Conduction through a plane wall: How does the total heat flow rate depend on area, temperature difference, and thickness, according to elementary steady 1-D conduction relations?

Introduction / Context:Fourier’s law for steady, one-dimensional conduction through a homogeneous plane wall leads to a simple proportionality that is widely used for first-cut thermal sizing of walls, insulations, and heat exchanger plates.

Given Data / Assumptions:

• Plane wall of thickness L and area A.
• Constant thermal conductivity k.
• Steady state with boundary temperatures T_hot and T_cold.

Concept / Approach:For 1-D conduction, q = -k * A * dT/dx. With linear temperature distribution and constant k, integration yields Q = k * A * (T_hot - T_cold) / L. This shows direct proportionality to area and temperature difference, and inverse proportionality to thickness; it also highlights dependence on material via k.

Step-by-Step Solution:

Verification / Alternative check:Compare two walls of the same material: doubling area doubles Q; doubling thickness halves Q; doubling ΔT doubles Q. Experimental results match these trends in the linear regime.

Why Other Options Are Wrong:

• (a), (b), and (c) each state a true but partial relationship; the complete statement is “All of the above”.
• (e) is false—material property k is central to conduction.

Common Pitfalls:Applying this 1-D formula to multilayer walls without using the appropriate series thermal resistance model; neglecting contact resistances and temperature-dependent k.

Final Answer:All of the above