A model for planning the product portfolio and launch timings under resource constraints

Product design is increasingly becoming a critical function in many organisations having significant impact on their performance. It aims at the selection of a near-optimal mix of products and attribute-levels to offer in the target market. The standard product portfolio planning approach has focused on selecting optimum product profiles based on part-worth utility data. However, given that product development happens in multiple stages, combining the product definition decisions with the product development feasibility will provide organisations with a more inclusive and global solution. This paper considers a resource-constrained environment with a multi-stage product development cycle and presents an approach for helping an organisation to select the definitions of products for its product portfolio and the feasible launch timings. The proposed framework will aid product managers and researchers to identify and evaluate alternative product definitions using a Mixed Integer Linear Programming model in order to determine the alternatives which best balance product features and product development.     

Micropolar couple stress thermofluidics and entropy in Forchheimer channel

This paper presents an analysis of the entropy generated in thermofluidic configuration involving micropolar couple stress fluid flow inside a Forchheimer channel. The channel is composed of a porous medium trapped between two parallel permeable plates separated by distance H through which the fluid can be sucked out/injected in. One of the plate bears a constant temperature and other is subjected to a uniform heat flux. A Cartesian coordinate system is chosen to model the flow configuration. The nondimensional nonlinear governing equations are solved by the differential transform method and Runge–Kutta–Fehlberg method to ascertain the accuracy of the results. Both the methods do match to the order of 10⁻⁶ for the quantities velocity, microrotation, and temperature. These quantities and their gradients are required to the compute entropy generation number. The effects of the parameters on entropy generation and Bejan number are discussed through various plots.     

Irreversibility analysis for Casson thermo-fluidics inside a cone: Cattaneo–Christov heat flux

In this communication, thermodynamic irreversibility arising in dissipative Casson fluid flow inside a cone is investigated. The boundary–layer flow is considered wherein the motion is caused due to a point sink at the cone's vertex and the movement of the wall of the cone. The wall of the cone is subjected to mass transpiration that alters the flow and thermal regime. The cone having fluid-saturated porous medium experiences Cattaneo–Christov heat flux. The configuration admits a similarity transformation that yields a boundary value problem (BVP) comprising an ordinary differential equation. The BVP is treated by the fourth-order R-K method along with the shooting algorithm. The system yields a dual solution for momentum and energy, which gives rise to a dual regime for entropy distribution. Numerical computations provide quantities of interest viz. velocity and temperature distributions, skin friction coefficient, Nusselt number, and entropy distribution. Phenomena exhibited through profiles/tables for velocity, temperature, entropy, streamlines, and other quantities of interest reveal interesting results.     

Cattaneo–Christov flux and entropy in thermofluidics involving shrinking surface

The paper examines radiative Casson boundary layer flow over an exponentially shrinking permeable sheet in a Cattaneo–Christov heat flux environment. The sheet is placed at the bottom of the fluid-saturated porous medium and suction is applied normally to the sheet to contain the vorticity. The radiative heat flux in the energy equation is assumed to follow the Rosseland approximation. Similarity transformation is performed to convert the governing partial differential equations into ordinary differential equations. The resulting boundary value problem is treated numerically employing Runge–Kutta fourth-order integration scheme along with the shooting method. The effects of pertinent parameters on quantities of interest are showcased graphically/in tabular form and are discussed. The dual profiles for velocity and temperature lead to a dual solution regime for entropy. It is found that critical mass suction rate and Nusselt number are substantially responsive to various parameters' values. Critical suction values decrease with a rise in Casson parameter β and permeability parameter K. Skin friction coefficient and Nusselt number show peculiar behavior for distinct branches of solutions.     

Differential transform method for couple stress fluid flow in a channel with a porous base

The paper presents an application of the semi-analytical differential transform method (DTM) to thermofluidics of generalized Couette flow of couple stress fluid inside a composite channel. The channel comprises a fluid-saturated porous layer and a clear fluid region. The flow is caused by a uniformly favorable pressure gradient applied at the mouth of the channel and the shear of the moving upper wall of the channel. The matching conditions are taken such that the velocity, temperature, and respective gradients are continuous at a clear fluid–porous medium. The problem is novel because this is the first mathematical endeavor to treat fluidic systems involving composite channels. Besides the mathematical rigor, it presents an analysis of thermodynamic irreversibility and other quantities of interest, viz, skin friction and Nusselt number. The results derived from DTM are compared with those obtained by exact solution showing excellent agreement. The plots and tables are drawn and discussed.