Consider a long, thin, uniform rod of constant cross-section whose temperature distribution is θ(x,t), surrounded by an atmosphere of constant uniform temperature θ0. The sides of the rod are not insulated so that heat is lost from the longitudinal surface at a rate h(θ(x,t)- θ0) per unit length, for some constant h. Derive the equation which describes the temperature distribution in the rod and show that it can be written

∂φ/∂t=k/ρc (∂^2 φ)/(∂x^2 ) - (h/ρAc) φ

where φ(x,t) = (θ(x,t)- θ0), k is the thermal conductivity, ρ the density , c the thermal capacity and A the cross-sectional a

Question

Consider a long, thin, uniform rod of constant cross-section whose temperature distribution is θ(x,t), surrounded by an atmosphere of constant uniform temperature θ0. The sides of the rod are not insulated so that heat is lost from the longitudinal surface at a rate h(θ(x,t)- θ0) per unit length, for some constant h. Derive the equation which describes the temperature distribution in the rod and show that it can be written

 ∂φ/∂t=k/ρc (∂^2 φ)/(∂x^2 ) - (h/ρAc) φ 

where φ(x,t) = (θ(x,t)- θ0), k is the thermal conductivity, ρ the density , c the thermal capacity and A the cross-sectional a

anonymous · Answer

I think this is the wrong subject for this to be in

anonymous · Answer

@Echdip Try putting this in the algebra/geometry subject

anonymous · Answer

Yeah, there's no way this is history, lol.

anonymous · Answer

oh ya. thanx mate. i dint realise