Jicheng He

Existence and estimate of positive solutions to a nonlinear singular boundary value problem in the theory of dilatant non-Newtonian fluids

This paper presents a rigorous proof of existence and uniqueness of solutions to laminar boundary layer flow in power law non-Newtonian fluid. A theoretical estimate for skin friction coefficient is given, which is characterized by a power law exponent. The reliability and efficiency of the proposed estimate formula are verified by numerical results with a good agreement. The estimate formula can be successfully applied to give the value of the skin friction coefficient.

Transfer behavior for a class of generalized N-diffusion equations in an infinite medium

Suitable similarity transformations were introduced to reduce generalized N-diffusion equations to the singular nonlinear boundary value problems and the similarity solutions were established. The results indicate that for specified a or N, the general diffusion flux θ(s) decrease with the increase of power law parameter N, but increase with the increase of k(s) or σ. For 0 1, θ(s) increase with σ and the diffusion profiles is nearly symmetry.

Transfer behavior of a class of generalized N-diffusion equations in a semi-infinite medium

Abstract Suitable similarity transformations were used for reducing the generalized N -diffusion equations to a class of singular nonlinear boundary value problems. Similarity solutions are presented analytically and numerically. The results indicated that for each fixed α , the general diffusion flux θ ( s ) decreases with the increase of the power law N and sharply with the increase of σ . For 0 σ ⩽1, θ ( s ) decrease with the increase of α , however, the behavior is quite opposite for σ >1.

Skin Friction and Heat Transfer on a Continuous Moving Flat Surface in Power Fluids

A theoretical analysis for the laminar momentum and energy boundary layer on a moving flat surface in power law fluids is made. The results indicate that while the plate moves in the direction of the flow, the boundary layer problem has a unique solution. Both skin friction and shear stress decrease with the increase of the ratio of the surface velocity to the free stream velocity and the power law n, the thermal diffusion ratio increases with the increase of n and ξ. However, in the case of the plate moving opposite to the flow, it is shown that the boundary layer solutions do not exist when velocity ratio ξ is larger than a positive critical value ξ* . For 0 < ξ < ξ* , the boundary layer solutions are found to be non-unique. Both superior and inferior solutions are noticeable. Skin friction and shear force for the superior solution decrease with the increase of the velocity ratio ξ. This is opposite for the inferior solution. The skin friction for both superior solution and inferior solution decrease with the increase of power law n. The result reveal the relations between momentum and thermal transfer, as well as the effects of parameters Pr , n and ξ on the transport process.Copyright