Heat and mass transfer in an unsteady squeezed Casson fluid flow with novel thermophysical properties: Analytical and numerical solution

This study investigates the heat and mass transfer in an unsteady squeezing flow between parallel plates under the influence of novel variable diffusivity. In most of the literature, it is believed that the thermophysical properties of the fluid are unchanged. However, this present study bridges this gap by assuming that viscosity, conductivity, and diffusivity are all temperature-dependent. Physically, an appropriate analysis of thermophysical variables in such a system is required to achieve the best performance for effective heat and mass transfer processes. The equations controlled were first nondimensional and then simplified by a similarity transformation to ordinary nonlinear differential equations. The present study provides a fast convergent method on finite parallel plates, namely, the optimal homotopy analysis method (OHAM) and spectral collocation method (SCM) are used to analyze the fluid flow, heat, and mass transport. The graphical and table understanding is given via an error table and flow behavior of physical parameters. The result reveals that the SCM is more accurate than OHAM. However, the method employed in this paper offers excellent convergence solutions with good accuracy. The solution convergence is also discussed. In this type of problem, squeeze numbers play an important role and the rise in the squeezing parameter increases the fluid temperature.     

Solution of strongly nonlinear ordinary differential equations arising in heat transfer with optimal homotopy asymptotic method

An analytic approximate procedure, called optimal homotopy asymptotic method (OHAM) is considered for the solution of strongly nonlinear differential equations arising in heat transfer. Two particular applications are chosen: convecting-radiating cooling of a lumped system with variable specific heat and fins with temperature dependent surface heat flux. The effectiveness of the method, which is independent of the small parameter, is investigated by comparing the results obtained with the exact and the results already present in the literature.     

Approximate Analytical Solution of Stagnation Point Flow and Heat Transfer over an Exponential Stretching Sheet with Convective Boundary Condition

This study is concerned with the stagnation point flow and heat transfer over an exponential stretching sheet via an approximate analytical method known as optimal homotopy asymptotic method (OHAM). The governing partial differential equations are converted into ordinary nonlinear differential equations using similarity transformations available in the literature. The heat transfer problem is modeled using two‐point convective boundary condition. These equations are then solved using the OHAM approach. The effects of controlling parameters on the dimensionless velocity, temperature, friction factor, and heat transfer rate are analyzed and discussed through graphs and tables. It is found that the OHAM results match well with numerical results obtained by Runge–Kutta Fehlberg fourth‐fifth order method for different assigned values of parameters. The rate of heat transfer increases with the stretching parameter. It is also found that the stretching parameter reduces the hydrodynamic boundary layer thickness whereas the Prandtl number reduces the thermal boundary layer thickness.     

Optimal Homotopy Asymptotic Solutions for Nonlinear Ordinary Differential Equations Arising in Flow and Heat Transfer due to Nonlinear Stretching Sheet

Optimal homotopy asymptotic method (OHAM) is used to obtain solutions for nonlinear ordinary differential equations (ODEs) arising in fluid flow and heat transfer at a nonlinear stretching sheet. The solutions for skin friction and temperature gradient for some special cases are tabulated and compared with the available numerical results in the literature. Moreover, OHAM is found to be very easy to use and the technique could be used for solving coupled nonlinear systems of ordinary differential equations arising in science and engineering.     

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

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

Heat transfer from hollow cylinder using optimal homotopy asymptotic method

Optimal homotopy asymptotic method (OHAM) is employed to investigate steady‐state heat conduction with temperature dependent thermal conductivity and uniform heat generation in a hollow cylinder. Analytical models are developed for dimensionless temperature distribution and heat transfer for two cases using mixed boundary conditions (Dirichlet, Neumann, and Robin). The inner cylinder is assumed to be insulated in both cases. In the first case, the outer cylinder is assumed to be isothermal whereas in the second case, the outer cylinder is convectively cooled by a fluid of temperature T₂ through a uniform heat transfer coefficient h. The effects of Biot number, dimensionless heat generation, and thermal conductivity parameters on the temperature distribution and heat transfer are determined analytically and validated numerically using MAPLE 14. In both cases, the results obtained by OHAM are found to be in good agreement with the numerical results. It is found that as the Biot number increases, the results approach that of the isothermal case. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20407     

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     

MWCNTs/SWCNTs Nanofluid Thin Film Flow over a Nonlinear Extending Disc: OHAM Solution

The aim of this research is the improvement towards the consumption of energy in the field of engineering and industry. The efforts have been paid to the enhancement of heat transmission and cooling process through a nanofluid coating of a nonlinear stretching disc. The combination of Water(H2 O) and multiple walled carbon nanotubes(MWCNT)/single walled carbon nanotubes(SWCNT) have been used as a nanofluid. The spreading of a thin nano-layer with variable thickness over a nonlinear and radially stretching surface has been considered. The estimated results of the problem have been accomplished using the Optimal Homotopy Analysis Method(OHAM). The residual errors of the OHAM method have been shown physically and numerically. The important physical parameters of skin friction and Nusselt number have been calculated and discussed. The other embedding parameters like generalized magnetic parameter, Prantl number, nanofluid volume fraction and Eckert number have been intended and discussed. The obtained results have been compared with the Numerical(ND-Solve) method for both sorts of CNTs. The closed agreement of both methods has been achieved.     

