Application of the two-dimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins

Ndlovu, Partner L.; Moitsheki, Raseelo Joel

doi:10.1016/j.cnsns.2013.02.019

Cited by 29 publications

(21 citation statements)

References 15 publications

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“…Recently, (8) has been analyzed using the differential transform methods (DTM) [9]. A proposition in the work of Ndlovu and Moitsheki in [9] concluded that ( ), in equations such as (8), needs to be given by an exponential or power law with exponent being strictly 0.5 for DTM to work successfully. Here, we employ basic integration and Lie point symmetry techniques.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…Accurate and efficient exact, analytical, and approximate schemes for solving differential equations have been devised through considerable effort, particularly those arising in heat conduction through one-dimensional fin problems (see, e.g., [2][3][4][5][6][7][8]). The obtained solutions include series solutions [3,4,7], homotopy methods [2], and differential transformation methods (approximate analytical methods) [9]. Few exact solutions exist for one-dimensional problems.…”

Section: Introductionmentioning

confidence: 99%

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Some Exact Solutions of Nonlinear Fin Problem for Steady Heat Transfer in Longitudinal Fin with Different Profiles

Mhlongo

Moitsheki

2014

Advances in Mathematical Physics

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One-dimensional steady-state heat transfer in fins of different profiles is studied. The problem considered satisfies the Dirichlet boundary conditions at one end and the Neumann boundary conditions at the other. The thermal conductivity and heat coefficients are assumed to be temperature dependent, which makes the resulting differential equation highly nonlinear. Classical Lie point symmetry methods are employed, and some reductions are performed. Some invariant solutions are constructed. The effects of thermogeometric fin parameter, the exponent on temperature, and the fin efficiency are studied.

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Section: Mathematical Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some Exact Solutions of Nonlinear Fin Problem for Steady Heat Transfer in Longitudinal Fin with Different Profiles

Mhlongo

Moitsheki

2014

Advances in Mathematical Physics

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“…Ndlovu and Moitsheki [10] derived analytical solutions for the temperature distribution in longitudinal rectangular and convex parabolic fins with K and h a as temperature parameters. The transient heat conduction problem is solved, for the first time, using the Two-dimensional Differential transformation method (2D DTM).…”

Section: Introductionmentioning

confidence: 99%

Heat transfer characteristics and entropy generation for wing-shaped-tubes with longitudinal external fins in cross-flow

2016

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A numerical study is conducted to clarify heat transfer characteristics, effectiveness and entropy generation for a bundle of wingshaped-tubes attached to Longitudinal fins (LF) at downstream side. The air-side Re a ranged from 1.8 x 10 3 to 9.7 x 10 3 . The fin height (h f ) and fin thickness (δ) have been changed as: (2 mm ≤ h f ≤ 12 mm) and (1.5 mm ≤ δ ≤ 3.5 mm). The analysis of entropy generation is based on the principle of minimizing the rate of total entropy generation that includes the generation of entropy due to heat transfer and friction losses. The temperature field around the wing-shaped-tubes with (LF) is predicted using commercial CFD FLUENT 6.3.26 software package. Correlations of Nu a , St a , and Bejan number (Be), as well as the irreversibility distribution ratio (Φ) in terms of Re a and design parameters for the studied bundle are presented. Results indicated that, installing fins with heights from 2 to 12 mm results in an increase in Nu a from 11 to 36% comparing with that of wing-shaped tubes without fins (NOF). The highest and lowest values of effectiveness (ε) at every value of the considered Re a range are occurred at h f = 6 mm and (NOF), respectively. The wing-shaped-tubes heat exchanger with h f = 6 mm has the highest values of (ε), efficiency index (η) and area goodness factor (G a ) and also the lowest values of Φ and hence the best performance comparing with other arrangements. The minimum values of Φ are occurred at h f = 6 mm. (Be) decreases with increasing Re a for all studied h f . The heat transfer irreversibility predominates for (1800 ≤ Re a ≤ 4200) while the opposite is true for (6950 < Re a ≤ 9700). δ has negligible effect on Nu a and heat transfer irreversibility. Comparisons between the experimental and numerical results of the present study and those, previously, obtained for similar available studies showed good agreements.

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“…A brief review of the relevant literature published before 2011 can be found in our previous paper [20]. Research achievements in recent years include nonlinear steady heat conduction analysis for a convective n [21], convective-radiative ns of porous material [22], convective-radiative moving ns (or plates) [23][24][25], a Tshaped n [26] and variable thickness ns [27][28][29], and nonlinear transient heat conduction analysis for variable thickness ns [30]. Recently, the range of application of the DTM has been extended to the analysis of heat conduction in nonhomogeneous bodies [31,32] and phase-change problems [33,34].…”

Section: Introductionmentioning

confidence: 99%

Series solution to coupled nonlinear heat and moisture transfer in slabs with temperature-dependent diffusivities

Chiba

2014

Nonlinear Engineering

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The two-dimensional di erential transform method (DTM) is applied to solve the one-dimensional coupled heat and moisture di usion problem for a slab with temperature-dependent thermal and moisture diffusivities, which are expressed by a linear function and an exponential function of temperature, respectively. One surface of the slab is subjected to convective hygrothermal loading and the other has constant prescribed temperature and moisture. Approximate analytical (series) solutions for the temperature and moisture pro les in the slab are derived. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical results for a slab subjected to a sudden change in surface temperature illustrate the e ects of temperature-dependent di usivities on the transient temperature and moisture pro les of the slab. The results indicate that the nonlinear e ect originating from the varying moisture di usivity is not negligible for resin composites. The DTM is a useful new analytical method for solving nonlinear coupled transient problems.

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Application of the two-dimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins

Cited by 29 publications

References 15 publications

Some Exact Solutions of Nonlinear Fin Problem for Steady Heat Transfer in Longitudinal Fin with Different Profiles

Some Exact Solutions of Nonlinear Fin Problem for Steady Heat Transfer in Longitudinal Fin with Different Profiles

Heat transfer characteristics and entropy generation for wing-shaped-tubes with longitudinal external fins in cross-flow

Series solution to coupled nonlinear heat and moisture transfer in slabs with temperature-dependent diffusivities

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