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

An 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     

Experimental and numerical investigation on solar parabolic trough collector integrated with thermal energy storage unit

Solar parabolic trough collector (PTC) is the best recognized and commercial‐industrial‐scale, high temperature generation technology available today, and studies to assess its performance will add further impetus in improving these systems. The present work deals with numerical and experimental investigations to study the performance of a small‐scale solar PTC integrated with thermal energy storage system. Aperture area of PTC is 7.5 m², and capacity of thermal energy storage is 60 L. Paraffin has been used as phase change material and water as heat transfer fluid, which also acts as sensible heat storage medium. Experiments have been carried out to investigate the effect of mass flow rate on useful heat gain, thermal efficiency and energy collected/stored. A numerical model has been developed for the receiver/heat collecting element (HCE) based on one dimensional heat transfer equations to study temperature distribution, heat fluxes and thermal losses. Partial differential equations (PDE) obtained from mass and energy balance across HCE are discretized for transient conditions and solved for real time solar flux density values and other physical conditions of the present system. Convective and radiative heat transfers occurring in the HCE are also accounted in this study. Performance parameters obtained from this model are compared with experimental results, and it is found that agreement is good within 10% deviations. These deviations could be due to variations in incident solar radiation fed as input to the numerical model. System thermal efficiency is mainly influenced by heat gain and solar flux density whereas thermal loss is significantly influenced by concentrated solar radiation, receiver tube temperature and heat gained by heat transfer fluid. Copyright © 2016 John Wiley & Sons, Ltd.     

Momentum boundary layer and its influence on the convective heat transfer in porous media

Convective heat transfer in a channel filled with a porous medium has been analyzed in this paper. The flow field is analyzed considering both the inertia and solid boundary effects and the thickness of the momentum boundary layer is found as a function of the Darcy and the Reynolds number. The two-equation model is applied for the heat transfer analysis and theoretical solutions are obtained for both fluid and solid phase temperature fields. The Nusselt number is obtained in terms of the relevant physical parameters, such as the Biot number for the internal heat exchange, the ratio of effective conductivities between the fluid and solid phases, and the thickness of the momentum boundary layer. The results indicate that the influence of the velocity profile is characterized within two regimes according to the two parameters, the Biot number and the conductivity ratio between the phases. The decrease in the heat transfer due to the momentum boundary layer is 15% at most within a practical range of the pertinent parameters.     

Transient surface heating rates from a nickel film sensor using inverse analysis

Convective surface heat transfer measurements play an important role in many industrial, environmental and aerodynamic problems. In most of the cases, the flow is unsteady which results in temperature variation in the body. The surface heating rates are then predicted from the measured temperature histories by suitable heat transfer modeling. In this paper, the temperature history obtained from a nickel film sensor during a flight test is considered to study the effect of sensor thickness on surface heat flux measurements during the flight measurement. Inverse methods using analytical solutions as well as control volume approximations are used to infer the surface heat flux. The experimental temperature data are discretized using cubic-spline method to obtain the closed form solution which is used for inverse analysis. The results are compared with that of standard bench mark results with thin film gauge analysis based on semi-infinite one dimensional medium. No significant change in surface heat flux is observed between inverse and thin film analysis. However, when the thickness of nickel film is increased by 100 times during numerical simulation of inverse method, it is seen that peak surface heat flux increases by 20%.     

Heat transport on steady MHD flow of copper and alumina nanofluids past a stretching porous surface

An attempt is made to investigate the steady magnetohydrodynamic convective flow of the viscous nanofluid due to a permeable exponentially stretching porous surface. Water is used as a traditional fluid while nanoparticles include copper and alumina. The fluid is electrically conducting, subject to an applied magnetic field with a constant strength. Convective type boundary conditions are employed in modeling the heat transfer process. The nonlinear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations and then solved using the Runge‐Kutta fourth‐order method. A parametric study of the physical parameters is made, and a representative set of numerical results for the velocity and temperature, as well as local shear stress and local Nusselt number, is presented graphically. Hartman number increase diminishes the velocity and has the contrary result in the subjective sense for the mass transfer parameter. An increase in the Prandtl number Pr lessens the temperature and thickness of the thermal boundary layer. The main conclusions have been indicated.     

Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet

The steady laminar flow and heat transfer of a second grade fluid over a radially stretching sheet is considered. The axisymmetric flow of a second grade fluid is induced due to linear stretching of a sheet. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). Introducing the dimensionless quantities the governing partial differential equations are transformed to ordinary differential equations. The developed non-linear differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence of these solutions is explicitly discussed. The analytical expressions for velocity and temperature are constructed and are shown graphically. The numerical values for the skin friction coefficient and the Nusselt number are entered in tabular form. Attention has been focused to the variations of the emerging parameters such as second grade parameter, Prandtl number and the Eckert number. Finally, comparison between the HAM and numerical solutions are also included and found in excellent agreement.     

Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet

This paper investigates the magnetohydrodynamic (MHD) flow and heat transfer characteristics in the presence of a uniform applied magnetic field. The boundary layer flow of a third-order fluid is induced due to linear stretching of a non-conducting sheet. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing non-linear differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence of these solutions is discussed. Velocity and temperature distributions are shown graphically. The numerical values for the skin friction coefficient and the Nusselt number are entered in tabular form. Emphasis has been given to the variations of the emerging parameters such as third-order parameter, magnetic parameter, Prandtl number and the Eckert number. It is noted that the skin friction coefficient decreases as the magnetic parameter or the third grade parameter increases.     

Numerical analysis of LEC growth of GaAs with an axial magnetic field

A set of numerical analyses for momentum and heat transfer for a 3 in. (0.075 m) diameter Liquid Encapsulant Czochralski (LEC) growth of single-crystal GaAs with or without an axial magnetic field was carried out using the finite-element method. The analyses assume a pseudosteady axisymmetric state with laminar flows. Convective and conductive heat transfers, radiative heat transfer between diffuse surfaces and the Navier-Stokes equations for both melt and encapsulant and electric current stream function equations for melt and crystal are considered together and solved simultaneously. The effect of the thickness of encapsulant, the imposed magnetic field strength as well as the rotation rate of crystal and crucible on the flow and heat transfer were investigated.     

Finite element analysis of the flow and heat transfer of solid particles in moving beds

A numerical analysis for the flow and heat transfer of solid particles in moving beds of heat exchangers is presented. The solid particles pass through a bundle of heat source tubes as the result of the gravitational force. Heat energy is transferred through direct contact of particles with the heat source tubes. A viscous-plastic fluid model and a convective heat transfer model are employed in the analysis. The flow field dominantly determines the total heat transfer in the heat exchanger. As the velocities of solid particles around the heat source tubes increase, the heat transfer from the tubes also increases. Examples are presented to show the performance of the numerical model. The effect of flow on heat transfer has also been studied. © 1998 John Wiley & Sons, Ltd.     

Three-dimensional viscous flow and heat transfer over a permeable shrinking sheet

This paper presents a numerical analysis of a steady three-dimensional fluid flow and heat transfer towards a permeable shrinking sheet. The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which are then solved numerically by a shooting method. The effects of the governing parameters on the skin friction and heat transfer from the surface of the shrinking surface are illustrated graphically. It is found that dual solutions exist for the shrinking case. A comparison with known results from the open literature has been done and it is shown to be in excellent agreement.     

Numerical study of convective heat transfer to supercritical water in rectangular ducts

Numerical investigation has been performed to analyze forced convective heat transfer to supercritical water in horizontal rectangular ducts. Convective heat transfer near the critical region in the rectangular ducts is strongly influenced by large variations of thermodynamic and transport properties of supercritical fluid with gravity force, especially close to pseudocritical temperature. Fluid flow and heat transfer characteristics such as velocity, temperature, and local heat transfer coefficient with water properties distribution in the ducts are presented. Flow accelerates along the horizontal ducts because of decreased water density from heat transfer at the duct walls. Center of large flow recirculation in the duct section locates near the middle of vertical surface and additional secondary recirculation in clockwise direction appears with the increase of duct height. Local wall temperature severely varies along the inner surface of the duct section and its variation depends on aspect ratio of the duct. The heat transfer coefficient distributions along the ducts for various aspect ratios are compared with the proximity effect to the critical pressure.     

