Type the date. Skip a line, and type the name of the chair of the committee and her title. Type her department name, the university name and the department address on separate lines. Skip an additional line and type "Dear Dr. (Last name)" followed by a colon.
Introduce yourself and explain that the student has asked you to serve on her committee as the adviser for her secondary area of focus. For example, "My name is Dr. LaShayla Brown and Jennifer Garza has asked me to serve on her dissertation committee as the outside adviser from Veterinary Medicine. It is my understanding that Jennifer intends to write her dissertation about engineering corn to create superior feed for domestic pigs, and she has asked me to contribute in the capacity of overseeing her discussion about the health of the animals."
Explain your area of expertise and how you can help the student. For instance, "I specialize in large breed medicine, and my research on alternative feeds for the domestic pig makes me a good fit for Jennifer's committee." You do not have to elaborate; this letter is not so much asking permission or selling yourself as it is to introduce yourself to the chair of the committee.
Thank the dissertation chair for her time. Provide your contact information, such as your personal telephone extension and email.
Type a professional closing, such as "Best regards," and skip three line spaces. Type your name and title. Print the letter on your department letterhead and sign above your name.