solving 1d heat equation

can anyone please help me solve this type of PDE, assume other values such as ml/Ml, hl, ah, Cl etc as constant values, I just need method to solve such type of equations, Thanks

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Is this flow from right to left in x-direction ?
from left to right sir
from left to right sir
Thus mdot_l/M_l is negative ?
No sir, it is same as shown

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