Heat Equation for No Heat Loss at x=a

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To model the scenario of two rods joined at x=a with no heat loss, the heat transfer rates must be equal at the junction. The equation representing this condition is derived from the principle of conservation of energy, stating that the heat leaving rod L1 must equal the heat entering rod L2. This can be expressed mathematically by equating the heat fluxes, which depend on the thermal conductivities and cross-sectional areas of the rods. The discussion emphasizes the importance of maintaining continuous temperature and energy balance at the junction. Understanding this relationship is crucial for analyzing thermal systems involving different materials.
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The question :Two rods L1 and L2 of different materials( hence different thermal conductivities) and different cross-sectional areas,are joined at x=a. The temperature is continuous,
And NO HEAT ENERGY IS LOST AT a, so all heat energy that flows from L1 flows into L2.

? What equation represents the condition that no energy is lost at a ?

My thoughts : Equate the rate at which heat leaves L1 to the rate at which heat enters L2. ?
 
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