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Thermal analysis of the convective-radiative fin with a step change in thickness and temperature dependent thermal conductivity

Torabi M., Yaghoobi H., Kiani M. R.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 3

593--602

EN

This paper provides heat transfer analysis in a straight fin with a step change in thickness and variable thermal conductivity, which is losing heat by simultaneous convection and radiation. The calculations are carried out by using the differential transformation method (DTM) that can be applied to various types of differential equations. The results obtained employing DTM are compared with an accurate numerical solution to verify the accuracy of the proposed method. Several graphs are provided to illustrate how the temperature distribution is affected by the (i) thickness parameter, (ii) dimensionless fin semi thickness, (iii) length ratio, (iv) thermal conductivity parameter, (vi) Biot’s number, and (vii) radiation-conduction parameter. This collection of graphs provides a comprehensive picture of the thermal performance of the system under steady state conditions.

2

Steady symmetrical temperature field in a hollow spherical particle with temperature-dependent thermal conductivity

Moosaie A.

Archives of Mechanics

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2012

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Vol. 64, nr 4

405-422

EN

In this work, an exact analytical solution to the axisymmetric heat conduction equation for hollow spherical objects with temperature-dependent thermal conductivity is presented. The nonlinear differential equation is first transformed into a linear one by means of an integral transform method. Then, the separation of variables method is employed to solve the transformed linear equation. Ultimately, we use the inverse transform to obtain the physical temperature field. Furthermore, two examples are worked out, i.e., the one-dimensional heat conduction in the radial direction and the two-dimensional case with axial symmetry. The solution is presented as an infinite series in terms of Legendre functions. The problem with spherical symmetry is also solved by using perturbation methods up to the third-order approximation, and the results are compared with the exact solution.

3

Stacjonarne przewodzenie ciepła przez wielowarstwową ściankę o zależnym od temperatury współczynniku przewodzenia ciepła

Mierzwiczak M.

Zeszyty Naukowe Politechniki Poznańskiej. Budowa Maszyn i Zarządzanie Produkcją

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2008

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Nr 9

67-79

PL

W artykule przedstawiono numeryczne rozwiązanie stacjonarnego zagadnienia przewodzenia ciepła przez wielowarstwową płaską i cylindryczną ściankę, której współczynnik przewodzenia zależy od temperatury. Do rozwiązania problemu zastosowano bezsiatkową metodę Kansy. Nieznane pole temperatury przyjmuje się w warstwach w postaci liniowej kombinacji radialnych funkcji bazowych (RBF). Kolokacyjne spełnienie równania rządzącego i warunków brzegowych prowadzi do nieliniowego układu równań rozwiązywanego metodą Newtona.

EN

This paper deals with numerical solution of heat transfer problem in multilayered plate and cylinder with temperature-dependent thermal conductivity. The Kansa meshless method was used for the solution of this problem. In this approach, the unknown's temperatures in layers are approximated by the radial basis functions, while the governing equation and the boundary conditions are imposed directly at the collocation points. The multiquadrics are used as the radial basis functions. Non-linear system of algebraic equations for coefficients at radial basis functions is solved by Newton method.