Acute Bronchitis: This is the most likely diagnosis given the progression of the cough over 1.5 weeks, especially with the description of a deep bark cough, which is often associated with inflammation of the bronchial tubes. The absence of fever makes a bacterial infection less likely, pointing more towards a viral cause.

Pertussis (Whooping Cough): Although the patient is an adult, pertussis can occur at any age, especially if vaccination status is not up to date. The deep bark cough could be indicative of the characteristic whoop sound often associated with pertussis.
Asthma: If the patient has a history of asthma, an exacerbation could present with a worsening cough. The bark-like quality might be due to airway constriction.
Allergic Rhinitis or Postnasal Drip: Chronic cough can be a symptom of allergic rhinitis, especially if the patient has allergies. The cough could be due to the irritation from postnasal drip.

Pneumonia: Although the patient is afebrile, pneumonia should always be considered, especially if there's a significant cough. Some forms of pneumonia, like those caused by Mycoplasma pneumoniae, can present without fever.
Pulmonary Embolism: A cough can be a symptom of a pulmonary embolism, especially if it's accompanied by other symptoms like chest pain or shortness of breath. This diagnosis is critical to not miss due to its high mortality rate.
Tuberculosis (TB): TB can present with a chronic cough, and although less common in immunocompetent individuals without risk factors, it's a diagnosis that should not be missed due to its public health implications and the need for specific treatment.

Cystic Fibrosis: Although rare in adults without a previous diagnosis, cystic fibrosis can present with recurrent respiratory infections and a chronic cough.
Foreign Body Aspiration: This is more common in children, but adults can also aspirate objects, leading to a persistent cough.
Sarcoidosis: A systemic disease that can affect the lungs, causing cough among other symptoms. It's less common but should be considered in the differential diagnosis of a chronic cough.