  Using a combination of accurate density-functional theory and a
nonequilibrium Green function's method, we calculate the ballistic thermal
conductance characteristics of tensile-strained armchair (AGNR) and zigzag
(ZGNR) edge graphene nanoribbons, with widths between 3-50 \AA. The optimized
lateral lattice constants for AGNRs of different widths display a three-family
behavior when the ribbons are grouped according to N modulo 3, where $N$
represents the number of carbon atoms across the width of the ribbon. Two
lowest-frequency out-of-plane acoustic modes play a decisive role in increasing
the thermal conductance of AGNR-N at low temperatures. At high temperatures the
effect of tensile strain is to reduce the thermal conductance of AGNR-N and
ZGNR-N. These results could be explained by the changes in force constants in
the in-plane and out-of-plane directions with the application of strain. This
fundamental atomistic understanding of the heat transport in graphene
nanoribbons paves a way to effect changes in their thermal properties via
strain at various temperatures.
