Steady-State Junctions and Thermal Networks
In a steady thermal network without internal energy storage at a node, energy conservation requires the algebraic sum of branch heat currents H_i=(T_node-T_i)/R_i to be zero.
Why this shows up in the exam
Y-shaped rod junctions · Multi-node composite slabs · Finding interface temperatures from branch conductances
Learn the idea
At a steady junction with no storage, incoming heat currents exactly equal outgoing currents. A junction temperature adjusts until it neither warms nor cools; write every connected branch current with a consistent sign and balance them at that node.
🧠 Memory hook: No heat piles up at a steady junction.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum_i (T_node-T_i)/R_i = 0 — steady nodal heat balance
- H_branch = (T_a-T_b)/R_branch — signed branch heat current between thermal nodes
How to approach it
- 1Label every fixed and unknown node temperature
- 2Write branch resistances and signed currents
- 3Apply zero net current at each unknown node
Common slip-ups that cost marks
- •Averaging junction temperatures without conductance weights
- •Changing heat-current sign between branches
- •Assuming equal currents in a branched network
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
More from Properties of Bulk Matter
Mechanical properties of solids
Study of how solids respond to applied forces, including stress, strain, elastic moduli (Young's modulus, bulk modulus), and breaking stress.
Fluid dynamics and Bernoulli's theorem
Covers the motion of fluids, including Bernoulli's theorem, Torricelli's law, dynamic lift, and viscous flow.
Surface tension and surface energy
Examines the molecular forces at liquid surfaces, including surface tension, surface energy, and related equations.
Capillarity and contact angle
Focuses on capillary action, meniscus formation, and the role of contact angle in wetting phenomena.
Thermal properties of matter
Deals with heat transfer, thermal conductivity, calorimetry, specific heat, and thermal expansion of solids.
Pressure in fluids and hydrostatics
Explores how pressure is transmitted in fluids, including hydrostatic pressure, Pascal's law, and related phenomena.