Convective heat transfer for steady laminar flow between two confocal elliptic pipes with longitudinal uniform wall temperature gradient

Convective heat transfer for steady laminar flow between two confocal elliptic pipes with longitudinal uniform wall temperature gradient under various heating conditions is presented in analytical closed form utilizing the exact solutions of the Navier-Stokes and energy equations. It is shown that one characteristic number, the product of the dimensionless longitudinal uniform wall temperature gradient and Peclet number, effects the problem. The values of Nusselt numbers for several values of ellipticity and core size are obtained.     

Heat Transfer Coefficient Correlation for Convective Boiling Inside Plain and Microfin Tubes Using Genetic Algorithms

Two-phase flow heat transfer has been exhaustively studied in recent years. However, in this field, several questions remain unanswered. Heat transfer coefficient prediction related to nucleate and convective boiling has been studied using different approaches—numerical, analytical, and experimental. In this study, an experimental analysis, data representation, and heat transfer coefficient prediction of two-phase heat transfer in nucleate and convective boiling are presented. An empirical correlation is obtained, based on a genetic algorithms search engine, of a dimensional analysis of the two-phase flow heat transfer problem.     

Exact solutions of micropolar SWCNTs nanofluid with heat transfer

The present study is aimed to analyze the unsteady micropolar nanofluid flow passing over an oscillating infinite vertical plate. The flow is affected by thermal radiation and Newtonian heating. Single‐walled carbon nanotubes (SWCNTs) are added to enrich the thermal properties of the micropolar fluid. Kerosene is taken as the base liquid to enhance heat transfer. By using dimensional analysis, the governing equations for temperature, velocity, and microrotation are reduced to dimensionless form and after that, these equations have been solved by applying Laplace transform method to get the exact solutions. Finally, we have presented the effects of material and flow parameters and illustrated graphically by the Mathcad software. We found that microrotation, temperature, and velocity are decreasing functions of Prandtl number but have shown increasing behavior for Grashof number. Furthermore, we found that SWCNTs‐water‐based nanofluid has a comparatively higher heat transfer rate than SWCNTs‐kerosene and SWCNTs‐engine oil‐based nanofluids.     

Mixed convection heat transfer in a passive solar building

Convective heat transfer through apertures such as doorways can be an important process by which thermal energy is transferred from one zone to another zone of a building. In this article, interzonal natural and forced convection in a two- and a three-zone, full-scale building are examined. Aperture velocity and temperature distributions are measured and the experimental interzonal mass flow rate and heat transfer are determined. A model based on zone temperature distributions is derived to predict the interzonal mass flow rate and heat transfer. The measured and predicted interzonal flow rate and heat transfer are compared and found to be in good agreement.     

Numerical investigation of effective parameters of falling film evaporation in a vertical-tube evaporator

Wastewater treatment is one of the most effective solutions to manage the problem of water scarcity. Falling film evaporators are excellent technology in wastewater treatment plants. These wastewater evaporators provide high heat transfer, short residence time in the heating zone, and high-purity distilled water. In the present study, the mechanism of turbulent falling film evaporation in a vertical tube has been investigated. A model has been developed for symmetrical two-dimensional pure and saline water flow in a vertical tube under constant wall heat flux. The numerical simulation has been carried out by a commercial computational fluid dynamics code. The evaporation of saturated liquid film is simulated utilizing a two-phase volume of fluid method and Tanasawa phase-change model. The main objective of this study is to evaluate the effects of water salinity, liquid Reynolds number, wall heat flux, and liquid film thickness on the two-phase heat transfer coefficient and vapor volume fraction. The numerical heat transfer coefficients are compared with the obtained results by Chen's empirical correlation. With a MAPE ≤ 11%, this study proves that the numerical method is highly effective at predicting the heat transfer coefficient. Moreover, the empirical coefficient of the Tanasawa model and the minimum thickness of the falling film are determined.     

