How do "Porphyria's Lover" and "My Last Duchess" appeal to our senses?
Browning appeals to the reader's senses in these two poems the same way poets usually appeal to a reader's senses--through imagery. That's the definition of imagery.
In "Porphyria's Lover," for instance, her beautiful red hair is wrapped around Porhyria's throat and she is strangled with it, without pain, according to the speaker. This creates a visual and tactile image that is experienced by the reader. This image, and the details that follow, contribute to the "beauty" and "peace" of the scene, as presented by the speaker, and the terror of the scene as experienced by the reader.
In "My Last Duchess," the "spot of joy," the glance, the beautiful look on the Duchess's face, as revealed in her portrait according to the Duke, is a vague but powerful visual image that creates beauty when first read, then terror when the Duchess's fate is revealed.
From the storm that Porphyria figuratively calms, to the works of art that the Duke wishes his wife would have behaved like, these two poems are filled with images that appeal to the reader's senses.