Characteristics of melting heat transfer during flow of Carreau fluid induced by a stretching cylinder.

This article provides a comprehensive analysis of the energy transportation by virtue of the melting process of high-temperature phase change materials. We have developed a two-dimensional model for the boundary layer flow of non-Newtonian Carreau fluid. It is assumed that flow is caused by stretching of a cylinder in the axial direction by means of a linear velocity. Adequate local similarity transformations are employed to determine a set of non-linear ordinary differential equations which govern the flow problem. Numerical solutions to the resultant non-dimensional boundary value problem are computed via the fifth-order Runge-Kutta Fehlberg integration scheme. The solutions are captured for both zero and non-zero curvature parameters, i.e., for flow over a flat plate or flow over a cylinder. The flow and heat transfer attributes are witnessed to be prompted in an intricate manner by the melting parameter, the curvature parameter, the Weissenberg number, the power law index and the Prandtl number. We determined that one of the possible ways to boost the fluid velocity is to increase the melting parameter. Additionally, both the velocity of the fluid and the momentum boundary layer thickness are higher in the case of flow over a stretching cylinder. As expected, the magnitude of the skin friction and the rate of heat transfer decrease by raising the values of the melting parameter and the Weissenberg number.

Spreading dynamic of acute and carrier hepatitis B with nonlinear incidence.

Hepatitis B infection caused by the hepatitis B virus. It is one of the serious viral infection and a global health problem. In the transmission of hepatitis B infection different phases, i.e., acute and chronic carrier stages play an important role. The chronic carries individuals do not exhibit any symptoms and are able to transmit the infection. Here we assessed the transmissibility associated with different infection stages of hepatitis B and generated an epidemic model with nonlinear incidence rate. In order to do this, first we formulate the model by splitting the infectious class into two subclasses, namely acutely infected and chronic carries with both horizontal and vertical transmission. The basic properties of the proposed model are presented. The basic reproductive number is obtained by using the next generation matrix approach. Biological sense of the threshold condition is investigated and discussed in detail. We also find the conditions to investigate all possible equilibria of the model in terms of the basic reproduction number. Finally, we perform numerical simulations to support our analytical work.