Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

This article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.     

Coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes

The coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes is investigated numerically. The medium flows in a laminar and fully developed state with a Poiseuille velocity distribution, but the thermal status is developing. By the discrete ordinate method, the nonlinear integrodifferential radiative transfer equation in a cylindrical coordinate form is solved to give the radiative source term in the energy equation of coupled heat transfer. The energy equation is solved by the control volume method. The local Nusselt number and wall heat flux of convection as well as the total wall heat flux are employed to evaluate the influence of radiation heat transfer on convection. The analysis shows that the radiation heat transfer weakens the convection effect, promotes the temperature development, and significantly shortens the tube length with obvious heated/cooled effect. There is an obvious difference between the coupled heat transfer in a heated tube and that in a cooled tube, even though the medium properties are kept constant. The wall emissivity, the medium thermal conductivity and scattering albedo have significant influences on the coupled heat transfer, but the effect of medium scattering phase function is small. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 64–72, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10137     

Lie group analysis of hyperbolic tangent fluid flow in the presence of thermal radiation

The present study is devoted to the flow and heat transfer analysis of the hyperbolic tangent fluid through a stretching sheet by considering the effect of thermal radiation in addition to an applied transverse magnetic field, as well as thermal and velocity slip conditions. The Lie group analysis technique has been utilized for establishing similarity transformations, which effectively transform the governing equations to a system of nonlinear ordinary differential equations (ODEs). These ODEs are numerically solved by utilizing the shooting method. The heat transfer properties and flow features under the influence of various physical parameters are also studied. We noted that by increasing the thermal radiation parameter, the temperature profile increases and also the thermal boundary layer thickens. Furthermore, it is deduced that rising the thermal radiation parameter reduces the local Nusselt number. Moreover, the numerical results obtained are in agreement with the existing results in the literature.     

Heat transfer analysis of parabolic trough solar receiver

Solar Parabolic Trough Collectors (PTCs) are currently used for the production of electricity and applications with relatively higher temperatures. A heat transfer fluid circulates through a metal tube (receiver) with an external selective surface that absorbs solar radiation reflected from the mirror surfaces of the PTC. In order to reduce the heat losses, the receiver is covered by an envelope and the enclosure is usually kept under vacuum pressure. The heat transfer and optical analysis of the PTC is essential to optimize and understand its performance under different operating conditions. In this paper a detailed one dimensional numerical heat transfer analysis of a PTC is performed. The receiver and envelope were divided into several segments and mass and energy balance were applied in each segment. Improvements either in the heat transfer correlations or radiative heat transfer analysis are presented as well. The partial differential equations were discretized and the nonlinear algebraic equations were solved simultaneously. Finally, to validate the numerical results, the model was compared with experimental data obtained from Sandia National Laboratory (SNL) and other one dimensional heat transfer models. Our results showed a better agreement with experimental data compared to other models.     

Analysis of nonlinear thermal radiation and higher‐order chemical reactions on the non‐orthogonal stagnation point flow over a lubricated surface

A numerical study is performed to discuss the heat and mass transfer on oblique stagnation point flow over a lubricated surface with nonlinear thermal radiation and higher‐order chemical reactions. The problem is formulated using basic conservation laws of mass, momentum, energy, and mass concentration in terms of partial differential equations along with nonlinear boundary conditions. These governing equations are transformed into ordinary differential equations by means of similarity transformations. The system of resulting ordinary differential equations are solved numerically by an implicit finite difference scheme known as the Keller–box method. The quantities elaborated in the problem, such as velocity, temperature, skin friction, and local Nusselt and Sherwood numbers are analyzed for several values of involved parameters. The obtained results are presented through various graphs and tabular data and showed a good agreement with the existing results in the literature, which are the subcases of the present work. The heat transfer rate enhances with nonlinear thermal radiation and mass transfer rate decreases with increasing the order of chemical reaction.     

Radiative flow of micropolar nanofluid accounting thermophoresis and Brownian moment

This article describes the Brownian motion and thermophoresis aspects in nonlinear flow of micropolar nanoliquid. Stretching surface with linear velocity creates the flow. Energy expression is modeled subject to consideration of thermal radiation phenomenon. Effect of Newtonian heating is considered. The utilization of transformation procedure yields nonlinear differential systems which are computed through homotopic approach. The important features of several variables like material parameter, conjugate parameter, Prandtl number, Brownian motion parameter, radiation parameter, thermophoresis parameter and Lewis number on velocity, micro-rotation velocity, temperature, nanoparticles concentration, surface drag force and heat and mass transfer rates are discussed through graphs and tables. The presented analysis reveals that the heat and mass transfer rates are enhanced for higher values of radiation and Brownian motion parameters. Present computations are consistent with those of existing studies in limiting sense.     

