Heat Transfer—Asian Research, 43 (2), 2014 Optimal Homotopy Asymptotic Method for Heat Transfer in Hollow Sphere with Robin Boundary Conditions Fazle Mabood, 1 Waqar A. Khan, 2 and Ahmad Izani Md Ismail 1 1 School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia 2 Department of Engineering Sciences, National University of Sciences and Technology, PNEC, Karachi, Pakistan In this article, we have investigated heat transfer from a hollow sphere using a powerful and relatively new semi-analytic technique known as the optimal homo- topy asymptotic method (OHAM). Robin boundary conditions are applied on both the inner and outer surfaces. The effects of Biot numbers, uniform heat generation, temperature-dependent thermal conductivity, and temperature parameters on the dimensionless temperature and heat transfer are investigated. The results of OHAM are compared with a numerical method and are found to be in good agreement. It is shown that the dimensionless temperature increases with an increase in Biot number at the inner surface and temperature and heat generation parameters, whereas it de- creases with an increase in the Biot number at the outer surface and the dimension- less thermal conductivity and radial distance parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 124–133, 2014; Published online 20 June 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21067 Key words: OHAM, Robin boundary condition, heat transfer, hollow sphere 1. Introduction Heat transfer is of importance in numerous applications in science and engineering [5, 12]. The study of heat transfer problems in hollow spheres has received considerable interest due to the many possible applications. For example in biomedical ultrasonic imaging and underwater hy- drophones, hollow sphere transducers may provide higher resolution due to smaller sphere sizes than presently in use [1]. A discussion of standard solution techniques, both analytical and numerical, for heat conduc- tion problems can be found in books such as Refs. 2 to 4. Some work on hollow shapes include that of Jiang and Sousa [5] who derived an analytical expression for the temperature profile in a hollow sphere with sudden temperature changes on its inner and outer surfaces. The authors also reported the presence of hyperbolic anomalies inside the hollow sphere with the use of Dirichlet boundary conditions. © 2013 Wiley Periodicals, Inc. 124