Analytical Solution and Numerical Simulation for One‐Dimensional Steady Nonlinear Heat Conduction in a Longitudinal Radial Fin with Various Profiles

In this article we consider a model describing the temperature profile in a longitudinal fin with rectangular, concave, triangular, and convex parabolic profiles. Both thermal conductivity and the heat transfer coefficient are assumed to be temperature‐dependent, and given by a linear function and by power laws, respectively. In addition, the effects of the thermal conductivity gradient have been investigated. Optimal homotopy analysis method (OHAM) is employed to analyze the problem. The effects of the physical applicable parameters such as thermo‐geometric fin, thermal conductivity, and heat transfer mode are analyzed. The OHAM solutions are obtained and validity of obtained solutions is verified by the Runge–Kutta fourth‐order method and numerical simulation. A very good agreement is found between analytical and numerical results. Also for investigation of lateral effects on the accuracy of results, numerical simulation (by Ansis software) is compared with the homotopy analysis method (HAM) and numerical solution (by Runge–Kutta) of the energy balance equation. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21104     

A spherical cell model for multi‐component droplet combustion in a dilute spray

A model for sphericosymmetric thin‐flame combustion of a multi‐component fuel droplet in a dilute spray has been developed using a unit cell approach. The gas‐phase transport has been modelled as convective–diffusive while the liquid‐phase processes as transient–diffusive. Convective heat and mass transfer condition has been used at the cell surface. The results indicate that evaporation and combustion characteristics of the droplet are strongly affected by the variation of both ambient conditions and convective transfer coefficients. Using the model, the effects of droplet spacing in spray, ambient oxidizer concentration, ambient temperature and pressure have been considered. Droplet life increases with decrease in droplet spacing, ambient temperature and ambient oxidizer concentration. However, droplet life has a weak dependence on ambient pressure. Copyright © 2001 John Wiley & Sons, Ltd.     

Explicit analytical solutions of 2-D laminar natural convection

There are many natural convection processes in various fields, and it is still a hot topic to investigate the fluid dynamics and heat transfer of natural convection. The analytical solutions are meaningful in both theoretical investigation and practical applications. Specially, they are very useful to computational fluid dynamics and heat transfer as the benchmark solutions to check the numerical solutions and to develop numerical differencing schemes, grid generation methods and so forth. Two explicit analytical solutions of 2-D steady laminar natural convection along a vertical porous plate and between two vertical plates were derived for better understanding the flow and heat transfer as well as promoting the computational fluid dynamics and computational heat transfer.     

Computational Study of Convective Transport in a Coating Applicator for a Non-Newtonian Fluid

Convective transport in an optical fiber coating applicator and die system has been simulated for a non-Newtonian fluid. Low-density polyethylene (LDPE) is employed for the numerical analysis, though ultraviolet (UV) curable acrylates are more commonly used, because of a lack of property information for acrylates and similar behavior of these two materials. The equations governing fluid flow and heat transfer are transformed to obtain flow in a cylindrical domain. A numerical scheme similar to the SIMPLE algorithm is developed and employed with a nonuniform grid. Variable fluid properties are employed because of the strong dependence of these on the temperature. In contrast to the isothermal case, streamlines for the non-Newtonian fluid are found to be quite different for various fiber speeds. The temperature level in the applicator is much higher for the Newtonian case, due to the larger fluid viscosity and associated viscous dissipation. The shear near the fiber is found to be lower for the Newtonian fluid. As expected, the effects become larger with increasing fiber speed. A fairly high temperature rise is observed in the die, regardless of fiber speed. This study focuses on the computational modeling of non-Newtonian effects during the coating process, and several interesting and important features, as compared to the Newtonian case, are observed.