Assessment of homotopy analysis method and homotopy perturbation method in non-linear heat transfer equation

Two new analytical methods to solve nonlinear heat transfer equations are homotopy perturbation method and homotopy analysis method. Here, homotopy analysis method, which gives us a vast freedom to choose the answer type, is applied to solve nonlinear heat transfer differential equations and analytical results are compared with those of HPM and the numerical results. In this study, the procedure of HAM is applied to two cases in different ways according to the physics of the target problem. Comparing the two methods, our attention is focused on the results accuracy; and applicability of different methods in many cases with different limitation is studied. In the two examples of this paper, the effect of small parameter increaser on the accuracy of the analytical results of two methods also has been studied. The first differential equation is the modeling equation of a cooling lumped system with combined convection and radiation. The second one is the modeling equation of heat transfer with conduction in a slab of thermal dependent conductivity.     

Numerical solution for Sisko nanofluid flow through stretching surface in a Darcy–Forchheimer porous medium with thermal radiation

The heat transfer assessments in a Sisko nanofluid flow over a stretching surface in a Darcy–Forchheimer porous medium with heat generation and thermal radiation are studied. The numerical analysis technique is used to assess the governing nonlinear equations of the model. The influence of Forchheimer number, porosity, heat generation, radiation, and material parameters is examined. The outlines of Nusselt number and skin friction coefficient corresponding to pertinent parameters are revealed. The comparison of Nusselt number outlines of working fluid and Newtonian fluid is depicted. From the analysis, it has been examined that with the increase in Forchheimer number and material parameter values, heat transfer function decreases, whereas heat transfer characteristics of Sisko nanofluid increase with heat generation and material parameters. Moreover, working fluid velocity outlines depreciate when there is an increase in porosity parameter for both shear-thinning and shear-thickening. The comparison of this study with previous research has been conducted.     

Nonlinear radiation and cross-diffusion effects on the micropolar nanoliquid flow past a stretching sheet with an exponential heat source

Metallurgy, polymer and processing engineering, and petrochemical enterprises frequently encounter polar nanoliquid flows due to stretchable surfaces with radiative heat energy. Therefore, the radiative flow of a polar nanoliquid over a stretchable sheet is analyzed considering cross-diffusion and magnetic heat flux effects. The heat transport phenomenon is explored, including the characteristics of nonlinear radiation and exponential space-based heat generation. The highly nonlinear governing equations are converted to ordinary differential equations using apt transformations. These are, in turn, solved employing the finite difference method. The behavior of contributing parameters is presented using graphical visualizations. The interactive impacts of the pertinent constraints on the rate of heat transfer and skin friction are analyzed using three-dimensional surface plots. The enhancement of the temperature profile is observed by incrementing the radiation and exponential heat generation parameters. The magnetic field can be used to regulate the fluid flow as it decreases the flow field. Also, the heat generation factor has a predominant decreasing effect on the Nusselt number.     

Magnetohydrodynamic MgO/CuO‐water hybrid nanofluid flow driven by two distinct geometries

Research regarding the heat transit mechanism of magnetohydrodynamic hybrid nanoliquid flow over contrasting flow profiles is predominantly employed in transpiration, coolants, fiber coatings, heat exchangers, and so on. Owing to this, we intend to dissect the heat transport behavior of MHD hybrid nanofluid flow past a cone as well as a wedge. For the analysis, we take nonlinear radiation and viscous dissipation into consideration with 30% of ethylene glycol and water (or EGW) as base fluid with suspended copper oxide (CuO) and magnesium oxide (MgO) nanoparticles. The Runge‐Kutta method with the shooting technique is utilized to figure out the deduced nonlinear gotverning equations. The influence of the concerned different admissible parameters on similar distributions (cone and wedge) are graphically illustrated and interpreted accordingly via computed numerical values. It is worth noting that the heat transport rate is greater past the cone rather than the wedge. The presence of CuO and MgO hybrid nanoparticles increases the heat transfer rate of the EGW base fluid.     

Thermal radiation and the second law

The purpose of this paper is to collect and interrelate the fundamental concepts about second law analysis of thermal radiation. This heat transfer mode plays a leading role in solar energy utilization and in high-temperature devices, representing a significant contribution to irreversibility that is frequently omitted in engineering analysis. Entropy and exergy of thermal radiation are reviewed first. Radiative transfer processes are reviewed next, including exchange between surfaces, the presence of a participative medium, and the analysis of combined heat transfer modes. Emphasis is put on grey body radiation when treating with non-black body radiation, due to its relevance in engineering applications. The mathematical formulation of second law analysis of thermal radiation is complex, which limits its use in conventional heat transfer analysis. For this reason, numerical approaches reported to date deal with quite simple cases, leaving an open promising field of research.     

TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH VARIABLE THERMAL CONDUCTIVITY

The effect of variable thermal conductivity on transient conduction and radiation heat transfer in a planar medium is investigated. Thermal conductivity of the medium is assumed to vary linearly with temperature, while the other thermophysical properties and the optical properties are assumed constant. The radiative transfer equation is solved using the discrete transfer method, (DTM) and the nonlinear energy equation is solved using an implicit scheme. Transient as well as steady state results are found for an absorbing, emitting, and anisotropically scattering gray medium. Thermal conductivity has been found to have significant effects on both transient as well as steady state temperature and heat flux distributions. Some steady state results are compared with the results reported in the literature.     

Influence of homogeneous‐heterogeneous reactions and induced magnetic field on the nonlinear thermal convective radiative Jeffrey liquid flow with heat source/sink

An analysis has been carried out to investigate the effect of homogeneous‐heterogeneous reactions and induced magnetic field on the unsteady two‐dimensional incompressible nonlinear thermal convective velocity slip flow of a Jeffrey fluid in the presence of nonlinear thermal radiation and heat source/sink. We assumed that the flow is generated due to injection at the lower plate and suction at the upper plate. We obtained a numerical solution for the reduced nonlinear governing system of equations via the shooting technique with fourth‐order Runge‐Kutta integration. We plotted the graphs for various nondimensional parameters, like Deborah number, heat source/sink parameter, nonlinear convection parameter, nonlinear radiation parameter, magnetic Reynolds number, Strommer's number, velocity slip parameter, strengths of homogeneous, heterogeneous reaction parameters and skin friction over the nondimensional flow, temperature, concentration profiles and magnetic diffusivity fields. Also, we calculated the numerical values of boundary properties, such as the skin friction and heat transfer rate. We noticed that the temperature of the fluid is enhanced with the radiation parameter, whereas the concentration decreases with increase of the magnetic Reynolds number. The present results have good agreement with published work for the Newtonian case.     

Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant

The heat transfer and thermal distribution through porous fins have gotten a lot of attention in recent years due to their extensive applications in the manufacturing and engineering field. In porous fins, the impact of magnetic field aids in improved heat transfer enhancement. Also, the combination of an electric effect and a magnetic field considerably enhances heat transfer. In this direction, the thermal distribution through a convective–radiative longitudinal trapezoidal porous fin with the impact of an internal heat source and an electromagnetic field is discussed in the present analysis. The governing heat equation is nondimensionalized with nondimensional terms, and the transformed nonlinear ordinary differential equation is solved analytically using the DTM–Pade approximant algorithm. Furthermore, the graphical discussion is presented to explore the impact of various nondimensional parameters, such as convection-conduction parameter, fin taper ratio, thermomagnetic field, radiation–conduction parameter, internal heat generation parameter, and thermoelectrical field on the temperature gradient of the fin. The investigation's key findings disclose that as the magnitude of the convection–conduction parameter, fin taper ratio, and radiation–conduction parameter increase, the thermal distribution through the fin reduces. The thermal distribution inside the fin increases for the heat-generating parameter, thermoelectric, and thermomagnetic fields.     

Inverse and efficiency of heat transfer convex fin with multiple nonlinearities

In this article, we first propose the novel semi‐analytical technique—modified Adomian decomposition method (MADM)—for a closed‐form solution of the nonlinear heat transfer equation of convex profile with singularity where all thermal parameters are functions of temperature. The longitudinal convex fin is subjected to different boiling regimes, which are defined by particular values of n (power index) of heat transfer coefficient. The energy balance equation of the convex fin with several temperature‐dependent properties are solved separately using the MADM and the spectral quasi‐linearization method. Using the values obtained from the direct heat transfer method, the unknown parameters of the profile, such as thermal conductivity, surface emissivity, heat generation number, conduction‐convection parameter, and radiation‐conduction parameter are inversely predicted by an inverse heat transfer analysis using the simplex search method. The effect of the measurement error and the number of measurement points has been presented. It is found that present measurement points and reconstruction of the exact temperature distribution of the convex fin are fairly in good agreement.     

