Application of differential transformation method in micropolar fluid flow and heat transfer through permeable walls

Reddy

et al. 2018

Heat Trans. Asian Res.

In the present article, the transient rheological boundary layer flow over a stretching sheet with heat transfer is investigated, a topic of relevance to non‐Newtonian thermal materials processing. Stokes couple stress model is deployed to simulate non‐Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The nondimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter (β), unsteadiness parameter (A), Prandtl number (Pr), buoyancy parameter (λ). The semi‐analytical differential transform method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built‐in solver “bvp4c” to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter, whereas it is decreased with unsteadiness parameter. Temperature is elevated with couple stress parameter, whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid), whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness, and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach.

Section: Solution Of the Problemmentioning

confidence: 99%

Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet

Reddy

et al. 2018

Heat Trans. Asian Res.

“…The DTM is a strong mathematical tool for solving systems of linear and nonlinear differential equations and requires significantly less computational resources. Mirzaaghaian and Ganji 18 carried out an application of DTM on micropolar fluid flow and heat transfer through permeable walls. Results obtained from their work were in excellent agreement when compared with Runge‐Kutta method.…”

Section: Introductionmentioning

confidence: 99%

Steady natural convection heat and mass transfer flow through a vertical porous channel with variable viscosity and thermal conductivity

Ajibade

Ojeagbase

2020

Engineering Reports

The present article studies the effects of suction/injection and variable physical properties on steady natural convection flow through a vertical channel. The investigation was done analytically using Differential Transformation Method (DTM). The variability in viscosity and thermal conductivity are considered linear function of temperature. The governing equations are transformed into a set of coupled nonlinear ordinary differential equations. Results obtained were compared with exact solution when some of the flow conditions were relaxed and results from DTM show an excellent agreement with the exact solution which was obtained analytically. The influence of the flow parameters on fluid temperature, concentration, and velocity are presented graphically and discussed for variations of the governing parameters. From the course of investigation, it was found that an increase in suction (S > 0) through the heated plate causes fluid temperature, velocity as well as concentration to decrease. However, an increase in injection causes heat transfer rate as well as skin friction at the heated plate to decrease.

“…where s denotes the boundary parameter representing the degree to which microelements are free to rotate near the channel walls. The case s = 0 means the strong concentration which shows that microelements are not rotating near the channel walls, s = 1/2 shows the weak concentrations and vanishing of the anti-symmetric part of the stress tensor, whereas s = 1 represents turbulent flow [26]. We introduced the following non-dimensional similarity variables in the case of strong concentration as:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…where,T 2 = T 1 + Ax, C 2 = C 1 + Bx with A and B as constants [26]. The velocity components of flow are defined by stream function as u = ∂ψ ∂y , v = − ∂ψ ∂x .…”

Section: Formulation Of the Problemmentioning

confidence: 99%

See 1 more Smart Citation

Steady Magnetohydrodynamic Micropolar Fluid Flow and Heat and Mass Transfer in Permeable Channel with Thermal Radiation

Agarwal¹,

Singh

Kumari

et al. 2021

Coatings

The present work is devoted to the study of magnetohydrodynamic micropolar fluid flow in a permeable channel with thermal radiation. The Rosseland approximation for thermal radiation is taken into account in the modelling of heat transfer. The governing equations are expressed in non-dimensional form. The Homotopy Perturbation Method (HPM) is briefly introduced and applied to derive the solution of nonlinear equations. The effects of various involved parameters like Reynolds number, microrotation parameter and Prandtl number on flow and heat transfer are discussed. Further, their effects on Nusselt and Sherwood numbers are also investigated from the physical point of view. Analytic solutions of the problem are obtained by HPM and a numerical technique bvp4c package MATLAB is applied to predict the graphs between different parameters.