Conduction shape factor

In the heat transfer literature the corresponding quantity, hoAjK, is sometimes called the conduction shape factor. 

In a two-dimensional system where only two temperature limits are involved, we may define a conduction shape factor 5 such that... 

Table 3-1 Conduction Shape Factors, Summarized from Refs. 6 and 7... 

We stait this chapter with one-dimensional steady heat conduction in a plane wall, a cylinder, and a sphere, and develop relations for thennal resistances in these geometries. We also develop thermal resistance relations for convection and radiation conditions at the boundaries. Wc apply this concept to heat conduction problems in multilayer plane wails, cylinders, and spheres and generalize it to systems that involve heat transfer in two or three dimensions. We also discuss the thermal contact resislance and the overall heat transfer coefficient and develop relations for the critical radius of insulation for a cylinder and a sphere. Finally, we discuss steady heat transfer from finned surfaces and some complex geometries commonly encountered in practice through the use of conduction shape factors. 

Conduction shape factors have been determined for a number of configurations encountered in practice and are given in Table 3-7 for some common cases. More comprehensive tables are available in the literature. Once the value of the shape factor is known for a specific geometry, the total steady heat transfer rate can be determined from the equation above using the specified two constant temperatures of the two surfaces and the thermal conductivity of the medium between them. Note that conduction shape factors are applicable only when heat transfer between the two surfaces is by conduction. Therefore, they cannot be used when the medium between the surfaces is a liquid or gas, which involves natural or forced convection currents. 

A comparison of Eqs. 3-4 and 3-79 reveals that the conduction shape factor 5isrelated to the thermal resistance/ by/ = l/kSoTS= 1/i / . Thus, these two quantities are the inverse of each other when the thermal conductivity of the medium is unity. The use of the conduction shape factors is ilJustraled with Examples 3-13 and 3-14. 

Conduction shape factors Sfor several configurations for use in Q = frS(T, - T2) to determine the steady rate of heat transfer through a medium of thermal conductivity k between the surfaces at temperatures Ti and... 

C What is a conduction shape factor How is it related to the thermal resistance ... 

C What is the value of conduction shape factors in engineering ... 

Two- and Three-Dimensional Steady-State Conduction Shape Factors.493... 

When steady-state conduction occurs within and outside solids, or between two contacting solids, it is frequently handled by means of conduction shape factors and thermal contact conductances (or contact resistances), respectively. This chapter covers the basic equations, definitions, and relationships that define shape factors and the thermal contact, gap, and joint conductances for conforming, rough surfaces, and nonconforming, smooth surfaces. 

Shape Factor and Thermal Resistance in Orthogonal Curvilinear Coordinates. The definition of thermal resistance of a system (total temperature drop across the system divided by the total heat flow rate) yields the following general expression for the thermal resistance R and the conduction shape factor S ... 

A. V. Hassani and K. G. T. Hollands, Conduction Shape Factor for a Region of Uniform Thickness Surrounding a Three-Dimensional Body of Arbitrary Shape, Journal of Heat Transfer, Vol. 112, pp. 492-495,1990. 

M. M. Yovanovich, A General Expression for Predicting Conduction Shape Factors, in Thermophysics and Spacecraft Thermal Control, AlAA Progress in Astronautics and Aeronautics Vol. 35, pp. 265-291, MIT Press, Cambridge, MA, 1974. 

In Eq. (4.4-4) the factor M/N is called the conduction shape factor S, where... 

X component of force, N (Ibj, dyn) compressibility constant, dimensionless mean surface renewal factor, s" conduction shape factor, m (ft)... 

Conduction shape factor Dimensionless factor used to account for the geometrical effects in steady-state heat conduction between surfaces at different temperatures. 

Shrivastava, D. and R.B. Roemer, An analytical study of Poisson conduction shape factors for two thermally significant vessels in a finite, heated tissue. Physics in Medicine and Biology, 2005. 50(15) 3627-3641. 

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