Analytical investigation of the one dimensional heat transfer in logarithmic various surfaces

Vahabzadeh, A.; Fakour, M.; Ganji, D.D.; Bakhshi, Hamid

doi:10.1016/j.aej.2015.12.027

Cited by 4 publications

(9 citation statements)

References 23 publications

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“…A confirmation of this can be found, for example, in [7]. It is demonstrated here that, when solving a nonstationary inverse problem on heat transfer, good results are obtained when using the one-dimensional model in particular.…”

Section: A Simplified Methods For the Numerical Calculation Of Nonstatsupporting

confidence: 66%

A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall

Brunetkin

Maksymov

Lysiuk

2017

EEJET

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4process. But at the same time, its application is cumbersome and covers only particular cases. As a rule, they are confined by the description of the process of heating-cooling the bodies of simple shapes: infinite plate, cylinder, and sphere. Such solutions have been known for a long time, but up to now they have been applied only for a similar kind of processes. Only the object of application has changed in favor of contemporary equipment as, for example, in [3], where the problem on cooling a display is solved. Article [4] examines a process of cooling the plate with an internal heat source. The difference is that the examined plate is a multilayer one. A special feature of paper [5] is the application, instead of the frequently utilized Fourier expansion, the Trefftz functions. In this case, only the approximate solution is obtained. The problem of nonstationary heat transfer is of practical interest and it does not have the analytical solution.Numerical methods are more universal and can be used to solve any problems on heat transfer. From the above enumeration of simple shapes of bodies, a plate appears the most important one. It has two surfaces, which corresponds to the process of heat transfer. Furthermore, for the case of coaxial cylinders (a pipe) at the ratio between outer and inside diameters of d 2 /d 1 <2, heat transfer through the cylindrical wall with an error less than 4 % can be described using the model for a flat wall. Such a relationship of diameters corresponds to the majority of variants of tubular heat exchangers. Heat transfer is predetermined by taking account of the combined processes of heat exchange at the surfaces of a plate. These IntroductionThe use in energy equipment of fuel with variable composition [1, 2] instead of the certified constant formulation leads to an increase in the number of transient modes. A change in calorific fuel capacity, amount of products of combustion, their thermophysical properties predetermines the non-stationary processes of heating-cooling the elements of power equipment design, as well as nonstationary processes of heat transfer through the heat exchange surfaces. As a consequence, in the processes of energy conversion a more important role is played by its variable accumulation -release in all equipment components in contact with the combustion products. The accumulation of energy (heating -cooling) affects inertness in the processes of heat transfer and, therefore, manageability of the process of energy transformations. In turn, the magnitude of energy accumulation is determined by temperature of the elements of design. Thus, determining the non-stationary temperature and, as a result, the nonstationary magnitude of energy accumulation, is an important element in solving the problem on optimal control of power equipment under conditions of using a non-certified fuel of variable composition. Literature review and problem statementAnalytical solution is a reliable and universal means to calculate parameters of the nonstationary heat exchange O ....

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Section: A Simplified Methods For the Numerical Calculation Of Nonstatsupporting

confidence: 66%

A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall

Brunetkin

Maksymov

Lysiuk

2017

EEJET

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“…This investigation desired to use the weighted residual methods named LSM, CM, and GM to define an analytical explanation for logarithmic area shapes of the heat transfer equation in Figure 1. According to Figure 2, a particular case indicates the efficiency of suggested techniques, and the outcomes are evaluated with the numerical and analytical methods conducted by Vahabzadeh et al [18]. According to the obtained results, the percentage error of the present study compared to reported data in literature [18] is equal to 1.7%.…”

Section: Resultsmentioning

confidence: 73%

“…β indicates the effective rate of temperature change with respect to thermal conductivity, and k0 defines the fin's thermal conductivity with respect to the environment. To simplify this equation [18]:…”

Section: Geometry and Governing Equationsmentioning

confidence: 99%

“…By making the boundary conditions dimensionless in order to apply the desired methods, appropriate boundary conditions should be considered [18]:…”

Section: Geometry and Governing Equationsmentioning

confidence: 99%

“…Hatami and Ganji [16] discovered that LSM is more practical than other analytical and semi-analytical methods for cracking nonlinear heat transfer problems in many problems. Recently, several researchers have studied this issue and heat transfer [17][18][19][20][21][22][23][24][25]. Abbaszadeh et al [26] have presented the Galerkin method to solve the Navier-Stokes equation in combination with the heat transfer equation.…”

Section: Introductionmentioning

confidence: 99%

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Thermal Analysis of Fluid Flow with Heat Generation for Different Logarithmic Surfaces

Jalili

Mousavi

Jalili

et al. 2022

IJE

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This study investigated the effect of temperature changes on different logarithmic surfaces. Onedimensional heat transfer was considered. The heat generation source term is added to the governing equations. Most scientific problems and phenomena such as heat transfer occur nonlinearly, and it is not easy to find exact analytical solutions. Using the appropriate similarity transformation for temperature and the generation components causes the basic equations governing flow and heat transfer to be reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions with numerical and analytical techniques. According to the given boundary conditions, Collocation, Galerkin, and least squares methods were used to find an answer to the governing differential equations. The validation of the present techniques has been done with the fourth-order Runge-Kutta method as a numerical method. The temperature profiles for different values of β and α have been obtained. The results showed that the proposed methods could consider nonlinear equations in heat transfer. Therefore, the results accepted by current analytical methods are very close to those of numerical methods. Comparing the results provides a more realistic solution and reinforces the conclusions regarding the efficiency of these methods. Furthermore, changes in temperature profiles occur with decreasing and increasing β and α numbers.

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Flow and heat transfer of nanofluid with injection through an expanding or contracting porous channel under magnetic force field

Akinshilo

2018

Engineering Science and Technology, an International Journal

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Analytical investigation of the one dimensional heat transfer in logarithmic various surfaces

Cited by 4 publications

References 23 publications

A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall

A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall

Thermal Analysis of Fluid Flow with Heat Generation for Different Logarithmic Surfaces

Flow and heat transfer of nanofluid with injection through an expanding or contracting porous channel under magnetic force field

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