A novel analytical solution of mixed convection about an inclined flat plate embedded in a porous medium using the DTM-Padé

Rashidi, Majid; Laraqi, Najib; Sadri, Seyed Majid

doi:10.1016/j.ijthermalsci.2010.07.005

Cited by 77 publications

(55 citation statements)

References 35 publications

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“…3, where the concept of a differential transform is briefly described. The method was subsequently used to obtain analytical solutions of higher-order ordinary differential equations, partial differential equations, difference equations, and integro-differential equations [13][14][15][16][17][18][19][20][21]. Chu and Chen [13] applied a hybrid method of a differential transform and finite difference method to solve a transient heat conduction problem which had complex nonlinear terms.…”

Section: Introductionmentioning

confidence: 99%

“…Jang et al [17] investigated a two-dimensional transient heat conduction problem with discontinuous boundary and initial conditions. Rashidi et al [18] applied the DTM to find the analytic solution for the problem of mixed convection about an inclined flat plate embedded in a porous medium. Rashidi and Mohimanian Pour [19] applied the DTM to steady flow over a rotating disk in a porous medium with heat transfer.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

2012

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In this article, heat transfer in a moving fin with variable thermal conductivity, which is losing heat by simultaneous convection and radiation to its surroundings, is analyzed. The calculations are carried out by using the differential transformation method (DTM) which is an analytical solution technique that can be applied to various types of differential equations. The effects of parameters such as the Peclet number, Pe, thermal conductivity parameter, a, convection-conduction parameter, N c , radiation-conduction parameter, N r , dimensionless convection sink temperature, θ a , and dimensionless radiation sink temperature, θ s , on the temperature distribution are illustrated and explained. The analytical solution is found to be in good agreement with the direct numerical solution. Moreover, the results demonstrate that the DTM is very effective in generating analytical solutions for even highly nonlinear problems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

2012

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“…The objective of this paper is to solve the problem of a fully developed combined mixed convection and radiation effect in a vertical channel, with the effect of viscous dissipation and different thermal boundary conditions using a semi-numerical-analytical method called Differential Transformation Method (DTM) (See Zhou [15], Bert [16], Chu and Chen [17], Chu and Lo [18], Joneidi et al [19], Rashidi et al [20], Yaghoobi and Torabi [21] ). This method obtains a solution in the form of a polynomial.…”

Section: Introductionmentioning

confidence: 99%

Mixed Convective Fully Developed Flow in a Vertical Channel in the Presence of Thermal Radiation and Viscous Dissipation

Prasad¹,

Mallikarjun

Vaidya³

2017

International Journal of Applied Mechanics and Engineering

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The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux). The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM) and regular perturbation method (PM). The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM) and regular perturbation method (PM) methods shows the versatility of the Differential Transform Method (DTM). The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.

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“…Jang et al [26] investigated and characterized a two-dimensional thermal conductive boundary value problem with discontinuous boundary and initial conditions. Rashidi et al [27] applied DTM to find the analytic solution for the problem of mixed convection about an inclined flat plate embedded in a porous medium. Yaghoobi and Torabi [28] applied DTM to solve the problems of convective and convective-radiative cooling of a lumped system with temperature-dependent specific heat.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

Torabi

Yaghoobi

Colantoni

et al. 2013

Chinese Journal of Engineering

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Radiative radial fin with temperature-dependent thermal conductivity is analyzed. The calculations are carried out by using differential transformation method (DTM), which is a seminumerical-analytical solution technique that can be applied to various types of differential equations, as well as the Boubaker polynomials expansion scheme (BPES). By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced and then applied to the aforementioned equations. Solutions are subsequently obtained by a process of inverse transformation. The current results are then compared with previously obtained results using variational iteration method (VIM), Adomian decomposition method (ADM), homotopy analysis method (HAM), and numerical solution (NS) in order to verify the accuracy of the proposed method. The findings reveal that both BPES and DTM can achieve suitable results in predicting the solution of such problems. After these verifications, we analyze fin efficiency and the effects of some physically applicable parameters in this problem such as radiation-conduction fin parameter, radiation sink temperature, heat generation, and thermal conductivity parameters.

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A novel analytical solution of mixed convection about an inclined flat plate embedded in a porous medium using the DTM-Padé

Cited by 77 publications

References 35 publications

Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

Mixed Convective Fully Developed Flow in a Vertical Channel in the Presence of Thermal Radiation and Viscous Dissipation

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

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