Nonlinear Boussinesq buoyancy driven flow and radiative heat transport of magnetohybrid nanoliquid in an annulus: A statistical framework

The effect of nonlinear Boussinesq buoyancy force on the flow of Cu-Al₂O₃-H₂O hybrid nanoliquid in a vertical annulus, which is adjacent to the radial magnetic field and thermal radiation, is analyzed through a statistical approach. The phenomena of movement of annuli are taken into account. The aspect of nonlinear density temperature is also accounted based on nonlinear Boussinesq approximation (NBA). The exact solution is obtained for the two-point boundary value problem comprised dimensionless governing equations. The skin friction coefficient and Nusselt number expressions are also estimated. The impacts of various physical parameters on the velocity, temperature, skin friction coefficient, and Nusselt number distributions are analyzed. The statistical techniques, such as correlation coefficient, probable error, and a multivariate regression model, are employed for the detailed analysis. It is found that the NBA is favorable for the skin friction coefficient and the rate of heat transfer. The maximum heat transfer is found on the wall of the internal annuli.     

Performance optimization of a solar driven heat engine with finite-rate heat transfer

An optimal performance analysis for an equivalent Carnot-like cycle heat engine of a parabolic-trough direct-steam-generation solar driven Rankine cycle power plant at maximum power and maximum power density conditions is performed. Simultaneous radiation-convection and only radiation heat transfer mechanisms from solar concentrating collector, which is the high temperature thermal reservoir, are considered separately. Heat rejection to the low temperature thermal reservoir is assumed to be convection dominated. Irreversibilities are taken into account through the finite-rate heat transfer between the fixed temperature thermal reservoirs and the internally reversible heat engine. Comparisons proved that the performance of a solar driven Carnot-like heat engine at maximum power density conditions, which receives thermal energy by either radiation-convection or only radiation heat transfer mechanism and rejects its unavailable portion to surroundings by convective heat transfer through heat exchangers, has the characteristics of (1) a solar driven Carnot heat engine at maximum power conditions, having radiation heat transfer at high and convective heat transfer at low temperature heat exchangers respectively, as the allocation parameter takes small values, and of (2) a Carnot heat engine at maximum power density conditions, having convective heat transfer at both heat exchangers, as the allocation parameter takes large values. Comprehensive discussions on the effect of heat transfer mechanisms are provided.     

Radiative nanofluid flow and heat transfer between parallel disks with penetrable and stretchable walls considering Cattaneo–Christov heat flux model

In this work, we explore the unsteady squeezing flow and heat transfer of nanofluid between two parallel disks in which one of the disks is penetrable and the other is stretchable/shrinkable, in the presence of thermal radiation and heat source impacts, and considering the Cattaneo–Christov heat flux model instead of the more conventional Fourier's law of heat conduction. A similarity transformation is utilized to transmute the governing momentum and energy equations into nonlinear ordinary differential equations with the proper boundary conditions. The achieved nonlinear ordinary differential equations are solved by the Duan–Rach Approach (DRA). This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The impacts of diverse active parameters, such as the suction/injection parameter, the solid volume fraction, the heat source parameter, the thermal relaxation parameter, and the radiation parameter on flow and heat transfer traits are examined. In addition, the value of the Nusselt number is calculated and portrayed through figures.     

Effect of thermophoresis and Brownian motion on the melting heat transfer of a Jeffrey fluid near a stagnation point towards a stretching surface: Buongiorno's model

This analysis intends to address the coupled effect of phase change heat transfer, thermal radiation, and viscous heating on the MHD flow of an incompressible chemically reactive nanofluid in the vicinity of the stagnation point toward the stretching surface, taking a Jeffrey fluid as the base fluid. Convergent analytical solutions for the nonlinear boundary layer equations are obtained by the successive application of scaling variables and the highly efficacious homotopy analysis method. Error analysis is implemented to endorse the convergence of the solutions. Through parametric examination, influence of various physical parameters occurring in analysis of the profiles of velocity, temperature, and nanoparticle concentration, coefficient of surface drag, rates of mass and heat transfer is explored pictorially. The Deborah number and the melting parameter are found to enhance velocity, and the associated momentum boundary layers are thicker, whereas the magnetic field depreciates the flow rate. Temperature is observed to enhance with the thermophoresis parameter, Prandtl number and Eckert number, whereas a reduction is seen with the thermal radiation parameter and Brownian motion parameter. Nanoparticle concentration is depleted by the chemical reaction parameter, the thermophoresis parameter, and the Lewis number.     

辐射通道一维稳态温度场数值模拟

为得到辐射对流通道中的温度分布,依据能量守恒原理,建立了辐射、对流非线性边界条件下圆形管壁与管内空气的传热数学模型,提出了管壁温度、管内冷却空气温度一维稳态换热有限差分求解方法,其中辐射换热计算采用基于辐射传递系数的蒙特卡罗法。分析了相关参数对辐射通道温度分布的影响,所研究的参数包括辐射器表面温度、管道长度与半径比、管内冷却空气流速等。计算结果表明：辐射器表面温度是影响辐射通道最高温度的主要因素。此方法可为辐射通道精细的热工特性计算提供温度场数据。