Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity,non-uniform heat source and radiation

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.     

Application of the two-dimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins

In this article, approximate analytical (series) solutions for the temperature distribution in a longitudinal rectangular and convex parabolic fins with temperature dependent thermal conductivity and heat transfer coefficient are derived. The transient heat conduction problem is solved for the first time using the two-dimensional differential transform method (2D DTM). The effects of some physical parameters such as the thermo-geometric parameter, exponent and thermal conductivity gradient on temperature distribution are studied. Furthermore, we study the temperature profile at the fin tip.     

Multidimensional two-phase quasistationary stefan problem

Existence and uniqueness of the classic solution to a two-dimensional quasistationary Stefan problem are considered. The family of model problems dependent on the parameter ε>0 which defines a heat conductivity of a matter in the direction of thex-axis is analysed. When ε→0 it is approximated by the approximate model problem having less dimensions. Analogous results are also valid for a three-dimensional problem.     

Electrohydrodynamic linear stability of finitely conducting flows through porous fluids with mass and heat transfer

In this work, a linear stability analysis is used to investigate a capillary surface waves between two horizontal finite fluid layers. The system is acted upon by a vertical periodic electric field. The problem examines few representatives of porous media. It is also includes finite conductivity, mass and heat transfer. It is assumed that the basic flow is two-dimensional streaming flow. A general dispersion relation governing the linear stability is derived. In contrast with our previous work [23], the present problem shows that the stability criterion depends on the mass and heat transfer parameter. The present study recovers some special cases upon appropriate data choices. The presence of finite conductivity’s together with the dielectric permeability’s make the uniform electric field plays a dual role in the stability criterion. This shows some analogy with the nonlinear stability theory. In addition, the mass and heat transfer parameter as well as the Darcy’s coefficients play a stabilizing role in the stability picture. In case of the Rayleigh–Taylor instability, by means of the Whittaker technique, the parametric excitation of the electrohydrodynamic surface waves is obtained. The transition curve equations are calculated up to the fourth order for a small dimensionless parameter. The analytical results are numerically confirmed.     

Steady one-dimensional heat flow in a longitudinal triangular and parabolic fin

We consider a heat transfer problem of a longitudinal fin with triangular and parabolic profiles. Both thermal conductivity and heat transfer coefficient are assumed to be temperature-dependent, and given by power laws. We construct exact solution when the problem is linearizable. In the other case, classical Lie symmetry techniques are employed to analyze the problem. The obtained exact solutions satisfy the realistic boundary conditions. The effects of the physical applicable parameters such as thermo-geometric fin parameter and the fin efficiency are analyzed.     

Retrieving the time-dependent thermal conductivity of an orthotropic rectangular conductor

The aim of this paper is to determine the thermal properties of an orthotropic planar structure characterized by the thermal conductivity tensor in the coordinate system of the main directions (Oxy) being diagonal. In particular, we consider retrieving the time-dependent thermal conductivity components of an orthotropic rectangular conductor from nonlocal overspecified heat flux conditions. Since only boundary measurements are considered, this inverse formulation belongs to the desirable approach of non-destructive testing of materials. The unique solvability of this inverse coefficient problem is proved based on the Schauder fixed point theorem and the theory of Volterra integral equations of the second kind. Furthermore, the numerical reconstruction based on a nonlinear least-squares minimization is performed using the MATLAB optimization toolbox routine lsqnonlin. Numerical results are presented and discussed in order to illustrate the performance of the inversion for orthotropic parameter identification.     

Steady heat transfer through a radial fin with rectangular and hyperbolic profiles

We construct some exact solutions for thermal diffusion in a fin with a rectangular profile and another with a hyperbolic profile. Both the thermal conductivity and the heat transfer coefficient are assumed to be temperature dependent. Moreover, the thermal conductivity and the heat transfer terms are given by the same power law in one case and distinct power laws in the other. A point transformation is introduced to linearize the problem when the power laws are equal. In the other case, classical Lie symmetry techniques are employed to analyze the problem. The exact solutions obtained satisfy the realistic boundary conditions. The effects of applicable physical parameters such as the thermo-geometric fin parameter and the fin efficiency are analyzed.     

Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity

This study investigates the exact solutions of a nonlinear fin problem with temperature-dependent thermal conductivity and the heat transfer coefficient. Both the conduction and heat transfer terms are given by the same power law in one case and the distinct power law in the other. Classical Lie symmetry techniques are employed to construct the exact solutions which satisfy the realistic boundary conditions. The effects of the physical applicable parameters such as the thermo-geometric fin parameter and the fin efficiency are analyzed.     

Global existence of solutions for the 1-D radiative and reactive viscous gas dynamics

In this paper, we prove the existence of a global solution to an initial-boundary value problem for 1-D flows of the viscous heat-conducting radiative and reactive gases. The key point here is that the growth exponent of heat conductivity is allowed to be any nonnegative constant; in particular, constant heat conductivity is allowed.     

An inverse problem in estimating simultaneously the effective thermal conductivity and volumetric heat capacity of biological tissue

An inverse problem utilizing the Levenberg–Marquardt method (LMM) is applied in this study to determine simultaneously the unknown spatial-dependent effective thermal conductivity and volumetric heat capacity for a biological tissue based on temperature measurements. The accuracy of this inverse problem is examined by using the simulated exact and inexact temperature measurements in the numerical experiments. A statistical analysis is performed to obtain the 99% confidence bounds for the estimated thermal properties. Results show that good estimation on the spatial-dependent thermal conductivity and volumetric heat capacity can be obtained using the present algorithm for the test cases considered in this study.     

热泳和Brown运动对太阳能辐射下热分层纳米流体边界层流动的影响

在太阳辐射下的纳米流体中,数值地研究竖向延伸壁面具有可变流条件时的层流运动.使用的纳米流体模型为,在热分层中综合考虑了Brown运动和热泳的影响.应用一个特殊形式的Lie群变换,即缩放群变换,得到相应边值问题的对称群.对平移对称群得到一个精确解,对缩放对称群得到数值解.数值解依赖于Lewis数、Brown运动参数、热分层参数和热泳参数.得到结论:上述参数明显地影响着流场、温度和纳米粒子体积率的分布.显示出纳米流体提高了基流体热传导率和对流的热交换性能,基流体中的纳米粒子还具有改善液体辐射性能的作用,直接提高了太阳能集热器的吸热效率.     

Perturbation analysis of the heat transfer in porous media with small thermal conductivity

An approximate analytical solution for the one-dimensional problem of heat transfer between an inert gas and a porous semi-infinite medium is presented. Perturbation methods based on Laplace transforms have been applied using the solid thermal conductivity as small parameter. The leading order approximation is the solution of Nusselt (or Schumann) problem. Such solution is corrected by means of an outer approximation. The boundary condition at the origin has been taking into account using an inner approximation for a boundary layer. The gas temperature presents a discontinuous front (due to the incompatibility between initial and boundary conditions) which propagates at constant velocity. The solid temperature at the front has been smoothed out using an internal layer asymptotic approximation. The good accuracy of the resulting asymptotic expansion shows its usefulness in several engineering problems such as heat transfer in porous media, in exhausted chemical reactions, mass transfer in packed beds, or in the analysis of capillary electrochromatography techniques.     

Numerical study of dynamic thermal conductivity of nanofluid in the forced convective heat transfer

In this work, forced convective heat transfer of nanofluid in the developing laminar flow (entrance region) in a circular tube is considered. The nanofluid thermal conductivity, as an important parameter, is considered as two parts: static and dynamic part. Simulated results show that the dynamic part of nanofluid thermal conductivity due to the Brownian motion has a minor effect on the heat transfer coefficients, on the other hand, static part of thermal conductivity including nanolayer around nanoparticle has an important role in heat transfer.     

Effects of temperature-dependent viscosity and variable thermal conductivity on MHD non-Darcy mixed convective diffusion of species over a stretching sheet

A numerical model is presented to study the effects of temperature-dependent viscosity and variable thermal conductivity on mixed convection problem. Two important types of wall heating conditions namely, prescribed surface temperature and prescribed wall heat flux which arise in polymer industries are considered. The problem is solved numerically by using the fifth-order Runge–Kutta Fehlberg method with shooting technique. It is found that the Prandtl number is to decrease the skin friction coefficient, local Nusselt number and local Sherwood number. The effects of non-uniform heat source/sink and porous parameter are analyzed on velocity, temperature, skin friction co-efficient, Nusselt and Sherwood numbers.     

