Manipulating thermal conductivities are fundamentally important for controlling the conduction of heat at will. Thermal cloaks and concentrators, which have been extensively studied recently, are actually graded mater...Manipulating thermal conductivities are fundamentally important for controlling the conduction of heat at will. Thermal cloaks and concentrators, which have been extensively studied recently, are actually graded materials designed according to coordinate transformation approaches, and their effective thermal conductivity is equal to that of the host medium outside the cloak or concentrator. Here we attempt to investigate a more general problem: what is the effective thermal conductivity of graded materials? In particular, we perform a first-principles approach to the analytic exact results of effective thermal conductivities of materials possessing either power-law or linear gradation profiles. On the other hand, by solving Laplace's equation, we derive a differential equation for calculating the effective thermal conductivity of a material whose thermal conductivity varies along the radius with arbitrary gradation profiles.The two methods agree with each other for both external and internal heat sources, as confirmed by simulation and experiment. This work provides different methods for designing new thermal metamaterials(including thermal cloaks and concentrators), in order to control or manipulate the transfer of heat.展开更多
The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T ...The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T 〉 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.展开更多
In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both ...In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both viscous and Darcy dissipations. The coupled nonlinear governing equations are solved analytically. The expressions for the temperature, the axial velocity, the local wall shear stress and the pressure gradient are obtained. The effects of various physical parameters such as the Jeffrey parameter λ1, the permeability parameter σ and the heat source/sink parameter β are analyzed through graphs, and the results are discussed in detail. It is observed that the velocity field increases with increasing values of the Jeffrey parameter but it decreases with increasing values of the permeability parameter. It is found that the pressure rise increases with decreasing Jeffrey parameter and increasing permeability parameter. We notice that the effect of the permeability parameter a is the strongest on the bolus trapping phenomenon. For λ1 = 0, N =0, the results of the present study reduce to the results of Tripathi [Math. Comput.Modelling 57 （2013） 1270-1283]. Further the effect of viscous and Darcy dissipations is to reduce the rate of heat transfer in the finite vertical porous channel under peristalsis.展开更多
基金Support by the National Natural Science Foundation of China under Grant No.11725521the Science and Technology Commission of Shanghai Municipality under Grant No.16ZR1445100
文摘Manipulating thermal conductivities are fundamentally important for controlling the conduction of heat at will. Thermal cloaks and concentrators, which have been extensively studied recently, are actually graded materials designed according to coordinate transformation approaches, and their effective thermal conductivity is equal to that of the host medium outside the cloak or concentrator. Here we attempt to investigate a more general problem: what is the effective thermal conductivity of graded materials? In particular, we perform a first-principles approach to the analytic exact results of effective thermal conductivities of materials possessing either power-law or linear gradation profiles. On the other hand, by solving Laplace's equation, we derive a differential equation for calculating the effective thermal conductivity of a material whose thermal conductivity varies along the radius with arbitrary gradation profiles.The two methods agree with each other for both external and internal heat sources, as confirmed by simulation and experiment. This work provides different methods for designing new thermal metamaterials(including thermal cloaks and concentrators), in order to control or manipulate the transfer of heat.
基金supported by the National Natural Science Foundation of China (No. 10671040)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200522) the Program for the New Century Excellent Talents in University of China (No. 06-0359)
文摘The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T 〉 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.
文摘In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both viscous and Darcy dissipations. The coupled nonlinear governing equations are solved analytically. The expressions for the temperature, the axial velocity, the local wall shear stress and the pressure gradient are obtained. The effects of various physical parameters such as the Jeffrey parameter λ1, the permeability parameter σ and the heat source/sink parameter β are analyzed through graphs, and the results are discussed in detail. It is observed that the velocity field increases with increasing values of the Jeffrey parameter but it decreases with increasing values of the permeability parameter. It is found that the pressure rise increases with decreasing Jeffrey parameter and increasing permeability parameter. We notice that the effect of the permeability parameter a is the strongest on the bolus trapping phenomenon. For λ1 = 0, N =0, the results of the present study reduce to the results of Tripathi [Math. Comput.Modelling 57 （2013） 1270-1283]. Further the effect of viscous and Darcy dissipations is to reduce the rate of heat transfer in the finite vertical porous channel under peristalsis.
