A vast number of heat exchanger types, a diversity of fluid flow arrangements, a variety of constructions, multiplicity of process conditions and associated fluids’ thermodynamic states clearly impose a virtual impossibility to structure a single, generalized design procedure (either sizing or rating) of a heat exchanger. Still, the basic design problem task may be generalized for various designs. This chapter compiles procedures for solving any one of all possible (twenty one) design problems. A design problem solution is reduced to a determination of a complete set of possible unknowns appearing in two key design relationships.

The relevant design relationships include: (1) the heat transfer rate equation q = UA Δ\(\overline{T}\), and (2) the enthalpy rate change of either of the fluids, q = ΔḢ_i, where “i ” signifies each of the two fluids involved. Note that an enthalpy rate change ΔḢ may be determined as a product of the mass flow rate, specific heat and temperature change for a single phase fluid having constant properties. The enthalpy rate change should be determined differently if the single phase fluids’ set of assumptions cannot be implemented, e.g., if the phase change of one or both fluids takes place. For the sake of obviousness, in what follows the former case will be considered. Similar algorithms can be devised if these assumptions are relaxed.

The heat transfer rate equation states that heat transfer exchanged in a heat exchanger is proportional to (i) the heat exchanger “thermal size” (UA), [W/K], a product of the overall heat exchanger coefficient (U, [W/m²K], and the heat transfer area A, [m²]), and to (ii) a conveniently selected mean temperature difference along the fluids’ thermal interaction length (Δ\(\overline{T}\), [K], e.g. a logarithmic mean). This is true assuming that the basic set of idealizations is invoked (Shah and Sekulic, 2003).

The basic set of idealizations involves the set of statements as follows: a steady state operation, adiabatic conditions, no energy sources or sinks, uniform temperatures over every fluid passage cross section, no phase change, longitudinal heat conduction in the fluids and/or ducts/channels’ walls negligible, the overall heat transfer coefficient constant, the specific heat of each fluid constant, the heat transfer surface area uniformly distributed, and uniform mass flow rates and inlet ports temperatures.

In cases where specific heat at constant pressure can be defined, ΔḢ [W], can be calculated as ΔḢ = C ΔT = (ṁc_p) ΔT, where ṁ [kg/s] represents the mass flow rate of a fluid, and c_p , [J/kg·K], the specific heat at constant pressure. ΔT is a fluid temperature difference between the inlet and outlet ports.