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Heat Transfer Handbook part 18. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | CHAPTER 3 Conduction Heat Transfer A. AZIZ Department of Mechanical Engineering Gonzaga University Spokane Washington 3.1 Introduction 3.2 Basic equations 3.2.1 Fourier s law 3.2.2 General heat conduction equations 3.2.3 Boundary and initial conditions 3.3 Special functions 3.3.1 Error functions 3.3.2 Gamma function 3.3.3 Beta functions 3.3.4 Exponential integral function 3.3.5 Bessel functions 3.3.6 Legendre functions 3.4 Steady one-dimensional conduction 3.4.1 Plane wall 3.4.2 Hollow cylinder 3.4.3 Hollow sphere 3.4.4 Thermal resistance 3.4.5 Composite systems Composite plane wall Composite hollow cylinder Composite hollow sphere 3.4.6 Contact conductance 3.4.7 Critical thickness of insulation 3.4.8 Effect of uniform internal energy generation Plane wall Hollow cylinder Solid cylinder Hollow sphere Solid sphere 3.5 More advanced steady one-dimensional conduction 3.5.1 Location-dependent thermal conductivity The author dedicates this chapter to little Senaan Asil Aziz whose sparkling smile makes my day. 161 162 CONDUCTION HEAT TRANSFER Plane wall Hollow cylinder 3.5.2 Temperature-dependent thermal conductivity Plane wall Hollow cylinder Hollow sphere 3.5.3 Location-dependent energy generation Plane wall Solid cylinder 3.5.4 Temperature-dependent energy generation Plane wall Solid cylinder Solid sphere 3.5.5 Radiative-convective cooling of solids with umiorm ener generation 3.6 Extended surfaces 3.6.1 Longitudinal convecting fins Rectangular fin Trapezoidal fin Triangular fin Concave parabolic fin Convex parabolic fin 3.6.2 Radial convecting fins Rectangular fin Triangular fin Hyperbolic fin 3.6.3 Convecting spines Cylindrical spine Conical spine Concave parabolic spine Convex parabolic spine 3.6.4 Longitudinal radiating fins 3.6.5 Longitudinal convecting-radiating fins 3.6.6 Optimum dimensions of convecting ins and spines Rectangular fin Triangular fin Concave parabolic fin Cylindrical spine Conical spine Concave parabolic spine Convex parabolic spine 3.7 .
