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

[Torsten]

Is this flow from right to left in x-direction ?

[hussain soomro]

from left to right sir

[Torsten]

from left to right sir

Thus mdot_l/M_l is negative ?

[hussain soomro]

No sir, it is same as shown

[Torsten]

If mdot_l/M_l is positive, the flow is from right to left, not from left to right. And this is important because it determines at which side of the spatial x-interval the boundary condition for T_l has to be set.

Here are some YouTube videos for an introduction:

https://www.google.com/search?q=advection+equation+with+source+term+%26+numerical+treatment+%26+Youtube&client=firefox-b-d&sca_esv=c640cfee960680c8&ei=cJlTZ9GeKM-I7NYP-7GK8QQ&ved=0ahUKEwjRlr2AtpSKAxVPBNsEHfuYIk4Q4dUDCA8&uact=5&oq=advection+equation+with+source+term+%26+numerical+treatment+%26+Youtube&gs_lp=Egxnd3Mtd2l6LXNlcnAiQ2FkdmVjdGlvbiBlcXVhdGlvbiB3aXRoIHNvdXJjZSB0ZXJtICYgbnVtZXJpY2FsIHRyZWF0bWVudCAmIFlvdXR1YmUyBBAhGApI4DBQoglYgC1wAXgBkAEAmAGMAaABqgaqAQM0LjS4AQPIAQD4AQGYAgWgAsIDwgIKEAAYsAMY1gQYR8ICBRAhGKABmAMAiAYBkAYFkgcDMi4zoAffGQ&sclient=gws-wiz-serp