the pipe wall". However, one needs to select if the heat flux is based on the pipe inner or the outer diameter. Selecting to base the heat flux on the pipe inner diameter, and assuming that the pipe wall thickness is small in comparison with the pipe inner diameter, then the heat transfer coefficient for the pipe wall can be calculated as if the wall were not curved: where k is the effective thermal conductivity of the wall material and x is the wall thickness. If the above assumption does not hold, then the wall heat transfer coefficient can be calculated using the following expression: where di and do are the inner and outer diameters of the pipe, respectively. The thermal conductivity of the tube material usually depends on temperature; the mean thermal conductivity is often used. Combining convective heat transfer coefficients For two or more heat transfer processes acting in parallel, convective heat transfer coefficients simply add: For two or more heat transfer processes connected in series, convective heat transfer coefficients add inversely: For example, consider a pipe with a fluid flowing inside. The approximate rate of heat transfer between the bulk of the fluid inside the pipe and the pipe external surface is: where q = heat transfer rate (W) h = convective heat transfer coefficient (W/(m2·K)) t = wall thickness (m) k = wall thermal conductivity (W/m·K) A = area (m2) = difference in temperature. Overall heat transfer coefficient The overall heat transfer coefficient is a measure of the overall ability of a series of conductive and convective barriers to transfer heat. It is commonly applied to the calculation of heat transfer in heat exchangers, but can be applied equally well to other problems. For the case of a heat exchanger, can be used to determine the total heat transfer between the two streams in the heat exchanger by the following relationship: where: = heat transfer rate (W) = overall heat transfer coefficient (W/(m2·K)) = heat transfer surface area (m2) = logarithmic mean temperature difference (K). The overall heat transfer coefficient takes into account the individual heat transfer coefficients of each stream and the resistance of the pipe material. It can be calculated as the reciprocal of the sum of a series of thermal resistances (but more complex relationships exist, for example when heat transfer takes place by different routes in parallel): where: R = Resistance(s) to