1. My Conceptual Questions (5) is at 3.
Case 1: two dissimilar slabs of material (say slab 1 and slab 2) connected in series (bonded at their interface). There is a temperature difference: T1 @ slab1 and T2 @ slab2.
Case 2: two dissimilar slabs of material bonded together, i.e. parallel configuration. There is a temperature difference: T1 @ the midpoint of the entering interfaces configuration and likewise T2 @ end.
-1-Dimensional Heat Flow (x-direction)
-thin yet long materials
2. None. There isn't really any equations other than parallel and series addition for thermal conductivity and resistivity for materials arranged longitunditally or traverse-ly relative to direction of heat flow.
3. My own conceptual questions posed try to use reason to determine/understand. So, I considered it an attempt.
Question 1) Despite that I say that I have constrained Case 2 to be a 1-Dimensional Heat Flow the heat will still move in a direction other than 'x', say 'y', even if just infinitesimally small because of the parallel configuration thereby violating the 1-Dimensional Heat Flow. Is this true? If so can you show this approximation mathematically?
Question 2) Also, would this necessitate for something like a '2-Dimensional Heat Flow'?
Question 3) Source 1 (below) talks about non-planar geometry (axisymmetric configurations?), however they constrain heat conduction along the single coordinate 'r', thus there is not a variation of heat flow in any other direction; could I not just constrain the heat to flow through series connected materials and drop the Quasi? Because would the Quasi part imply there is a slight variation in another dimension? -Also, the MIT source calls this Quasi-One-Dimensional-Heat-Flow-in-Non-Planar-Geometry.
Question 4) If this is just an assumption for non-planar geometry fine. But why? Empirically accurate?
Question 5) Wouldn't Case 2 be considered planar geometry? If so, how does that situation not contradict the 1-Dimensional Heat Flow Constraint? Or this just another assumption?
MISC. Similar Question Asked by student in the MIT course questioning the accuracy of the 1-Dimensional Heat Flow:
MP 16..2How specific do we need to be about when the one-dimensional assumption is valid? Is it enough to say that dA/dx is small?
The answer really is ``be specific enough to enable one to have confidence in the analysis or at least some idea of how good the answer is.'' This is a challenge that comes up a great deal. For now, if we say that A is an area defined per unit depth normal to the blackboard then saying dA/dx is small, which is a statement involving a non-dimensional parameter, is a reasonable criterion.
2) http://www.me.umn.edu/courses/old_me_course_pages/me3333/essays/essay 5.pdf