Inclinedsquarecavitiesplayacritical role inengineeringapplications,partic ularlyinthermalmanagement,energystorageandelectroniccooling,whereinclinationangles in°uence convectiveheat transfer.This studyexamines conjugate convectiveheat transfer withinaninclinedsquarecavity¯lledwithmicropolarnano°uidsunderatiltedLorentzforce usinga two-phasenano°uidmodel.The systemincludes aheat-generatingporousmedium underthermalnonequilibrium, introducingcomplexdynamics.Factorssuchasthermalbuoy ancy,°uid{solidheattransfercoe±cientandmicropolar°uidpropertiesareanalyzedfortheir impact onheat transfer e±ciency.Methods:The studyuses the¯nitedi®erencemethod (FDM) to solvenonlinear equations governingconvective°owandheat transfer.Physica