scholarly journals Survey of Some Exact and Approximate Analytical Solutions for Heat Transfer in Extended Surfaces

2021 ◽  
Author(s):  
Raseelo Joel Moitsheki ◽  
Partner Luyanda Ndlovu ◽  
Basetsana Pauline Ntsime
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Properties ◽  
Analytical Solutions ◽  
Nonlinear Problems ◽  
Transient Heat Transfer ◽  
Temperature Dependent ◽  
Approximate Analytical Solutions ◽  
Extended Surfaces ◽  
Insight Into

In this chapter we provide the review and a narrative of some obtained results for steady and transient heat transfer though extended surfaces (fins). A particular attention is given to exact and approximate analytical solutions of models describing heat transfer under various conditions, for example, when thermal conductivity and heat transfer are temperature dependent. We also consider fins of different profiles and shapes. The dependence of thermal properties render the considered models nonlinear, and this adds a complication and difficulty to solve these model exactly. However, the nonlinear problems are more realistic and physically sound. The approximate analytical solutions give insight into heat transfer in fins and as such assist in the designs for better efficiencies and effectiveness.

Thermally Symmetric Nonlinear Heat Transfer in Solids

1981 ◽  
Vol 103 (4) ◽  
pp. 745-752 ◽  
Author(s):  
M. Imber
Keyword(s):  
Heat Transfer ◽  
Thermal Properties ◽  
Analytical Solutions ◽  
Solution Method ◽  
Equivalent Linearization ◽  
Temperature Dependent ◽  
Numerical Examples ◽  
Nonlinear Heat Transfer ◽  
Composite Wall ◽  
Thermal Conductivities

Material thermal properties are temperature dependent, and this effect cannot be disregarded at elevated design temperatures. Based upon the principle of equivalent linearization, analytical solutions are developed for thermally symmetric planar solids. The solution method is, in turn, extended to a composite wall whose individual thermal conductivities are also temperature dependent. As a demonstration of the method’s accuracy several numerical examples are shown.

Analysis of Heat Transfer in a Cylindrical Spine Fin with Variable Thermal Properties

2018 ◽  
Vol 387 ◽  
pp. 10-22 ◽  
Author(s):  
Nkejane Fallo ◽  
Raseelo Joel Moitsheki ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Thermal Conductivity ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Numerical Techniques ◽  
Temperature Dependent ◽  
Approximate Analytical Solutions ◽  
Differential Transform ◽  
The Heat Transfer Coefficient

In this paper we analyse the heat transfer in a cylindrical spine fin. Here, both the heat transfer coefficient and thermal conductivity are temperature dependent. The resulting 2+1 dimension partial differential equation (PDE) is rendered nonlinear and difficult to solve exactly, particularly with prescribed initial and boundary conditions. We employ the three dimensional differential transform methods (3D DTM) to contract the approximate analytical solutions. Furthermore we utilize numerical techniques to determine approximate numerical solutions. The effects of parameters, appearing in the boundary value problem (BVP), on temperature profile of the fin are studied.

Heat Exchange Between a Tube and Water-Saturated Soil

1986 ◽  
Vol 108 (4) ◽  
pp. 298-302 ◽  
Author(s):  
C. A. van der Star ◽  
G. A. M. van Meurs ◽  
C. J. Hoogendoorn
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Properties ◽  
Saturated Soil ◽  
Mutual Distance ◽  
Tube Material ◽  
Surrounding Water ◽  
Analytical Approximations ◽  
Water Saturated ◽  
Regional Groundwater

The heat transfer between a cylinder and the surrounding water-saturated soil is studied numerically. Parameters which influence this heat transfer are thermal properties of the soil, dimension and thermal conductivity of the tube material, and a regional groundwater flow. The results are compared to analytical approximations. When two tubes are present, their mutual distance is also such a parameter.

A Fractional-Diffusion Theory for Calculating Thermal Properties of Thin Films From Surface Transient Thermoreflectance Measurements

2001 ◽  
Vol 123 (6) ◽  
pp. 1133-1138 ◽  
Author(s):  
Vladimir V. Kulish ◽  
Jose´ L. Lage ◽  
Pavel L. Komarov ◽  
Peter E. Raad
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Analytical Solutions ◽  
Laser Energy ◽  
Diffusion Theory ◽  
Complete Solution ◽  
Diffusion Problem ◽  
Gaas Sample ◽  
Volumetric Heating ◽  
Pulsed Laser Heating

The transient thermoreflectance (TTR) method consists of measuring changes in the reflectivity of a material (thin film) under pulsed laser heating, and relating these changes to the corresponding surface temperature variations. Analytical solutions of the diffusion problem are then used to determine the thermal conductivity of the material following an iterative matching process between the solutions and the experimental results. Analytical solutions are attainable either when the material absorbs the laser energy volumetrically or when the material absorbs the laser energy at the surface. Either solution allows for the determination of only one thermal property (thermal conductivity or diffusivity), with the other one assumed to be known. A new, single, analytical solution to the transient diffusion equation with simultaneous surface and volumetric heating, found using fractional calculus, is presented in a semi-derivative form. This complete solution provides the means to determine the two thermal properties of the material (thermal conductivity and diffusivity) concomitantly. In this preliminary study, the solution component for surface heating is validated by comparison with experimental data for a gold sample using the classical thermoreflectance method. Further results, for surface and volumetric heating, are obtained and analyzed considering a GaAs sample.

Analytical Solutions to the Problem of Transient Heat Transfer in Living Tissue

1978 ◽  
Vol 100 (4) ◽  
pp. 202-210 ◽  
Author(s):  
A. Shitzer ◽  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Temperature Profile ◽  
Analytical Solutions ◽  
Biological Tissue ◽  
Geometrical Parameter ◽  
Convective Transport ◽  
Transient Heat Transfer ◽  
Living Tissue ◽  
Cylindrical Coordinates

An analytical model of transient heat transfer in living biological tissue is considered. The model includes storage, generation, conduction, and convective transport of heat in the tissue. Solutions for rectangular and cylindrical coordinates are presented and discussed. Transient times for reaching the “locally fully developed” temperature profile were found to be of the order of 5–25 min. These transients are dominated by a geometrical parameter and, to a lesser extent, by a parameter representing the ratio of heat supplied by blood flow to heat conducted in the tissue.

Sign in / Sign up

Export Citation Format

Share Document