my work now is in renewable energy based on this article 'Unsteady flow and heat transfer adjacent to the sidewall wall of a differentially heated cavity with a conducting and an adiabatic fin'
Different symbols are usually used to distinguish between the dimensional temperatures (such as T, Th, Tc and T0 expressed in Kelvin) and the dimensionless temperatures (such as θ, θh, θc and θ0 without unity). So, it would have been better if the authors of the paper have used θ instead of T in the governing equations as well as in the boundary conditions to avoid confusion.
From the equations and boundary conditions, one can conclude that:
θ = (T - T0)/(Th - Tc) with T0=(Th + Tc)/2
So, at the cold sidewall : T = Tc which means that θ = θc = (Tc - T0)/(Th - Tc) = -1/2
and at the hot sidewall : T = Th which means that θ = θh = (Th - T0)/(Th - Tc) = 1/2