Micropolar flow in a porous channel with high mass transfer

In this research the injective micropolar flow in a porous channel is investigated. The flow is driven by suction or injection on the channel walls, and the micropolar model is used to describe the working fluid. This problem is mapped into the system of nonlinear coupled differential equations by using Berman's similarity transformation. These are solved for large mass transfer via Optimal Homotopy Asymptotic Method (OHAM). Also the numerical method is used for the validity of this analytical method and excellent agreement is observed between the solutions obtained from OHAM and numerical results. Trusting this validity, effects of some other parameters are discussed.     

Solution of nonlinear boundary layer equation for flat plate via optimal homotopy asymptotic method

In this article, we use the optimal homotopy asymptotic method (OHAM) to compute the solution of two‐dimensional incompressible laminar boundary layer flow over a flat plate (Blasius problem). The obtained results for the stream function and velocity profile were comparable in terms of accuracy with that obtained by Esmaeilpour and Ganji (2007) who studied the same problem using the homotopy perturbation method and results obtained by using a numerical method (RK4). The good agreement obtained shows the effectiveness of OHAM. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 197–203, 2014; Published online 19 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21070     

ANALYSIS/FINITE-ELEMENT COMBINED METHODOLOGY ON TRANSIENT HEAT CONDUCTION OF A FINITE DOMAIN WITH PLANAR-DISCRETE SOURCES

Abstract

A useful method, involving the combined use of the analysis and the finite-element methods, is successfully extended to the transient heat conduction problem with isolated heat sources. The results are compared in tables with exact solutions and other numerical data, and the agreement is found to be good. Previously reported analysis /finite-element combined method has been confined to the slow convergence in series solution of analytical method. By using the third Aitken's delta-squared process for accelerating the convergence of infinite series, this restriction is removed, and the new method provides a more powerful solution to transient problems with heat sources     

隔代强制进化遗传算法在换热网络优化中应用

在对换热网络分级超结构及其数学模型分析的基础上,对网络综合优化问题进行了研究．针对普通遗传算法及其它优化算法无法保证网络优化质量和效率的缺点,对遗传算法进行了改进,提出了换热网络隔代强制进化遗传算法。该方法将换热网络结构信息转化为种群中染色体信息,利用种群的进化实现网络结构的优化,在进化过程中使用隔代强制策略,使种群向更优方向稳步进化,保证各代优化结果的有效性,降低最优群体的生成代数,并利用最优个体保存技术记录优化过程中最佳换热网络结构。采用此方法对具体换热网络实例进行了优化综合,结果表明：隔代强制进化遗传算法能在网络优化过程中避免早熟收敛而陷入局部最小点的现象,使搜索质量和效率得到有效提高。用隔代强制进化遗传算法对有分流和无分流换热网络进行优化综合,均能获得综合性能良好的网络结构。     

Nonsimilar solution of a boundary layer flow of a Reiner–Philippoff fluid with nonlinear thermal convection

The thermodynamics modeling of a Reiner–Philippoff-type fluid is essential because it is a complex fluid with three distinct probable modifications. This fluid model can be modified to describe a shear-thinning, Newtonian, or shear-thickening fluid under varied viscoelastic conditions. This study constructs a mathematical model that describes a boundary layer flow of a Reiner–Philippoff fluid with nonlinear radiative heat flux and temperature- and concentration-induced buoyancy force. The dynamical model follows the usual conservation laws and is reduced through a nonsimilar group of transformations. The resulting equations are solved using a spectral-based local linearization method, and the accuracy of the numerical results is validated through the grid dependence and convergence tests. Detailed analyses of the effects of specific thermophysical parameters are presented through tables and graphs. The study reveals, among other results, that the buoyancy force, solute and thermal expansion coefficients, and thermal radiation increase the overall wall drag, heat, and mass fluxes. Furthermore, the study shows that amplifying the space and temperature-dependent heat source parameters allows fluid particles to lose their cohesive force and, consequently, maximize flow and heat transfer.     

A modified genetic algorithm for solving the inverse heat transfer problem of estimating plan heat source

This work considers a new approach for solving the inverse heat conduction problem of estimating unknown plan heat source. It is shown that the physical heat transfer problem can be formulated as an optimization problem with differential equation constraints. A modified genetic algorithm is developed for solving the resulting optimization problem. The proposed algorithm provides a global optimum instead of a local optimum of the inverse heat transfer problem with highly-improved convergence performance. Some numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.     