Unsteady flow and heat transfer in a thin film of Ostwald–de Waele liquid over a stretching surface

In this paper, the effects of viscous dissipation and the temperature-dependent thermal conductivity on an unsteady flow and heat transfer in a thin liquid film of a non-Newtonian Ostwald–de Waele fluid over a horizontal porous stretching surface is studied. Using a similarity transformation, the time-dependent boundary-layer equations are reduced to a set of non-linear ordinary differential equations. The resulting five parameter problem is solved by the Keller–Box method. The effects of the unsteady parameter on the film thickness are explored numerically for different values of the power-law index parameter and the injection parameter. Numerical results for the velocity, the temperature, the skin friction and the wall-temperature gradient are presented through graphs and tables for different values of the pertinent parameter. One of the important findings of the study is that the film thickness increases with an increase in the power-law index parameter (as well as the injection parameter). Quite the opposite is true with the unsteady parameter. Furthermore, the wall-temperature gradient decreases with an increase in the Eckert number or the variable thermal conductivity parameter. Furthermore, the surface temperature of a shear thinning fluid is larger compared to the Newtonian and shear thickening fluids. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena.     

非常量导热系数几例微分方程的推立

在本文里,曾先后假设物体的导热系数是依直线和指数函数空间地起改变,就这样来建立了六个二阶热传导微分方程;又对于变密度、变比热、变导热系数这样的更一般的情况也推立了六个二阶热传导的微分方程.     

Local Existence of Bounded Solutions to the Degenerate Stefan Problem with Joule's Heating

This paper deals with the degenerate Stefan problem with Joule's heating, which describes the combined effects of heat and electrical current Rows in a metal. The local existence of a bounded weak solution for the problem in proved. Also a degenerate thermistor problem with continuous conductivity is considered.     

基于动态热湿传递的纺织材料孔隙率决定的反问题

除纺织材料的厚度与导热系数外,其孔隙率也是影响人体热湿舒适性的一个重要因素.基于动态热湿传递模型,作者提出了满足人体热湿舒适性的纺织材料孔隙率决定反问题.通过吉洪诺夫正则化方法将纺织材料孔隙率决定反问题归结为目标函数极小值问题.应用巴拿赫不动点理论证明了正问题解的存在唯一性,揭示了织物内热湿传递变化规律.应用L-曲线方法获得了正则化参数的最优选择,采用粒子群最优化算法随机搜索目标函数极小值点,得到反问题的广义解.数值模拟结果验证了纺织材料孔隙率决定反问题提法的合理性和算法的有效性.     

The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet

An analysis has been carried out to study the momentum and heat transfer characteristics in an incompressible electrically conducting non-Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly non-linear coupled ordinary differential equations by similarity transformations. The effect of variable fluid viscosity, Magnetic parameter, Prandtl number, variable thermal conductivity, heat source/sink parameter and thermal radiation parameter are analyzed for velocity, temperature fields, and wall temperature gradient. The resultant coupled highly non-linear ordinary differential equations are solved numerically by employing a shooting technique with fourth order Runge–Kutta integration scheme. The fluid viscosity and thermal conductivity, respectively, assumed to vary as an inverse and linear function of temperature. The analysis reveals that the wall temperature profile decreases significantly due to increase in magnetic field parameter. Further, it is noticed that the skin friction of the sheet decreases due to increase in the Magnetic parameter of the flow characteristics.     

Approximation of the conductivity coefficient in the heat equation

In this paper, we study the conductivity coefficient determination in the heat equation from observation of the lateral Dirichlet-to-Neumann map. We define a bilinear form function Q_γ associated to the boundary condition and the Dirichlet-to-Neumann map, and prove that the linearized problem d?Q_γ is injective. Based on the idea of complex geometrical optics solutions, we give two approximations to the conductivity coefficient by using the Fourier truncation method and the mollification method. Under the a priori assumption of the conductivity, we estimate the errors between the conductivity coefficient and its approximations by setting a suitable bound of the frequency.