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This work solves the problem of thin-film withdrawal and drainage of a steady incompressible couple stress fluid on the outer surface of a vertical cylinder. The governing equations for velocity and temperature distributions are subjected to the boundary conditions and solved with the help of homotopy analysis method. The obtained expressions for f...
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Citations
This study examines the generalized Couette flow of couple stress fluid within the geometry of a helical screw rheometer (HSR). The geometry of the HSR is simplified by modeling the screw as an exposed rectangular channel and flattening the barrel surface. The screw and barrel are maintained at constant temperatures, and , respectively. The viscosity of the fluid is assumed to vary with temperature, and the Reynolds model is applied to describe this temperature‐viscosity relationship. The resulting mathematical formulation leads to nonlinearly coupled ordinary differential equations, with velocity and temperature as unknown functions. To solve for the velocity profiles and temperature distribution, an analytical technique known as the perturbation method is utilized. The expressions for volume flow rates are also derived. A graphical analysis is performed to examine the effects of various dimensionless parameters, such as the couple stress parameter , flight angle , constant number , Brinkman number , and pressure gradients in and ‐directions. It is observed that , and enhance the flow profiles and temperature distribution, while variations in reduce the velocity profile in the ‐direction but increase the net velocity and temperature distribution. The pressure gradient in ‐direction promotes the velocity component in ‐direction with no effects on the velocity component in ‐direction. Similarly, the pressure gradient in ‐direction increases the velocity component in ‐direction with no effects on the velocity component in ‐direction. These findings offer insights into optimizing flow behavior and heat transfer in HSR systems and provide a deeper understanding of the interactions between velocity, temperature, and material properties.
Energy utilization is a significant aspect of the manufacturing industrial processes, and inefficient transferring of heat is one of the disadvantages which can affect the quality measures of end product. Therefore, by controlling the heat transferring rate, the efficiency of manufacturing processes can be improved. Thus, the variable thermal relaxation time factor in the theory of Cattaneo-Christov is main concern of this analysis. The non-isothermal flow by means of a porous medium is modeled and analyzed for a viscous fluid. The fluid deformation is discussed under stretching mechanism. A study is also executed to interrogate the heat transfer features under the heat flux model of Cattaneo-Christov. Thermal relaxation time is also considered which is determined by temperature. The aspect of thermal stratification is also implemented to see the modifications in temperature. The flow and energy equations are reduced by appropriate variables. The reduced constitutive flow equations are then computed using an analytical convergent technique. The significant impacts of the numerous parameters on the flow field and heat transport features are evaluated in detail through various plots. Skin friction coefficient is evaluated mathematically. Results found that the temperature significantly decreases with increased stratification effects. For larger thermal relaxation time parameter, the temperature function shows increasing behavior.