BEM/FDM conjugate heat transfer analysis of a two-dimensional air-cooled turbine blade boundary layer

A coupled boundary element method （BEM） and finite difference method （FDM） are applied to solve conjugate heat transfer problem of a two-dimensional air-cooled turbine blade boundary layer. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. The Navier-Stokes equations are solved by HIT-NS code. In this code, the FDM is adopted and is used to resolve the convective heat transfer in the fluid region. The BEM code is used to resolve the conduction heat transfer in the solid region. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The numerical results from the BEM adopted in this paper are in good agreement with the results of analytical solution and the results of commercial code, such as Fluent 6.2. The BEM avoids the complicated mesh needed in other computation method and saves the computation time. The results prove that the BEM adopted in this paper can give the same precision in numerical results with less boundary points. Comparing the conjugate results with the numerical results of an adiabatic wall flow solution, it reveals a significant difference in the distribution of metal temperatures. The results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines.     

Convergence angle and dimple shape effects on the heat transfer characteristics in a rotating dimple-pin fin wedge duct

Abstract

A numerical method is employed to study effects of convergence angle and dimple shape on flow structure and heat transfer under a rotating frame. The investigated convergence angles are 0.0°, 6.3°, and 12.7°. The dimple shapes are circular, streamwise-elliptical, and spanwise-elliptical. The rotation number ranges from 0.0 to 0.4. Computed flow structures and heat transfer are compared. Higher rotation number generates better heat transfer in the dimple-pin wedge duct. The rotation direction also affects the flow structure and heat transfer. The spanwise-elliptical dimple shape shows best heat transfer augmentation as it generates the strongest vortex structure and turbulent kinetic energy in the dimples. Larger convergence angles exhibit larger Nusselt numbers and better heat transfer enhancement. Effects of the Coriolis force are considered as this force has favorable effects on enhancing the heat transfer on the surface it acts on.     

A new boundary meshfree method for calculating the multi-domain constant coefficient heat conduction with a heat source problem

A new high-precision boundary meshfree method, namely virtual boundary meshfree Galerkin method (VBMGM), for calculating the multi-domain constant coefficient heat conduction with a heat source problem is given. In the paper, the radial basis function interpolation is used to solve the virtual source function of virtual boundary and the heat source within each subdomain. Simultaneously, the equation of VBMGM for multi-domain constant coefficient heat conduction with a heat source problem is obtained by the Galerkin method. Therefore, the proposed method has common advantages of the boundary element method, meshfree method, and Galerkin method. Coefficient matrix of this specific expression is symmetrical and the specific expression of VBMGM for the multi-domain constant coefficient heat conduction with a heat source problem is given. Two numerical examples are given. The numerical results are also compared with other numerical methods. The accuracy and feasibility of the method for the multi-domain constant coefficient heat conduction with a heat source problem are proved.     

Fourier analysis of conjugate gradient method applied to inverse heat conduction problems

The convergence and regularization mechanism of the conjugate gradient algorithm applied to inverse heat conduction problems are studied within the context of a Fourier analysis, for a square enclosure subjected to an unknown time-varying heat flux on one side, and to known boundary conditions on the remaining sides. Analytic solutions are derived for the Fourier components of the unknown flux over a given time interval. The convergence rate of the algorithm is thereby shown to depend essentially on the time frequency of the data. Numerical solutions are also presented to describe in details the convergence process and solution regularization power of the conjugate gradient method, when the unknown heat flux contains many frequency components and the measurement data are noisy. It is found that an unknown time-dependent heat flux may be satisfactorily recovered using a single sensor even when the temperature field becomes two-dimensional, and that the sensor should be placed in a symmetric manner for better results.     

Multipopulation differential evolution algorithm based on the opposition-based learning for heat exchanger network synthesis

Multipopulation differential evolution combined with opposition-based learning is developed to improve the convergence efficiency and optimization accuracy for heat exchanger network synthesis. The algorithm is based on a stagewise superstructure simultaneous optimization model without considering stream splitting. The candidate population and its opposite population are searched in parallel. Mutation operations are implemented on both populations to provide a full information exchange among populations at each generation. A regrouping schedule is introduced to avoid premature convergence. The algorithm is applied to five heat exchanger network cases of different sizes. More economic networks are found using this method with less computational time.     

Recovering both the space-dependent heat source and the initial temperature by using a fast convergent iterative method

In this paper, we solve two types of inverse heat source problems: one recovers an unknown space-dependent heat source without using initial value, and another recovers both the unknown space-dependent heat source and the initial value. Upon inserting the adjoint Trefftz test functions into Green’s second identity, we can retrieve the unknown space-dependent heat source by an expansion method whose expansion coefficients are derived in closed form. We assess the stability of the closed-form expansion coefficients method by using the condition numbers of coefficients matrices. Then, numerical examples are performed, which demonstrates that the closed-form expansion coefficient method is effective and stable even when it imposes a large noise on the final time data. Next, we develop a coupled iterative scheme to recover the unknown heat source and initial value simultaneously, under two over specified temperature data at two different times. A simple regularization technique is derived to overcome the highly ill-posed behavior of the second inverse problem, of which the convergence rate and stability are examined. This results in quite accurate numerical results against large noise.