A loud roar is usually the cooling fan. The circumstances of loud noise are being in lower gears when engine is hot, so that the fan is engaged, and when the engine is cold and you are starting from a standstill, so that it has not yet declutched.
If your engine fan is spinning full load all the time, the fan clutch needs to be replaced. These are designed to make "engage" the failure mode, to ensure a flow of cooling air when you ate not moving. Thermostatic fan clutches operate based on temperature of air flowing past the clutch, so often may not come on until after you've climbed the hill and raised the temperature in the radiator.