"Heat transfer is defined as the transfer of energy across a system boundary caused solely by a temperature difference."
"[C]onduction heat transfer is the transfer of energy caused by physical interaction among molecular, atomic, and subatomic particles in a substance at different temperatures (level[s] of kinetic energy)." Steady-state conduction clearly implies that a fixed amount of energy (heat) is being transferred (or conducted) in each unit of time over a continuing period.
General Conductive Energy Equation. Temperature is a property of a substance at any time, an "index of kinetic energy" of its building blocks. Energy is conducted through a substance according to, and at a rate defined by: qx = -kAx dT/dx in which qx is the heat transfer gradient or rate (e.g., watts, or Joules/s), k is a property of the material known as the thermal conductivity (e.g., watts/m-(C), Ax is the cross-sectional area of the substance through which heat is being transferred (normal to the x-direction), T is the temperature, and x is the linear length of the material--such as the thickness of a radiator wall; this expression is known as the Fourier law of conductivity.
Holman has demonstrated, pictorially and algebraically, that the energy flow per unit volume (i.e., Adx) through an elemental slice of a heated wall or plate can be expressed as
(/(x (k (T/(x) + qi = ?c (T/( t, (1)
in which qi is the energy generated within the element, if any (W/m3), ? is the material's density (kg/m3), c is the specific heat of the material (J/kg-(C), t is time, and the other terms are as defined above.
Plane Wall Conduction. The total heat flux conducted (only) through a plane wall can be computed from
q = kA(T1 - T2) / (x2 - x1) = [T1 - T2] / (L/kA) (2)
in which L = the wall thickness (x2 - x1), the quantity, L/kA, being the thermal resistance or kA/L being the conductance. When the thermal conductivity, k, varie...