ORIGINAL Fangming Jiang Solution and analysis of hyperbolic heat propagation in hollow spherical objects Received: 14 September 2004 / Accepted: 24 November 2005 / Published online: 6 January 2006 Ó Springer-Verlag 2006 Abstract The hyperbolic heat conduction process in a hollow sphere with its two boundary surfaces subject to sudden temperature changes is solved analytically by means of integration transformation. An algebraic analytical expression of the temperature profile is ob- tained. Accordingly, the non-Fourier hyperbolic heat propagation in hollow spherical medium is analyzed and possible hyperbolic anomalies are discussed. List of symbols a Thermal diffusivity (m 2 s 1 ) c Velocity of thermal propagation (m s 1 ) f 1 , f 2 Source functions of F 1 , F 2 F 1 , F 2 Intermediate functions H () Heaviside’s unit step function I n() Modified Bessel function of the first kind and order n l Mean free path of molecule (m) L () Laplace transform L () 1 Inverse Laplace transform p Dimensionless quantity to designate position of the wave front q Heat flux (W m 2 ) r Radial or spatial coordinate (m) r i Inner radius (m) r o Outer radius (m) r c Relative thickness of the hollow sphere (=r i /r o ) s Laplace transformed variable S Heat source (W m 3 ) t Time (s) T Temperature (K) T 0 Initial temperature (K) T wi Temperature of inner surface (K) T wo Temperature of outer surface (K) T c Relative temperature change (=(T wi  T 0 )/T wo  T 0 )) v Velocity of phonon or electron (m s 1 ) Greek symbols b Intermediate function e Dimensionless characteristic time (=as/r o 2 ) g Dimensionless position (=r/r o ) k Thermal conductivity, (W m 1 K 1 ) h Dimensionless temperature (=(T  T 0 )/ (T wo  T 0 )) s Thermal characteristic (or relaxation) time (s) n Dimensionless time (=at/r o 2 ) Superscripts  Laplace transformed function fi Vector 1 Introduction Heat always conducts from warmer objects to cooler ones. Empirically, the heat conduction rate is related to the spatial temperature difference and the composition of material. Fourier (1,768–1,830) pondered this phe- nomenon and proposed the well-known and later widely used Fourier’s law of heat conduction, qr; t ð Þ¼krT r; t ð Þ; ð1Þ which states that heat flux q is directly proportional to the temperature gradient Ñ T. The proportionality k is the thermal conductivity of material. The negative sign F. Jiang Departamento de Engenharia Mecaˆnica, Universidade de Aveiro, Campus Universita´rio de Santiago, 3810-193 Averio, Portugal E-mail: fjiang@mec.ua.pt Tel.: +351-91-7657659 Fax: +351-234-370953 Heat Mass Transfer (2006) 42: 1083–1091 DOI 10.1007/s00231-005-0066-6