Effect of Newtonian heating on two-phase fluctuating flow of dusty fluid: Poincaré–Lighthill perturbation technique

Abstract

This article deals with the two phase fluctuating flow of dusty fluid and heat transfer in the presence of electrically conducting dust particles induces a strong magnetic field. The flow is considered between two parallel non-conducting plates, one at rest and the other in the state of fluctuation. Heat transfers due to free convection and Newtonian heating condition (NHC). The flow is generated due to plate fluctuation. In the sequence to scrutinize methodical solutions, we have used the Poincaré-Lighthill perturbation technique (PLPT). Results are obtained and plotted in graphs. The effect of pertinent parameters on the base fluid velocity such as Grashof number, magnetic parameter, radiation parameter and dusty fluid parameter has been studied. It is noticed that the velocity of the base fluid increases with the decrease in magnetic field and the applied shear stress, i.e., decreases up to some extent but gradually increases for the large magnetic parameter.

Enhancing heat transfer in MHD Falkner's‐Skan flow with thermal radiation, free convection and dusty fluid between parallel plates

“…• The equations for velocity, temperature fields, outflow and inflow, momentum, and energy are provided below 34 by using the premise of the Boussinesq approximation and in sequence to avoid similarities.…”

“… In the unsteady regime, a laminar flow has developed between the closed channel in one dimensional. The velocity of left plate is static, while the right plate is free stream velocity $${U}_{e}=\langle a{x}^{n}\rangle $$. Also, the given flow is Falkner's‐Skan flow 39 Left plate heated with surface temperature is $${\Theta }_{w}={\Theta }_{d}+b{x}^{2n-1}$$, 39 and the right plate is $${\Theta }_{d}$$. The role that radiation plays in the energy equation is also beginning to be described. The equations for velocity, temperature fields, outflow and inflow, momentum, and energy are provided below 34 by using the premise of the Boussinesq approximation and in sequence to avoid similarities. $$$\overrightarrow{V}=\psi (\zeta ,t)\mathop{i}\limits^{\wedge },$$$ $$$T=\Theta (\zeta ,t).$$$ $$$\nabla .\overrightarrow{V}=0$$$ …”

“…The solution of Equation (17) the PLPT 34,35 is used. $$$\psi (\zeta ,t)={\psi }_{0}(\zeta )+\varepsilon {\psi }_{1}(\zeta ){e}^{i\omega t}+O({\varepsilon }^{2}).$$$…”

“…Researchers may learn more about the dynamics, stability, and bifurcations of complicated nonlinear systems by dissecting them into linear and perturbation components. [34][35][36][37][38] The connection between the PLPT and other analytical and numerical techniques is another topic that is often discussed. Comparisons using approaches like perturbation theory, asymptotic methods, or numerical simulations may be done to evaluate the benefits and drawbacks of each strategy in various contexts.…”

“…Numerous systems, including celestial mechanics, fluid dynamics, oscillatory circuits, and nonlinear wave propagation, have all been studied using it. Researchers may learn more about the dynamics, stability, and bifurcations of complicated nonlinear systems by dissecting them into linear and perturbation components 34‐38 . The connection between the PLPT and other analytical and numerical techniques is another topic that is often discussed.…”