What is the relationship between Louisa and Tom in Hard Times?

In Charles Dickens's novel Hard Times, Louisa and Tom Gradgrind are sister and brother. The two siblings have very different responses to their difficult upbringing at the hands of Thomas Gradgrind Sr. and the passive, depressed Mrs. Grandgrind, their mother.
Louisa reacts to their unhappy home life by losing touch with her feelings. In one of the novel's most famous lines, we indirectly get a picture of the muffled, stifled quality of Louisa's emotional life through her comment on an industrial scene:

There seems to be nothing there but languid and monotonous smoke. Yet when the night comes, fire bursts out.

In contrast to Louisa, Tom responds to their cold, chilly home environment by drowning his sorrows in a futile search for pleasure and distraction.
Unfortunately, Tom and Louisa are unable to draw comfort from one another. Dickens's portrayal of the Gradgrind family's relationships reflects his sense that the philosophy of utilitarianism (to which Gradgrind Sr. adheres) has profoundly damaging effects on familial relationships, as well as individual prospects for happiness.