Cavendish bananas were determined experimentally using analytical solution of heat transfer for an infinite cylinder. Experiments were carried out in cooling chambers, and temperature change of bananas were recorded using thermistors. Thermal conductivity–diffusivity values of the green and yellow bananas changed from 0.302 to 0.338W/m-K and 1.442×10−7 to 1.500×10−7m2/s, respectively. These values were validated by literature data and additional experiments where simulated and experimental data were compared while the effect of banana peel on the cooling rates was also explained. These comparisons demonstrated the significance of knowing thermal conductivity–diffusivity values separately for designing and optimizing a cooling process.

Analytical solution of heat transfer of oscillating flow at a triangular pressure waveform

Oscillating motion of fluid flow in a capillary tube can produce a nonlinear thermal boundary layer resulting in an increase of heat transfer coefficient. In the current investigation, an oscillating motion of fluid flow in a round tube was investigated to determine a triangular waveform effect on the heat transfer coefficient. An analytical solution of laminar Newtonian flow with a triangular pressure waveform was obtained. Results show that the heat transfer coefficient of the oscillating flow depends on the fluid properties and oscillating waveform. The triangular waveform of oscillating motion can result in a higher heat transfer coefficient.

Analytical solution for heat transfer in a multilayer floor of a radiant floor system

In radiant floor systems, the distribution of the floor surface temperature, which can be used to determine the mean temperature and the lowest/highest temperature of the floor surface, is an important parameter. The mean temperature of the floor surface determines cooling/heating capacity and indoor thermal comfort. The lowest surface temperature, which considers the dew point in an indoor environment, is a crucial factor in the prevention of condensation on a floor surface. The highest surface temperature is typically considered for local thermal comfort. In this paper, an analytical solution for heat transfer in a multilayer floor structure of a radiant floor system is proposed based on the analysis of the heat transfer process of a multilayer floor, equivalent thermal resistance and separation of variables method. The corresponding formulas are derived to estimate the distribution of floor surface temperature. The calculation results are validated by experiments. The calculation and experimental results show good accordance. The absolute error between the calculation and experimental results for floor surface temperature is within 0.3°C. A method for the calculation of the dimensionless temperature of the floor surface, which can be used for radiant heating and cooling systems, is provided. Using this proposed method, the distribution of floor surface temperature and the influence of floor structure parameters on the thermal performance of floors can be estimated and analyzed.

Avaliação da perfuração na soldagem em operação pelo processo MIG/MAG de dutos de alta resistência e baixa espessura

O objetivo deste trabalho foi o desenvolvimento de reparo em dutos com pequena espessura (3,0 e 3,2 mm), fabricados em aços de alta resistência (API 5L X70) e em tubo ASTM 106 Grau B de forma a minimizar o risco de perfuração. Para o experimento, foi construída uma bancada de testes com ajuste variável de vazão e pressão do fluido, a saber, vazões de 20 l/min, 40 l/min e 80 l/min e pressões de 2 bar e 5 bar. Foram realizadas soldagens na direção longitudinal sobre tubos contendo água como fluido interno, utilizando-se o processo semiautomático MIG/MAG (GMAW) com posterior avaliação do aspecto da menor penetração do cordão. Desta forma, foram empregadas duas técnicas de soldagem, puxando e empurrando a poça de fusão, assim como os modos de transferência metálica em curto circuito ou em corrente pulsada. No estudo das condições limites para a ocorrência de perfuração foram pesquisados parâmetros de soldagem em função de condições específicas de vazão e de pressão. A temperatura interna da parede da tubulação foi determinada através de uma solução analítica para a transferência de calor na soldagem. Os resultados mostraram que para o processo MIG/MAG com corrente pulsada e com a técnica empurrando a poça de fusão, mantidas todas as outras variáveis de soldagem fixas, há pequena penetração do cordão de solda. Além disso, os níveis de energia de soldagem para a ocorrência da perfuração revelaram-se superiores aos obtidos na literatura para o processo SMAW, indicando o processo como robusto e apropriado para soldagem de reparo em operação.

Analytical solution for slip flow and heat transfer due to a stretching sheet

AbstractAn analysis has been carried out to investigate the analytical solution to the flow and heat transfer characteristics of a viscous flow over a stretching sheet in the presence of second‐order slip in flow. The governing partial differential equations of flow and heat transfer are converted into non‐linear ordinary differential equations by using suitable similarity transformations. The exact solution of momentum equation is assumed in exponential form and analytical solutions of heat transfer for both PST and PHF cases are obtained by the power series method in terms of Kummer's hypergeometric function. The temperature profiles are drawn for different governing parameters. The numerical values of wall temperature gradient and wall temperature are compared with earlier numerical results which have a good agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21044