Heat Transfer on the FE Exam
Heat transfer appears on the FE Mechanical exam (7-11%), the FE Chemical exam (7-11%), and the FE Other Disciplines exam (5-8%). This subject covers the three modes of heat transfer and their engineering applications. Understanding the fundamental mechanisms and knowing which formulas to apply is key to solving these problems efficiently.
Conduction
Conduction is heat transfer through a solid or stationary fluid due to a temperature gradient. Fourier's Law states that the heat flux (heat transfer rate per unit area) is proportional to the negative temperature gradient, with the proportionality constant being the thermal conductivity of the material.
For steady-state, one-dimensional conduction through a plane wall, the heat transfer rate equals the thermal conductivity times the area times the temperature difference divided by the wall thickness. For composite walls (multiple layers), use the thermal resistance concept: each layer has a resistance equal to its thickness divided by the product of its thermal conductivity and area.
For radial systems (cylinders and spheres), the thermal resistance formulas are different. For a hollow cylinder, the resistance equals the natural log of the outer radius divided by the inner radius, all divided by 2 times pi times the length times the thermal conductivity. Know how to solve multi-layer radial conduction problems using the resistance network approach.
Convection
Convection is heat transfer between a surface and a moving fluid. Newton's Law of Cooling states that the convection heat transfer rate equals the convection coefficient (h) times the surface area times the temperature difference between the surface and the fluid.
The challenge in convection is determining the convection coefficient, which depends on the flow conditions, fluid properties, and geometry. The FE exam tests your ability to use empirical correlations to find the convection coefficient. Key correlations include:
- External flow over a flat plate: Use Reynolds and Prandtl numbers to determine the Nusselt number
- Internal flow in pipes: Use the Dittus-Boelter equation for turbulent flow or Sieder-Tate correlation
- Natural convection: Use Rayleigh number correlations for vertical plates, horizontal plates, and cylinders
The FE Reference Handbook provides these correlations. Practice identifying which correlation to use based on the problem geometry and flow conditions.
Radiation
Thermal radiation is electromagnetic energy emitted by surfaces due to their temperature. The Stefan-Boltzmann Law gives the total emissive power of a blackbody as sigma times the absolute temperature to the fourth power, where sigma is the Stefan-Boltzmann constant.
Real surfaces emit less radiation than a blackbody. The emissivity (a value between 0 and 1) scales the actual emission relative to the blackbody value. For radiation exchange between two surfaces, the net heat transfer depends on the view factor (shape factor), emissivities, surface areas, and temperatures of both surfaces.
Key formulas to know include radiation exchange between two infinite parallel plates, radiation from a small surface to a large enclosure, and the radiosity-irradiation approach for more complex geometries. View factor relations (reciprocity rule, summation rule) help simplify multi-surface radiation problems.
Heat Exchangers
Heat exchangers are devices that transfer heat between two fluid streams. The FE exam tests two analysis methods:
Log Mean Temperature Difference (LMTD) Method
The heat transfer rate equals the overall heat transfer coefficient times the area times the log mean temperature difference. Calculate LMTD from the inlet and outlet temperatures of both fluid streams. For counterflow exchangers, the LMTD is higher than for parallel flow exchangers with the same temperatures.
Effectiveness-NTU Method
When only inlet temperatures are known, use the effectiveness-NTU method. The effectiveness depends on the number of transfer units (NTU) and the capacity ratio. The FE Reference Handbook provides effectiveness-NTU relationships for common heat exchanger configurations.
Fins and Extended Surfaces
Fins increase heat transfer by extending the surface area. The FE exam may test fin efficiency and fin effectiveness calculations. Know the formulas for rectangular and circular pin fins, and understand that fin efficiency decreases as the fin becomes longer or the convection coefficient increases.
Problem-Solving Approach
For every heat transfer problem, identify the mode(s) of heat transfer involved, draw a thermal circuit diagram if applicable, identify the relevant resistances, and solve for the unknown. The thermal resistance analogy (analogous to electrical resistance) is a powerful tool that simplifies multi-mode heat transfer problems into straightforward calculations.