Solution of the Boundary Layer Equation of the Power-Law Pseudoplastic Fluid Using Differential Transform Method

The boundary layer equation of the pseudoplastic fluid over a flat plate is considered. This equation is a boundary value problem (BVP) with the high nonlinearity and a boundary condition at infinity. To solve such problems, powerful numerical techniques are usually used. Here, through using differential transform method (DTM), the BVP is replaced by two initial value problems (IVP) and then multi-step differential transform method (MDTM) is applied to solve them. The differential equation and its boundary conditions are transformed to a set of algebraic equations, and the Taylor series of solution is calculated in every sub domain. In this solution, there is no need for restrictive assumptions or linearization. Finally, DTM results are compared with the numerical solution of the problem, and a good accuracy of the proposed method is observed

Investigation of Transient MHD Couette flow and Heat Transfer of Dusty Fluid with Temperature-Dependent Oroperties

In the present study, transient MHD Couette flow and heat transfer of dusty fluid between two parallel plates and the effect of the temperature dependent properties has been investigated. The thermal conductivity and viscosity of the fluid are assumed as linear and exponential functions of temperature, respectively. A constant pressure gradient and an external uniform magnetic field are considered in the main flow direction and perpendicular to the plates, respectively. A hybrid treatment based on finite difference method (FDM) and differential transform method (DTM) is used to solve the coupled flow and heat transfer equations. The effects of the variable properties, Hartman number, Hall current, Reynolds number and suction velocity on the Nusselt number and skin friction factor have been discussed. It is found that when Hartman number increases, skin friction of the upper and lower plates increases

Approximate solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient

In this paper, differential transform method (DTM) is used to solve the nonlinear heat transfer equation of a fin with the power-law temperature-dependent both thermal conductivity and heat transfer coefficient. Using DTM, the differential equation and the related boundary conditions transformed into a recurrence set of equations and finally, the coefficients of power series are obtained based on the solution of this set of equations. DTM overcame on nonlinearity without using restrictive assumptions or linearization. Results are presented for the dimensionless temperature distribution and fin efficiency for different values of the problem parameters. DTM results are compared with special case of the problem that has an exact closed-form solution, and an excellent accuracy is observed